diff --git a/acb_elliptic/roots.c b/acb_elliptic/roots.c
index a00f0512..07a3da49 100644
--- a/acb_elliptic/roots.c
+++ b/acb_elliptic/roots.c
@@ -16,12 +16,28 @@ void
 acb_elliptic_roots(acb_t e1, acb_t e2, acb_t e3, const acb_t tau, slong prec)
 {
     acb_t t1, t2, t3, t4;
+    int e1r, e23r;
+
+    if (!arb_is_positive(acb_imagref(tau)) || !arb_is_finite(acb_realref(tau)))
+    {
+        acb_indeterminate(e1);
+        acb_indeterminate(e2);
+        acb_indeterminate(e3);
+        return;
+    }
 
     acb_init(t1);
     acb_init(t2);
     acb_init(t3);
     acb_init(t4);
 
+    e1r = e23r = 0;
+
+    if (arb_is_int(acb_realref(tau)))
+        e1r = e23r = 1;
+    else if (arb_is_int_2exp_si(acb_realref(tau), -1))
+        e1r = 1;
+
     acb_modular_theta(t1, t2, t3, t4, t1, tau, prec);
 
     acb_pow_ui(t2, t2, 4, prec);
@@ -42,6 +58,15 @@ acb_elliptic_roots(acb_t e1, acb_t e2, acb_t e3, const acb_t tau, slong prec)
     acb_mul(e3, e3, t3, prec);
     acb_neg(e3, e3);
 
+    if (e1r)
+        arb_zero(acb_imagref(e1));
+
+    if (e23r)
+    {
+        arb_zero(acb_imagref(e2));
+        arb_zero(acb_imagref(e3));
+    }
+
     acb_clear(t1);
     acb_clear(t2);
     acb_clear(t3);
diff --git a/acb_modular/eisenstein.c b/acb_modular/eisenstein.c
index 06886ca7..286b5ad7 100644
--- a/acb_modular/eisenstein.c
+++ b/acb_modular/eisenstein.c
@@ -18,10 +18,20 @@ acb_modular_eisenstein(acb_ptr r, const acb_t tau, slong len, slong prec)
     arf_t one_minus_eps;
     acb_t tau_prime, t1, t2, t3, t4, q;
     slong m, n;
+    int real;
 
     if (len < 1)
         return;
 
+    if (!arb_is_positive(acb_imagref(tau)) || !arb_is_finite(acb_realref(tau)))
+    {
+        _acb_vec_indeterminate(r, len);
+        return;
+    }
+
+
+    real = arb_is_int_2exp_si(acb_realref(tau), -1);
+
     psl2z_init(g);
     arf_init(one_minus_eps);
     acb_init(tau_prime);
@@ -110,6 +120,13 @@ acb_modular_eisenstein(acb_ptr r, const acb_t tau, slong len, slong prec)
         }
     }
 
+    if (real)
+    {
+        arb_zero(acb_imagref(r));
+        if (len > 1)
+            arb_zero(acb_imagref(r + 1));
+    }
+
     /* compute more coefficients using recurrence */
     for (n = 4; n < len + 2; n++)
     {