Show commands:
SageMath
E = EllipticCurve("hn1")
E.isogeny_class()
Elliptic curves in class 78400.hn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 78400.hn1 | 78400bg1 | \([0, 1, 0, 10617, -2400637]\) | \(1124864/21875\) | \(-2573571875000000\) | \([]\) | \(368640\) | \(1.6374\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 78400.hn1 has rank \(0\).
Complex multiplication
The elliptic curves in class 78400.hn do not have complex multiplication.Modular form 78400.2.a.hn
sage: E.q_eigenform(10)