Show commands:
SageMath
E = EllipticCurve("ca1")
E.isogeny_class()
Elliptic curves in class 77760.ca
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 77760.ca1 | 77760eg1 | \([0, 0, 0, -37908, 2840832]\) | \(-8302761792/25\) | \(-18139852800\) | \([]\) | \(138240\) | \(1.1963\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 77760.ca1 has rank \(1\).
Complex multiplication
The elliptic curves in class 77760.ca do not have complex multiplication.Modular form 77760.2.a.ca
sage: E.q_eigenform(10)