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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 116380c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 116380.i1 | 116380c1 | \([0, -1, 0, -383739421, 2916457760745]\) | \(-164902021520455131136/1521088873046875\) | \(-57644990353792583500000000\) | \([]\) | \(49040640\) | \(3.7653\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 116380c1 has rank \(1\).
Complex multiplication
The elliptic curves in class 116380c do not have complex multiplication.Modular form 116380.2.a.c
sage: E.q_eigenform(10)