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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 429429c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 429429.c1 | 429429c1 | \([0, -1, 1, 974736, 630789356]\) | \(585728/1323\) | \(-231338621780818474923\) | \([]\) | \(22239360\) | \(2.5916\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 429429c1 has rank \(1\).
Complex multiplication
The elliptic curves in class 429429c do not have complex multiplication.Modular form 429429.2.a.c
sage: E.q_eigenform(10)