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SageMath
E = EllipticCurve("eg1")
E.isogeny_class()
Elliptic curves in class 379050eg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 379050.eg1 | 379050eg1 | \([1, 0, 1, -56817076, 164951749298]\) | \(-1103770289367265/891813888\) | \(-16389128925388800000000\) | \([]\) | \(68947200\) | \(3.1922\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 379050eg1 has rank \(1\).
Complex multiplication
The elliptic curves in class 379050eg do not have complex multiplication.Modular form 379050.2.a.eg
sage: E.q_eigenform(10)