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SageMath
E = EllipticCurve("gp1")
E.isogeny_class()
Elliptic curves in class 405720.gp
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 405720.gp1 | 405720gp1 | \([0, 0, 0, 3358068, 10416261044]\) | \(190737654201344/2245153696875\) | \(-49294879649223314400000\) | \([]\) | \(25344000\) | \(3.0353\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 405720.gp1 has rank \(0\).
Complex multiplication
The elliptic curves in class 405720.gp do not have complex multiplication.Modular form 405720.2.a.gp
sage: E.q_eigenform(10)