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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 458640.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
458640.j1 | 458640j1 | \([0, 0, 0, 4285932, -2247416948]\) | \(396555344454656/328867205355\) | \(-7220650119016647156480\) | \([]\) | \(31933440\) | \(2.8820\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 458640.j1 has rank \(1\).
Complex multiplication
The elliptic curves in class 458640.j do not have complex multiplication.Modular form 458640.2.a.j
sage: E.q_eigenform(10)