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SageMath
E = EllipticCurve("ho1")
E.isogeny_class()
Elliptic curves in class 383040.ho
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
383040.ho1 | 383040ho1 | \([0, 0, 0, 683988, 168084016]\) | \(185183253170999/171032148000\) | \(-32684752474472448000\) | \([]\) | \(8847360\) | \(2.4317\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 383040.ho1 has rank \(1\).
Complex multiplication
The elliptic curves in class 383040.ho do not have complex multiplication.Modular form 383040.2.a.ho
sage: E.q_eigenform(10)