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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 53312.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
53312.e1 | 53312i1 | \([0, 0, 0, -97804, 42435568]\) | \(-164384733177/1140850688\) | \(-718060257774927872\) | \([]\) | \(1198080\) | \(2.1095\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 53312.e1 has rank \(1\).
Complex multiplication
The elliptic curves in class 53312.e do not have complex multiplication.Modular form 53312.2.a.e
sage: E.q_eigenform(10)