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SageMath
E = EllipticCurve("ip1")
E.isogeny_class()
Elliptic curves in class 159936.ip
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
159936.ip1 | 159936bi1 | \([0, 1, 0, -1309345, 578551007]\) | \(-3352478521/15606\) | \(-1155611685262196736\) | \([]\) | \(2515968\) | \(2.3164\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 159936.ip1 has rank \(1\).
Complex multiplication
The elliptic curves in class 159936.ip do not have complex multiplication.Modular form 159936.2.a.ip
sage: E.q_eigenform(10)