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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 340032.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
340032.a1 | 340032a1 | \([0, -1, 0, -81025, 41632801]\) | \(-224412099736609/2722801160772\) | \(-713765987489415168\) | \([]\) | \(6580224\) | \(2.1076\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 340032.a1 has rank \(0\).
Complex multiplication
The elliptic curves in class 340032.a do not have complex multiplication.Modular form 340032.2.a.a
sage: E.q_eigenform(10)