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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 1035.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1035.e1 | 1035c1 | \([0, 0, 1, -6582, 205537]\) | \(-43258336804864/646875\) | \(-471571875\) | \([]\) | \(640\) | \(0.80119\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 1035.e1 has rank \(1\).
Complex multiplication
The elliptic curves in class 1035.e do not have complex multiplication.Modular form 1035.2.a.e
sage: E.q_eigenform(10)