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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 40733.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
40733.e1 | 40733k1 | \([0, 0, 1, 1058, -3042]\) | \(884736/539\) | \(-79791344171\) | \([]\) | \(48488\) | \(0.78109\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 40733.e1 has rank \(0\).
Complex multiplication
The elliptic curves in class 40733.e do not have complex multiplication.Modular form 40733.2.a.e
sage: E.q_eigenform(10)