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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 42042e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
42042.e1 | 42042e1 | \([1, 1, 0, 30992, -1579136]\) | \(571039705271/520401024\) | \(-3000008343556224\) | \([]\) | \(263424\) | \(1.6571\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 42042e1 has rank \(0\).
Complex multiplication
The elliptic curves in class 42042e do not have complex multiplication.Modular form 42042.2.a.e
sage: E.q_eigenform(10)