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SageMath
E = EllipticCurve("ew1")
E.isogeny_class()
Elliptic curves in class 450800.ew
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
450800.ew1 | 450800ew1 | \([0, 1, 0, -4254833, 8408909963]\) | \(-144814859264/435654247\) | \(-25627143252651500000000\) | \([]\) | \(24944640\) | \(2.9866\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 450800.ew1 has rank \(1\).
Complex multiplication
The elliptic curves in class 450800.ew do not have complex multiplication.Modular form 450800.2.a.ew
sage: E.q_eigenform(10)