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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 409101w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
409101.w1 | 409101w1 | \([0, -1, 1, 1936807, 10366453712]\) | \(1605632000/93710763\) | \(-46894940054863291174707\) | \([]\) | \(20697600\) | \(3.0298\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 409101w1 has rank \(0\).
Complex multiplication
The elliptic curves in class 409101w do not have complex multiplication.Modular form 409101.2.a.w
sage: E.q_eigenform(10)