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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 393129.w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
393129.w1 | 393129w1 | \([0, 0, 1, -19918536, 83216116167]\) | \(-56623104/161051\) | \(-2485797285751487035370163\) | \([]\) | \(54720000\) | \(3.3682\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 393129.w1 has rank \(2\).
Complex multiplication
The elliptic curves in class 393129.w do not have complex multiplication.Modular form 393129.2.a.w
sage: E.q_eigenform(10)