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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 457776w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
457776.w1 | 457776w1 | \([0, 0, 0, -155199936, -744193963024]\) | \(-5736108018368512/11042163\) | \(-795857215871195394048\) | \([]\) | \(53084160\) | \(3.2643\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 457776w1 has rank \(1\).
Complex multiplication
The elliptic curves in class 457776w do not have complex multiplication.Modular form 457776.2.a.w
sage: E.q_eigenform(10)