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SageMath
E = EllipticCurve("by1")
E.isogeny_class()
Elliptic curves in class 12480.by
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
12480.by1 | 12480z1 | \([0, 1, 0, -31, 59]\) | \(-53157376/1755\) | \(-112320\) | \([]\) | \(1152\) | \(-0.25616\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 12480.by1 has rank \(1\).
Complex multiplication
The elliptic curves in class 12480.by do not have complex multiplication.Modular form 12480.2.a.by
sage: E.q_eigenform(10)