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SageMath
E = EllipticCurve("by1")
E.isogeny_class()
Elliptic curves in class 15680by
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
15680.g1 | 15680by1 | \([0, 0, 0, -1372, -33614]\) | \(-110592/125\) | \(-322828856000\) | \([]\) | \(26880\) | \(0.90277\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 15680by1 has rank \(1\).
Complex multiplication
The elliptic curves in class 15680by do not have complex multiplication.Modular form 15680.2.a.by
sage: E.q_eigenform(10)