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SageMath
E = EllipticCurve("fk1")
E.isogeny_class()
Elliptic curves in class 271040.fk
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 271040.fk1 | 271040fk1 | \([0, 1, 0, -9115, 332275]\) | \(-738763264/875\) | \(-99207416000\) | \([]\) | \(274560\) | \(1.0216\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 271040.fk1 has rank \(0\).
Complex multiplication
The elliptic curves in class 271040.fk do not have complex multiplication.Modular form 271040.2.a.fk
sage: E.q_eigenform(10)