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SageMath
E = EllipticCurve("fk1")
E.isogeny_class()
Elliptic curves in class 162288.fk
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 162288.fk1 | 162288fu1 | \([0, 0, 0, -3712779, -2793738087]\) | \(-4124632486295808/70140333767\) | \(-96250629645454524912\) | \([]\) | \(3612672\) | \(2.6330\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 162288.fk1 has rank \(1\).
Complex multiplication
The elliptic curves in class 162288.fk do not have complex multiplication.Modular form 162288.2.a.fk
sage: E.q_eigenform(10)