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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 412224.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
412224.a1 | 412224a1 | \([0, -1, 0, -5505, 156801]\) | \(140787677378/2325201\) | \(304768745472\) | \([]\) | \(755712\) | \(1.0023\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 412224.a1 has rank \(2\).
Complex multiplication
The elliptic curves in class 412224.a do not have complex multiplication.Modular form 412224.2.a.a
sage: E.q_eigenform(10)