Show commands:
SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 412224r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
412224.r1 | 412224r1 | \([0, -1, 0, -8815, 336289]\) | \(-1183749898530304/65037218139\) | \(-4162381960896\) | \([]\) | \(622336\) | \(1.1794\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 412224r1 has rank \(1\).
Complex multiplication
The elliptic curves in class 412224r do not have complex multiplication.Modular form 412224.2.a.r
sage: E.q_eigenform(10)