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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 412224.x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
412224.x1 | 412224x1 | \([0, -1, 0, 41995, -159891]\) | \(499903512190976/289857231459\) | \(-4749020880224256\) | \([]\) | \(2515968\) | \(1.6975\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 412224.x1 has rank \(0\).
Complex multiplication
The elliptic curves in class 412224.x do not have complex multiplication.Modular form 412224.2.a.x
sage: E.q_eigenform(10)