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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 457776p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
457776.p1 | 457776p1 | \([0, 0, 0, -10404, 530604]\) | \(-27648/11\) | \(-49551146447616\) | \([]\) | \(1032192\) | \(1.3367\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 457776p1 has rank \(1\).
Complex multiplication
The elliptic curves in class 457776p do not have complex multiplication.Modular form 457776.2.a.p
sage: E.q_eigenform(10)