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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 17640.x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
17640.x1 | 17640p1 | \([0, 0, 0, -2163, 45038]\) | \(-15298178/3125\) | \(-228614400000\) | \([]\) | \(17280\) | \(0.90189\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 17640.x1 has rank \(1\).
Complex multiplication
The elliptic curves in class 17640.x do not have complex multiplication.Modular form 17640.2.a.x
sage: E.q_eigenform(10)