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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 31600.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
31600.f1 | 31600r1 | \([0, -1, 0, -1408, -18688]\) | \(4826809/316\) | \(20224000000\) | \([]\) | \(26880\) | \(0.72730\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 31600.f1 has rank \(1\).
Complex multiplication
The elliptic curves in class 31600.f do not have complex multiplication.Modular form 31600.2.a.f
sage: E.q_eigenform(10)