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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 116688.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
116688.s1 | 116688bc1 | \([0, 1, 0, -256789, 50225327]\) | \(-7315005991668416512/38160401310603\) | \(-9769062735514368\) | \([]\) | \(1082880\) | \(1.9138\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 116688.s1 has rank \(1\).
Complex multiplication
The elliptic curves in class 116688.s do not have complex multiplication.Modular form 116688.2.a.s
sage: E.q_eigenform(10)