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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 117117.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
117117.k1 | 117117s1 | \([1, -1, 1, 436, -1816]\) | \(74559407/53361\) | \(-6574128561\) | \([]\) | \(70656\) | \(0.57228\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 117117.k1 has rank \(2\).
Complex multiplication
The elliptic curves in class 117117.k do not have complex multiplication.Modular form 117117.2.a.k
sage: E.q_eigenform(10)