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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 377706.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 377706.k1 | 377706k1 | \([1, 1, 0, -1005651493, 12277507116301]\) | \(-759799852292647673818921/213978357595570176\) | \(-31676476393420133466046464\) | \([]\) | \(164229120\) | \(3.8743\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 377706.k1 has rank \(1\).
Complex multiplication
The elliptic curves in class 377706.k do not have complex multiplication.Modular form 377706.2.a.k
sage: E.q_eigenform(10)