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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 221067k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
221067.j1 | 221067k1 | \([1, -1, 1, -15269, -12292464]\) | \(-36883367257/6098396283\) | \(-65089945964984787\) | \([]\) | \(1244160\) | \(1.9056\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 221067k1 has rank \(1\).
Complex multiplication
The elliptic curves in class 221067k do not have complex multiplication.Modular form 221067.2.a.k
sage: E.q_eigenform(10)