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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 311696k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 311696.k1 | 311696k1 | \([0, 1, 0, -645, -43793]\) | \(-65536/1771\) | \(-803183239936\) | \([]\) | \(460800\) | \(0.96487\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 311696k1 has rank \(1\).
Complex multiplication
The elliptic curves in class 311696k do not have complex multiplication.Modular form 311696.2.a.k
sage: E.q_eigenform(10)