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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 291312.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 291312.k1 | 291312k1 | \([0, 0, 0, 11776461, 18654081266]\) | \(30004847/42336\) | \(-254851100073570557362176\) | \([]\) | \(28200960\) | \(3.1769\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 291312.k1 has rank \(1\).
Complex multiplication
The elliptic curves in class 291312.k do not have complex multiplication.Modular form 291312.2.a.k
sage: E.q_eigenform(10)