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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 259182.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 259182.k1 | 259182k1 | \([1, -1, 0, -31820916, 65235956176]\) | \(1090718342617689660877299/68598829524107395072\) | \(224112376055258859700224\) | \([]\) | \(46218240\) | \(3.2316\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 259182.k1 has rank \(1\).
Complex multiplication
The elliptic curves in class 259182.k do not have complex multiplication.Modular form 259182.2.a.k
sage: E.q_eigenform(10)