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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 21675f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 21675.x1 | 21675f1 | \([0, -1, 1, -31308, -2763817]\) | \(-5624320000/2255067\) | \(-1360795882803075\) | \([]\) | \(165888\) | \(1.6126\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 21675f1 has rank \(1\).
Complex multiplication
The elliptic curves in class 21675f do not have complex multiplication.Modular form 21675.2.a.f
sage: E.q_eigenform(10)