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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 3006f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3006.c1 | 3006f1 | \([1, -1, 1, 5071, -45471]\) | \(19785968032823/12608077824\) | \(-9191288733696\) | \([]\) | \(8832\) | \(1.1764\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 3006f1 has rank \(1\).
Complex multiplication
The elliptic curves in class 3006f do not have complex multiplication.Modular form 3006.2.a.f
sage: E.q_eigenform(10)