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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 28322f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
28322.e1 | 28322f1 | \([1, 1, 0, -711, -6971]\) | \(1171657/112\) | \(3808062832\) | \([]\) | \(13824\) | \(0.57611\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 28322f1 has rank \(2\).
Complex multiplication
The elliptic curves in class 28322f do not have complex multiplication.Modular form 28322.2.a.f
sage: E.q_eigenform(10)