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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 11109.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
11109.f1 | 11109d1 | \([1, 0, 1, -48415, 4073417]\) | \(160261033/1029\) | \(80582003854149\) | \([]\) | \(39744\) | \(1.5049\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 11109.f1 has rank \(1\).
Complex multiplication
The elliptic curves in class 11109.f do not have complex multiplication.Modular form 11109.2.a.f
sage: E.q_eigenform(10)