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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 42042.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
42042.f1 | 42042w1 | \([1, 1, 0, 20807, 20512549]\) | \(20329346580026519/3718228368007296\) | \(-182193190032357504\) | \([]\) | \(411264\) | \(1.9912\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 42042.f1 has rank \(0\).
Complex multiplication
The elliptic curves in class 42042.f do not have complex multiplication.Modular form 42042.2.a.f
sage: E.q_eigenform(10)