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SageMath
E = EllipticCurve("ef1")
E.isogeny_class()
Elliptic curves in class 52416ef
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
52416.eo1 | 52416ef1 | \([0, 0, 0, 5268, 416848]\) | \(2284322013/11927552\) | \(-84421877170176\) | \([]\) | \(104448\) | \(1.3544\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 52416ef1 has rank \(1\).
Complex multiplication
The elliptic curves in class 52416ef do not have complex multiplication.Modular form 52416.2.a.ef
sage: E.q_eigenform(10)