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SageMath
E = EllipticCurve("ek1")
E.isogeny_class()
Elliptic curves in class 20160ek
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
20160.cr1 | 20160ek1 | \([0, 0, 0, -48, 992]\) | \(-1024/35\) | \(-418037760\) | \([]\) | \(7680\) | \(0.33455\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 20160ek1 has rank \(0\).
Complex multiplication
The elliptic curves in class 20160ek do not have complex multiplication.Modular form 20160.2.a.ek
sage: E.q_eigenform(10)