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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 100010.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
100010.e1 | 100010k1 | \([1, 0, 0, -670, 6660]\) | \(-33265084589281/233623360\) | \(-233623360\) | \([]\) | \(51264\) | \(0.43904\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 100010.e1 has rank \(1\).
Complex multiplication
The elliptic curves in class 100010.e do not have complex multiplication.Modular form 100010.2.a.e
sage: E.q_eigenform(10)