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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 100773.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
100773.a1 | 100773a1 | \([1, -1, 0, -51, 44]\) | \(20346417/11197\) | \(8162613\) | \([]\) | \(29120\) | \(0.016865\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 100773.a1 has rank \(2\).
Complex multiplication
The elliptic curves in class 100773.a do not have complex multiplication.Modular form 100773.2.a.a
sage: E.q_eigenform(10)