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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 1001a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1001.c1 | 1001a1 | \([0, -1, 1, -15881, 778423]\) | \(-442980486619070464/1864582578859\) | \(-1864582578859\) | \([]\) | \(1680\) | \(1.2092\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 1001a1 has rank \(1\).
Complex multiplication
The elliptic curves in class 1001a do not have complex multiplication.Modular form 1001.2.a.a
sage: E.q_eigenform(10)