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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 1003.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1003.a1 | 1003c1 | \([1, -1, 1, 63, -332]\) | \(28066748319/59354531\) | \(-59354531\) | \([]\) | \(384\) | \(0.17588\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 1003.a1 has rank \(0\).
Complex multiplication
The elliptic curves in class 1003.a do not have complex multiplication.Modular form 1003.2.a.a
sage: E.q_eigenform(10)