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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 262.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
262.a1 | 262b1 | \([1, -1, 0, -2, 2]\) | \(-1157625/262\) | \(-262\) | \([]\) | \(12\) | \(-0.81597\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 262.a1 has rank \(1\).
Complex multiplication
The elliptic curves in class 262.a do not have complex multiplication.Modular form 262.2.a.a
sage: E.q_eigenform(10)