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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 142.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
142.a1 | 142b1 | \([1, 1, 0, -1, -1]\) | \(389017/142\) | \(142\) | \([]\) | \(4\) | \(-0.88664\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 142.a1 has rank \(1\).
Complex multiplication
The elliptic curves in class 142.a do not have complex multiplication.Modular form 142.2.a.a
sage: E.q_eigenform(10)