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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 675.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
675.a1 | 675h1 | \([0, 0, 1, -675, -14344]\) | \(-12288/25\) | \(-69198046875\) | \([]\) | \(864\) | \(0.76930\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 675.a1 has rank \(0\).
Complex multiplication
The elliptic curves in class 675.a do not have complex multiplication.Modular form 675.2.a.a
sage: E.q_eigenform(10)