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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 8027.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
8027.a1 | 8027b1 | \([0, 0, 1, 5, 0]\) | \(13824000/8027\) | \(-8027\) | \([]\) | \(1144\) | \(-0.56134\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 8027.a1 has rank \(2\).
Complex multiplication
The elliptic curves in class 8027.a do not have complex multiplication.Modular form 8027.2.a.a
sage: E.q_eigenform(10)