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SageMath
E = EllipticCurve("pq1")
E.isogeny_class()
Elliptic curves in class 487872pq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
487872.pq1 | 487872pq1 | \([0, 0, 0, -6465756, -6328649448]\) | \(-610325920583424/55240493\) | \(-2705685894685154304\) | \([]\) | \(14745600\) | \(2.5763\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 487872pq1 has rank \(1\).
Complex multiplication
The elliptic curves in class 487872pq do not have complex multiplication.Modular form 487872.2.a.pq
sage: E.q_eigenform(10)