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SageMath
E = EllipticCurve("pm1")
E.isogeny_class()
Elliptic curves in class 487872.pm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
487872.pm1 | 487872pm1 | \([0, 0, 0, 1868724, -939249432]\) | \(15185664/16807\) | \(-798758725983871048704\) | \([]\) | \(28385280\) | \(2.6973\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 487872.pm1 has rank \(1\).
Complex multiplication
The elliptic curves in class 487872.pm do not have complex multiplication.Modular form 487872.2.a.pm
sage: E.q_eigenform(10)