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SageMath
E = EllipticCurve("fm1")
E.isogeny_class()
Elliptic curves in class 123840fm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
123840.q1 | 123840fm1 | \([0, 0, 0, -1398, 20122]\) | \(-6476460544/1075\) | \(-50155200\) | \([]\) | \(46080\) | \(0.48557\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 123840fm1 has rank \(2\).
Complex multiplication
The elliptic curves in class 123840fm do not have complex multiplication.Modular form 123840.2.a.fm
sage: E.q_eigenform(10)