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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 51842m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
51842.o1 | 51842m1 | \([1, 0, 0, 1714, -12412]\) | \(8947391/6272\) | \(-390346205312\) | \([]\) | \(96768\) | \(0.91270\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 51842m1 has rank \(0\).
Complex multiplication
The elliptic curves in class 51842m do not have complex multiplication.Modular form 51842.2.a.m
sage: E.q_eigenform(10)