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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 213444m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
213444.r1 | 213444m1 | \([0, 0, 0, -1191729, -596688631]\) | \(-76995328/18711\) | \(-45487164018451334256\) | \([]\) | \(5529600\) | \(2.4905\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 213444m1 has rank \(1\).
Complex multiplication
The elliptic curves in class 213444m do not have complex multiplication.Modular form 213444.2.a.m
sage: E.q_eigenform(10)