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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 213444k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
213444.p1 | 213444k1 | \([0, 0, 0, -1210351989, -17825560621099]\) | \(-235165059164416/28529701497\) | \(-23789384720607288724544511216\) | \([]\) | \(141926400\) | \(4.1800\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 213444k1 has rank \(1\).
Complex multiplication
The elliptic curves in class 213444k do not have complex multiplication.Modular form 213444.2.a.k
sage: E.q_eigenform(10)