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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 19008.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
19008.k1 | 19008bo1 | \([0, 0, 0, -36, 86]\) | \(-2985984/121\) | \(-209088\) | \([]\) | \(1920\) | \(-0.21128\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 19008.k1 has rank \(1\).
Complex multiplication
The elliptic curves in class 19008.k do not have complex multiplication.Modular form 19008.2.a.k
sage: E.q_eigenform(10)