Properties

Label 12138.k
Number of curves $1$
Conductor $12138$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 12138.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
12138.k1 12138g1 \([1, 0, 1, -4218684, -3343946630]\) \(-344002044213921241/1011143540736\) \(-24406546983419510784\) \([]\) \(587520\) \(2.5904\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 12138.k1 has rank \(0\).

Complex multiplication

The elliptic curves in class 12138.k do not have complex multiplication.

Modular form 12138.2.a.k

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} - q^{7} - q^{8} + q^{9} + q^{10} - 5 q^{11} + q^{12} - q^{13} + q^{14} - q^{15} + q^{16} - q^{18} - 6 q^{19} + O(q^{20})\) Copy content Toggle raw display