Properties

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

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Show commands: SageMath
E = EllipticCurve("z1")
 
E.isogeny_class()
 

Elliptic curves in class 12138z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
12138.z1 12138z1 \([1, 0, 0, -91, -343]\) \(-288568081/1176\) \(-339864\) \([]\) \(1728\) \(-0.082518\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 12138z1 has rank \(0\).

Complex multiplication

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

Modular form 12138.2.a.z

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