Properties

Label 12138v
Number of curves $1$
Conductor $12138$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("v1")
 
E.isogeny_class()
 

Elliptic curves in class 12138v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
12138.y1 12138v1 \([1, 0, 0, -6, 252]\) \(-83521/95256\) \(-27528984\) \([]\) \(4320\) \(0.10657\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 12138v1 has rank \(1\).

Complex multiplication

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

Modular form 12138.2.a.v

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