Properties

Label 12274j
Number of curves $1$
Conductor $12274$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 12274j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
12274.m1 12274j1 \([1, 0, 0, -9574, -391610]\) \(-5714497/578\) \(-9816499437698\) \([]\) \(27360\) \(1.2329\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 12274j1 has rank \(0\).

Complex multiplication

The elliptic curves in class 12274j do not have complex multiplication.

Modular form 12274.2.a.j

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} - 2 q^{5} + q^{6} - 2 q^{7} + q^{8} - 2 q^{9} - 2 q^{10} - q^{11} + q^{12} - 2 q^{14} - 2 q^{15} + q^{16} - q^{17} - 2 q^{18} + O(q^{20})\) Copy content Toggle raw display