Properties

Label 12274k
Number of curves $1$
Conductor $12274$
CM no
Rank $2$

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

Elliptic curves in class 12274k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
12274.j1 12274k1 \([1, -1, 1, 654, -1935]\) \(237719583/147968\) \(-19283337728\) \([]\) \(18144\) \(0.66264\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 12274k1 has rank \(2\).

Complex multiplication

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

Modular form 12274.2.a.k

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