Properties

Label 67158k
Number of curves $1$
Conductor $67158$
CM no
Rank $1$

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

Elliptic curves in class 67158k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
67158.j1 67158k1 \([1, -1, 0, 139113, -1361633]\) \(408411137424575375/237392322963978\) \(-173059003440739962\) \([]\) \(935680\) \(1.9971\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 67158k1 has rank \(1\).

Complex multiplication

The elliptic curves in class 67158k do not have complex multiplication.

Modular form 67158.2.a.k

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{7} - q^{8} + 3 q^{11} + q^{13} + q^{14} + q^{16} - 8 q^{17} + 7 q^{19} + O(q^{20})\) Copy content Toggle raw display