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Properties

Label 279174.bk
Number of curves $2$
Conductor $279174$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bk1")
 
E.isogeny_class()
 

Elliptic curves in class 279174.bk

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
279174.bk1 279174bk1 \([1, 0, 1, -346991180, 2433141018506]\) \(191419196757975012994777/4816668944272195584\) \(116262678992527275690295296\) \([2]\) \(116121600\) \(3.7845\) \(\Gamma_0(N)\)-optimal
279174.bk2 279174bk2 \([1, 0, 1, 55481780, 7743852220298]\) \(782494606698830369063/1073710038353163337728\) \(-25916750136742126432679903232\) \([2]\) \(232243200\) \(4.1310\)  

Rank

sage: E.rank()
 

The elliptic curves in class 279174.bk have rank \(1\).

Complex multiplication

The elliptic curves in class 279174.bk do not have complex multiplication.

Modular form 279174.2.a.bk

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

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.