Properties

Label 112710ck
Number of curves 2
Conductor 112710
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("112710.ct1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 112710ck

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
112710.ct1 112710ck1 [1, 0, 0, -3936186, 2971212516] [2] 4423680 \(\Gamma_0(N)\)-optimal
112710.ct2 112710ck2 [1, 0, 0, -606906, 7837954020] [2] 8847360  

Rank

sage: E.rank()
 

The elliptic curves in class 112710ck have rank \(1\).

Modular form 112710.2.a.ct

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

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 Cremona 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 Cremona labels.