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Properties

Label 23826x
Number of curves $2$
Conductor $23826$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("x1")
 
E.isogeny_class()
 

Elliptic curves in class 23826x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
23826.x1 23826x1 \([1, 1, 1, -2354642543, -43978993085131]\) \(-235484681972809299625/3345408\) \(-20510918107377527808\) \([]\) \(8618400\) \(3.7127\) \(\Gamma_0(N)\)-optimal
23826.x2 23826x2 \([1, 1, 1, -2340958838, -44515377900685]\) \(-231403026519578265625/5706597418401792\) \(-34987526878817522331672379392\) \([]\) \(25855200\) \(4.2620\)  

Rank

sage: E.rank()
 

The elliptic curves in class 23826x have rank \(1\).

Complex multiplication

The elliptic curves in class 23826x do not have complex multiplication.

Modular form 23826.2.a.x

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{6} - q^{7} + q^{8} + q^{9} - q^{11} - q^{12} - 5 q^{13} - q^{14} + q^{16} + 6 q^{17} + q^{18} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.