Properties

Label 259210ch
Number of curves $2$
Conductor $259210$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("ch1")
 
E.isogeny_class()
 

Elliptic curves in class 259210ch

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
259210.ch1 259210ch1 \([1, -1, 1, -3413472, -2426561609]\) \(-5154200289/20\) \(-17067948818861780\) \([]\) \(10478160\) \(2.3279\) \(\Gamma_0(N)\)-optimal
259210.ch2 259210ch2 \([1, -1, 1, 23803578, 23025734869]\) \(1747829720511/1280000000\) \(-1092348724407153920000000\) \([]\) \(73347120\) \(3.3008\)  

Rank

sage: E.rank()
 

The elliptic curves in class 259210ch have rank \(0\).

Complex multiplication

The elliptic curves in class 259210ch do not have complex multiplication.

Modular form 259210.2.a.ch

sage: E.q_eigenform(10)
 
\(q + q^{2} + 3 q^{3} + q^{4} + q^{5} + 3 q^{6} + q^{8} + 6 q^{9} + q^{10} + 2 q^{11} + 3 q^{12} + 3 q^{15} + q^{16} + 4 q^{17} + 6 q^{18} + 6 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.