Properties

Label 23520br
Number of curves $4$
Conductor $23520$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("br1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 23520br

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
23520.ba3 23520br1 \([0, 1, 0, -312558766, -2126996800216]\) \(448487713888272974160064/91549016015625\) \(689321611854225000000\) \([2, 2]\) \(5160960\) \(3.3864\) \(\Gamma_0(N)\)-optimal
23520.ba4 23520br2 \([0, 1, 0, -311487136, -2142304820440]\) \(-55486311952875723077768/801237030029296875\) \(-48263544497109375000000000\) \([2]\) \(10321920\) \(3.7329\)  
23520.ba2 23520br3 \([0, 1, 0, -313630641, -2111674775841]\) \(7079962908642659949376/100085966990454375\) \(48230457059164023866880000\) \([4]\) \(10321920\) \(3.7329\)  
23520.ba1 23520br4 \([0, 1, 0, -5000940016, -136122808277716]\) \(229625675762164624948320008/9568125\) \(576348333120000\) \([2]\) \(10321920\) \(3.7329\)  

Rank

sage: E.rank()
 

The elliptic curves in class 23520br have rank \(0\).

Complex multiplication

The elliptic curves in class 23520br do not have complex multiplication.

Modular form 23520.2.a.br

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} + q^{9} - 4q^{11} + 6q^{13} - q^{15} - 6q^{17} + 4q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.