Properties

Label 23520.m
Number of curves $4$
Conductor $23520$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("m1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 23520.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
23520.m1 23520bf4 \([0, -1, 0, -5000940016, 136122808277716]\) \(229625675762164624948320008/9568125\) \(576348333120000\) \([4]\) \(10321920\) \(3.7329\)  
23520.m2 23520bf3 \([0, -1, 0, -313630641, 2111674775841]\) \(7079962908642659949376/100085966990454375\) \(48230457059164023866880000\) \([2]\) \(10321920\) \(3.7329\)  
23520.m3 23520bf1 \([0, -1, 0, -312558766, 2126996800216]\) \(448487713888272974160064/91549016015625\) \(689321611854225000000\) \([2, 2]\) \(5160960\) \(3.3864\) \(\Gamma_0(N)\)-optimal
23520.m4 23520bf2 \([0, -1, 0, -311487136, 2142304820440]\) \(-55486311952875723077768/801237030029296875\) \(-48263544497109375000000000\) \([2]\) \(10321920\) \(3.7329\)  

Rank

sage: E.rank()
 

The elliptic curves in class 23520.m have rank \(1\).

Complex multiplication

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

Modular form 23520.2.a.m

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.