Properties

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

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Show commands: SageMath
E = EllipticCurve("q1")
 
E.isogeny_class()
 

Elliptic curves in class 23520.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
23520.q1 23520k4 \([0, -1, 0, -15558545, -23615994303]\) \(864335783029582144/59535\) \(28689339248640\) \([2]\) \(737280\) \(2.4832\)  
23520.q2 23520k3 \([0, -1, 0, -1092520, -271803608]\) \(2394165105226952/854262178245\) \(51457582596273154560\) \([2]\) \(737280\) \(2.4832\)  
23520.q3 23520k1 \([0, -1, 0, -972470, -368707968]\) \(13507798771700416/3544416225\) \(26687809565121600\) \([2, 2]\) \(368640\) \(2.1366\) \(\Gamma_0(N)\)-optimal
23520.q4 23520k2 \([0, -1, 0, -853400, -462487500]\) \(-1141100604753992/875529151875\) \(-52738626144738240000\) \([2]\) \(737280\) \(2.4832\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 23520.2.a.q

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