Properties

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

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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 23520l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
23520.n3 23520l1 \([0, -1, 0, -11090, 444312]\) \(20034997696/455625\) \(3430644840000\) \([2, 2]\) \(55296\) \(1.1920\) \(\Gamma_0(N)\)-optimal
23520.n4 23520l2 \([0, -1, 0, 1160, 1360612]\) \(2863288/13286025\) \(-800300828275200\) \([2]\) \(110592\) \(1.5386\)  
23520.n2 23520l3 \([0, -1, 0, -24320, -804600]\) \(26410345352/10546875\) \(635304600000000\) \([2]\) \(110592\) \(1.5386\)  
23520.n1 23520l4 \([0, -1, 0, -176465, 28591137]\) \(1261112198464/675\) \(325275955200\) \([2]\) \(110592\) \(1.5386\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 23520.2.a.l

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} + q^{9} - 4 q^{11} - 6 q^{13} - q^{15} - 2 q^{17} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.