Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("z1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 23520.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
23520.z1 23520bs4 \([0, 1, 0, -54896, 4932360]\) \(303735479048/105\) \(6324810240\) \([2]\) \(73728\) \(1.2365\)  
23520.z2 23520bs3 \([0, 1, 0, -7121, -117825]\) \(82881856/36015\) \(17355279298560\) \([2]\) \(73728\) \(1.2365\)  
23520.z3 23520bs1 \([0, 1, 0, -3446, 75480]\) \(601211584/11025\) \(83013134400\) \([2, 2]\) \(36864\) \(0.88997\) \(\Gamma_0(N)\)-optimal
23520.z4 23520bs2 \([0, 1, 0, -16, 222284]\) \(-8/354375\) \(-21346234560000\) \([2]\) \(73728\) \(1.2365\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 23520.2.a.z

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.