Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("p1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 23520.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
23520.p1 23520bl4 \([0, -1, 0, -15876800, 24354934500]\) \(7347751505995469192/72930375\) \(4393055072448000\) \([2]\) \(737280\) \(2.5778\)  
23520.p2 23520bl3 \([0, -1, 0, -1421800, 20383000]\) \(5276930158229192/3050936350875\) \(183777080700975552000\) \([2]\) \(737280\) \(2.5778\)  
23520.p3 23520bl1 \([0, -1, 0, -993050, 380190000]\) \(14383655824793536/45209390625\) \(340405734249000000\) \([2, 2]\) \(368640\) \(2.2313\) \(\Gamma_0(N)\)-optimal
23520.p4 23520bl2 \([0, -1, 0, -576305, 701333697]\) \(-43927191786304/415283203125\) \(-200120949000000000000\) \([4]\) \(737280\) \(2.5778\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 23520.2.a.p

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