Properties

Label 10320s
Number of curves $4$
Conductor $10320$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("s1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 10320s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
10320.a3 10320s1 [0, -1, 0, -1096, 14320] [2] 4608 \(\Gamma_0(N)\)-optimal
10320.a2 10320s2 [0, -1, 0, -1416, 5616] [2, 2] 9216  
10320.a1 10320s3 [0, -1, 0, -13416, -589584] [2] 18432  
10320.a4 10320s4 [0, -1, 0, 5464, 38640] [2] 18432  

Rank

sage: E.rank()
 

The elliptic curves in class 10320s have rank \(1\).

Complex multiplication

The elliptic curves in class 10320s do not have complex multiplication.

Modular form 10320.2.a.s

sage: E.q_eigenform(10)
 
\( q - q^{3} - q^{5} - 4q^{7} + q^{9} - 2q^{13} + q^{15} + 2q^{17} - 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.