Properties

Label 3520j
Number of curves $2$
Conductor $3520$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 3520j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3520.l1 3520j1 \([0, -1, 0, -5665, 167585]\) \(-76711450249/851840\) \(-223304744960\) \([]\) \(5376\) \(0.99253\) \(\Gamma_0(N)\)-optimal
3520.l2 3520j2 \([0, -1, 0, 18975, 852577]\) \(2882081488391/2883584000\) \(-755914244096000\) \([]\) \(16128\) \(1.5418\)  

Rank

sage: E.rank()
 

The elliptic curves in class 3520j have rank \(0\).

Complex multiplication

The elliptic curves in class 3520j do not have complex multiplication.

Modular form 3520.2.a.j

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} + 5 q^{7} - 2 q^{9} - q^{11} - 2 q^{13} - q^{15} + 3 q^{17} + 7 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.