Properties

Label 3465.l
Number of curves $6$
Conductor $3465$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("3465.l1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3465.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3465.l1 3465e5 [1, -1, 0, -119250, 15879325] [2] 16384  
3465.l2 3465e3 [1, -1, 0, -7875, 220000] [2, 2] 8192  
3465.l3 3465e2 [1, -1, 0, -2430, -42449] [2, 2] 4096  
3465.l4 3465e1 [1, -1, 0, -2385, -44240] [2] 2048 \(\Gamma_0(N)\)-optimal
3465.l5 3465e4 [1, -1, 0, 2295, -190814] [2] 8192  
3465.l6 3465e6 [1, -1, 0, 16380, 1292071] [2] 16384  

Rank

sage: E.rank()
 

The elliptic curves in class 3465.l have rank \(0\).

Modular form 3465.2.a.l

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{4} - q^{5} - q^{7} - 3q^{8} - q^{10} - q^{11} - 2q^{13} - q^{14} - q^{16} + 6q^{17} - 4q^{19} + O(q^{20}) \)

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 LMFDB numbering.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 8 & 4 \\ 2 & 1 & 2 & 4 & 4 & 2 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 2 & 4 & 8 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.