Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3465i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3465.n6 3465i1 [1, -1, 0, 315, 624456] [2] 7680 \(\Gamma_0(N)\)-optimal
3465.n5 3465i2 [1, -1, 0, -107730, 13395375] [2, 2] 15360  
3465.n4 3465i3 [1, -1, 0, -229005, -22186710] [2] 30720  
3465.n2 3465i4 [1, -1, 0, -1715175, 865019736] [2, 2] 30720  
3465.n1 3465i5 [1, -1, 0, -27442800, 55340692911] [2] 61440  
3465.n3 3465i6 [1, -1, 0, -1706670, 874016325] [2] 61440  

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 3465i do not have complex multiplication.

Modular form 3465.2.a.i

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.