Properties

Label 1470.m
Number of curves $8$
Conductor $1470$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("1470.m1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1470.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1470.m1 1470m7 [1, 1, 1, -316100, -43167433] [2] 27648  
1470.m2 1470m4 [1, 1, 1, -282290, -57846265] [2] 9216  
1470.m3 1470m6 [1, 1, 1, -132350, 17984567] [2, 2] 13824  
1470.m4 1470m3 [1, 1, 1, -131370, 18272295] [4] 6912  
1470.m5 1470m2 [1, 1, 1, -17690, -904345] [2, 2] 4608  
1470.m6 1470m5 [1, 1, 1, -3970, -2254393] [2] 9216  
1470.m7 1470m1 [1, 1, 1, -2010, 11367] [4] 2304 \(\Gamma_0(N)\)-optimal
1470.m8 1470m8 [1, 1, 1, 35720, 60741575] [2] 27648  

Rank

sage: E.rank()
 

The elliptic curves in class 1470.m have rank \(0\).

Modular form 1470.2.a.m

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} + q^{8} + q^{9} + q^{10} - q^{12} - 2q^{13} - q^{15} + q^{16} + 6q^{17} + q^{18} + 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 2 & 4 & 6 & 12 & 12 & 4 \\ 3 & 1 & 6 & 12 & 2 & 4 & 4 & 12 \\ 2 & 6 & 1 & 2 & 3 & 6 & 6 & 2 \\ 4 & 12 & 2 & 1 & 6 & 12 & 3 & 4 \\ 6 & 2 & 3 & 6 & 1 & 2 & 2 & 6 \\ 12 & 4 & 6 & 12 & 2 & 1 & 4 & 3 \\ 12 & 4 & 6 & 3 & 2 & 4 & 1 & 12 \\ 4 & 12 & 2 & 4 & 6 & 3 & 12 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.