Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("1470.b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1470.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1470.b1 1470b7 [1, 1, 0, -17210393, 27473941797] [2] 55296  
1470.b2 1470b6 [1, 1, 0, -1075673, 428924133] [2, 2] 27648  
1470.b3 1470b8 [1, 1, 0, -997273, 494199973] [2] 55296  
1470.b4 1470b4 [1, 1, 0, -213518, 37218672] [2] 18432  
1470.b5 1470b3 [1, 1, 0, -72153, 5639397] [2] 13824  
1470.b6 1470b2 [1, 1, 0, -28298, -973692] [2, 2] 9216  
1470.b7 1470b1 [1, 1, 0, -24378, -1474668] [2] 4608 \(\Gamma_0(N)\)-optimal
1470.b8 1470b5 [1, 1, 0, 94202, -7025192] [2] 18432  

Rank

sage: E.rank()
 

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

Modular form 1470.2.a.b

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.