Properties

Label 55470.i
Number of curves $2$
Conductor $55470$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("55470.i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 55470.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
55470.i1 55470g2 [1, 0, 1, -3291259, -2689109818] [] 3120768  
55470.i2 55470g1 [1, 0, 1, 286556, 21442826] [3] 1040256 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 55470.i have rank \(0\).

Modular form 55470.2.a.i

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} + 2q^{7} - q^{8} + q^{9} + q^{10} - 3q^{11} + q^{12} - 4q^{13} - 2q^{14} - q^{15} + q^{16} - 3q^{17} - q^{18} - q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.