Properties

Label 55470t
Number of curves $4$
Conductor $55470$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("55470.r1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 55470t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
55470.r4 55470t1 [1, 1, 1, -198806, -10196881] [2] 887040 \(\Gamma_0(N)\)-optimal
55470.r3 55470t2 [1, 1, 1, -2510056, -1530074881] [2] 1774080  
55470.r2 55470t3 [1, 1, 1, -9212681, 10758748919] [2] 2661120  
55470.r1 55470t4 [1, 1, 1, -9582481, 9847709639] [2] 5322240  

Rank

sage: E.rank()
 

The elliptic curves in class 55470t have rank \(1\).

Modular form 55470.2.a.r

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

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.