Properties

Label 53067.r
Number of curves 6
Conductor 53067
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("53067.r1")
sage: E.isogeny_class()

Elliptic curves in class 53067.r

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
53067.r1 53067q6 [1, 0, 1, -13868545, -19880151427] 2 1327104  
53067.r2 53067q4 [1, 0, 1, -867130, -310421569] 4 663552  
53067.r3 53067q3 [1, 0, 1, -690240, 219328603] 2 663552  
53067.r4 53067q5 [1, 0, 1, -601795, -503903851] 2 1327104  
53067.r5 53067q2 [1, 0, 1, -71125, -1571629] 4 331776  
53067.r6 53067q1 [1, 0, 1, 17320, -191887] 2 165888 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curves in class 53067.r have rank \(0\).

Modular form 53067.2.a.r

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.