Properties

Label 69366w
Number of curves 2
Conductor 69366
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("69366.u1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 69366w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
69366.u2 69366w1 [1, 0, 0, 430484, 453494672] [7] 1893360 \(\Gamma_0(N)\)-optimal
69366.u1 69366w2 [1, 0, 0, -203025076, -1113860484568] [] 13253520  

Rank

sage: E.rank()
 

The elliptic curves in class 69366w have rank \(1\).

Modular form 69366.2.a.u

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

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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.