Properties

Label 69828y
Number of curves 2
Conductor 69828
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("69828.v1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 69828y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
69828.v2 69828y1 [0, 1, 0, 1411, 11736] [2] 76032 \(\Gamma_0(N)\)-optimal
69828.v1 69828y2 [0, 1, 0, -6524, 94260] [2] 152064  

Rank

sage: E.rank()
 

The elliptic curves in class 69828y have rank \(0\).

Modular form 69828.2.a.v

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

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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.