Properties

Label 179520.p
Number of curves 2
Conductor 179520
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("179520.p1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 179520.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
179520.p1 179520ht2 [0, -1, 0, -752641, 251427841] [2] 2064384  
179520.p2 179520ht1 [0, -1, 0, -56321, 2284545] [2] 1032192 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 179520.p have rank \(1\).

Modular form 179520.2.a.p

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

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 LMFDB 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 LMFDB labels.