Properties

Label 179520bs
Number of curves 2
Conductor 179520
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("179520.fr1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 179520bs

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
179520.fr2 179520bs1 [0, 1, 0, -56321, -2284545] [2] 1032192 \(\Gamma_0(N)\)-optimal
179520.fr1 179520bs2 [0, 1, 0, -752641, -251427841] [2] 2064384  

Rank

sage: E.rank()
 

The elliptic curves in class 179520bs have rank \(0\).

Modular form 179520.2.a.fr

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 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.