Properties

Label 152592w
Number of curves $2$
Conductor $152592$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("w1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 152592w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
152592.ct1 152592w1 [0, 1, 0, -4180192, -3264988300] [2] 7741440 \(\Gamma_0(N)\)-optimal
152592.ct2 152592w2 [0, 1, 0, -1220832, -7795176588] [2] 15482880  

Rank

sage: E.rank()
 

The elliptic curves in class 152592w have rank \(1\).

Complex multiplication

The elliptic curves in class 152592w do not have complex multiplication.

Modular form 152592.2.a.w

sage: E.q_eigenform(10)
 
\( q + q^{3} + 2q^{5} - 4q^{7} + q^{9} - q^{11} - 4q^{13} + 2q^{15} + 8q^{19} + O(q^{20}) \)

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.