Properties

Label 129360gd
Number of curves $2$
Conductor $129360$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("gd1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 129360gd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
129360.eq2 129360gd1 [0, 1, 0, -7009221, 8362172979] [] 11520000 \(\Gamma_0(N)\)-optimal
129360.eq1 129360gd2 [0, 1, 0, -21003621, -700462254381] [] 57600000  

Rank

sage: E.rank()
 

The elliptic curves in class 129360gd have rank \(0\).

Complex multiplication

The elliptic curves in class 129360gd do not have complex multiplication.

Modular form 129360.2.a.gd

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

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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.