Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("cw1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 129360.cw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
129360.cw1 129360fb2 \([0, -1, 0, -25300, 1554652]\) \(59466754384/121275\) \(3652577913600\) \([2]\) \(368640\) \(1.2970\)  
129360.cw2 129360fb1 \([0, -1, 0, -1045, 41140]\) \(-67108864/343035\) \(-645723595440\) \([2]\) \(184320\) \(0.95045\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 129360.2.a.cw

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

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.