Properties

Label 129360.co
Number of curves $2$
Conductor $129360$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("co1")
 
E.isogeny_class()
 

Elliptic curves in class 129360.co

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
129360.co1 129360bl2 \([0, -1, 0, -1372800, 45267552]\) \(3462051528686/1993006125\) \(164710371157694208000\) \([2]\) \(3354624\) \(2.5688\)  
129360.co2 129360bl1 \([0, -1, 0, 342200, 5479552]\) \(107245762628/62390625\) \(-2578111244016000000\) \([2]\) \(1677312\) \(2.2222\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 129360.co have rank \(1\).

Complex multiplication

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

Modular form 129360.2.a.co

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