Properties

Label 364560.ca
Number of curves $2$
Conductor $364560$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("ca1")
 
E.isogeny_class()
 

Elliptic curves in class 364560.ca

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
364560.ca1 364560ca2 \([0, -1, 0, -29354936, 57116705136]\) \(5805223604235668521/435937500000000\) \(210074054400000000000000\) \([2]\) \(46448640\) \(3.2205\)  
364560.ca2 364560ca1 \([0, -1, 0, 1754184, 3957440880]\) \(1238798620042199/14760960000000\) \(-7113163501731840000000\) \([2]\) \(23224320\) \(2.8739\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 364560.ca have rank \(0\).

Complex multiplication

The elliptic curves in class 364560.ca do not have complex multiplication.

Modular form 364560.2.a.ca

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} + q^{9} + 4 q^{11} + 4 q^{13} + q^{15} + 6 q^{17} + O(q^{20})\) 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.