Properties

Label 84966.ca
Number of curves $4$
Conductor $84966$
CM no
Rank $1$
Graph

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

Elliptic curves in class 84966.ca

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
84966.ca1 84966bs3 \([1, 0, 1, -10628126, 10081769744]\) \(46753267515625/11591221248\) \(32916296364971780210688\) \([2]\) \(7464960\) \(3.0310\)  
84966.ca2 84966bs1 \([1, 0, 1, -3618431, -2648601070]\) \(1845026709625/793152\) \(2252362001887835712\) \([2]\) \(2488320\) \(2.4817\) \(\Gamma_0(N)\)-optimal
84966.ca3 84966bs2 \([1, 0, 1, -3051991, -3505738078]\) \(-1107111813625/1228691592\) \(-3489190286174493497352\) \([2]\) \(4976640\) \(2.8283\)  
84966.ca4 84966bs4 \([1, 0, 1, 25624034, 63937978640]\) \(655215969476375/1001033261568\) \(-2842695071035072667140608\) \([2]\) \(14929920\) \(3.3776\)  

Rank

sage: E.rank()
 

The elliptic curves in class 84966.ca have rank \(1\).

Complex multiplication

The elliptic curves in class 84966.ca do not have complex multiplication.

Modular form 84966.2.a.ca

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{6} - q^{8} + q^{9} + q^{12} - 2 q^{13} + q^{16} - q^{18} + 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.