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Properties

Label 6942.l
Number of curves $3$
Conductor $6942$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 6942.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6942.l1 6942n3 \([1, 0, 0, -2256837, -4804811139]\) \(-1271230499775148533281233/9236796227344140050076\) \(-9236796227344140050076\) \([]\) \(590976\) \(2.8979\)  
6942.l2 6942n1 \([1, 0, 0, -210177, 37101321]\) \(-1026784744653907139473/1008907331567616\) \(-1008907331567616\) \([9]\) \(65664\) \(1.7993\) \(\Gamma_0(N)\)-optimal
6942.l3 6942n2 \([1, 0, 0, 247743, 166305609]\) \(1681619673059345371247/12918257254341107136\) \(-12918257254341107136\) \([3]\) \(196992\) \(2.3486\)  

Rank

sage: E.rank()
 

The elliptic curves in class 6942.l have rank \(0\).

Complex multiplication

The elliptic curves in class 6942.l do not have complex multiplication.

Modular form 6942.2.a.l

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} - 3 q^{5} + q^{6} - q^{7} + q^{8} + q^{9} - 3 q^{10} + 3 q^{11} + q^{12} + q^{13} - q^{14} - 3 q^{15} + q^{16} + q^{18} - 7 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.