Properties

Label 76440.ce
Number of curves $4$
Conductor $76440$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("ce1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 76440.ce

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
76440.ce1 76440cq4 \([0, 1, 0, -407696, -100332576]\) \(31103978031362/195\) \(46984304640\) \([2]\) \(442368\) \(1.6533\)  
76440.ce2 76440cq3 \([0, 1, 0, -35296, -262816]\) \(20183398562/11567205\) \(2787061966940160\) \([2]\) \(442368\) \(1.6533\)  
76440.ce3 76440cq2 \([0, 1, 0, -25496, -1572096]\) \(15214885924/38025\) \(4580969702400\) \([2, 2]\) \(221184\) \(1.3068\)  
76440.ce4 76440cq1 \([0, 1, 0, -996, -43296]\) \(-3631696/24375\) \(-734129760000\) \([2]\) \(110592\) \(0.96019\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 76440.ce have rank \(0\).

Complex multiplication

The elliptic curves in class 76440.ce do not have complex multiplication.

Modular form 76440.2.a.ce

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

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.