Properties

Label 6762.bc
Number of curves $4$
Conductor $6762$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("bc1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 6762.bc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6762.bc1 6762bb4 \([1, 1, 1, -8763602, 9981900641]\) \(632678989847546725777/80515134\) \(9472524999966\) \([2]\) \(184320\) \(2.3499\)  
6762.bc2 6762bb3 \([1, 1, 1, -626662, 107865953]\) \(231331938231569617/90942310746882\) \(10699271917059920418\) \([2]\) \(184320\) \(2.3499\)  
6762.bc3 6762bb2 \([1, 1, 1, -547772, 155767961]\) \(154502321244119857/55101928644\) \(6482686803037956\) \([2, 2]\) \(92160\) \(2.0034\)  
6762.bc4 6762bb1 \([1, 1, 1, -29352, 3145113]\) \(-23771111713777/22848457968\) \(-2688098231477232\) \([4]\) \(46080\) \(1.6568\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 6762.bc have rank \(0\).

Complex multiplication

The elliptic curves in class 6762.bc do not have complex multiplication.

Modular form 6762.2.a.bc

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} + 2 q^{5} - q^{6} + q^{8} + q^{9} + 2 q^{10} + 4 q^{11} - q^{12} - 2 q^{13} - 2 q^{15} + q^{16} - 6 q^{17} + q^{18} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.