Properties

Label 6762.m
Number of curves $2$
Conductor $6762$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("m1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 6762.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6762.m1 6762t2 \([1, 0, 1, -12262962, -16528997180]\) \(1733490909744055732873/99355964553216\) \(11689129873721309184\) \([2]\) \(405504\) \(2.7224\)  
6762.m2 6762t1 \([1, 0, 1, -722482, -289233724]\) \(-354499561600764553/101902222098432\) \(-11988694527658426368\) \([2]\) \(202752\) \(2.3759\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 6762.2.a.m

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - 2 q^{5} - q^{6} - q^{8} + q^{9} + 2 q^{10} - 4 q^{11} + q^{12} + 4 q^{13} - 2 q^{15} + q^{16} + 4 q^{17} - q^{18} + 2 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.