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Properties

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

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Show commands: SageMath
E = EllipticCurve("s1")
 
E.isogeny_class()
 

Elliptic curves in class 6762.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6762.s1 6762r1 \([1, 0, 1, -15965, -777724]\) \(1311889499494111/438012\) \(150238116\) \([2]\) \(7680\) \(0.92697\) \(\Gamma_0(N)\)-optimal
6762.s2 6762r2 \([1, 0, 1, -15895, -784864]\) \(-1294708239486271/23981814018\) \(-8225762208174\) \([2]\) \(15360\) \(1.2735\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 6762.2.a.s

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.