Properties

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

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("o1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 6762.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6762.o1 6762k1 \([1, 0, 1, -4681, 456236]\) \(-1967079625/14486688\) \(-83512873469088\) \([3]\) \(15120\) \(1.3544\) \(\Gamma_0(N)\)-optimal
6762.o2 6762k2 \([1, 0, 1, 41624, -11527498]\) \(1383521234375/10764582912\) \(-62055678335680512\) \([]\) \(45360\) \(1.9037\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 6762.2.a.o

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.