Properties

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

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Show commands: SageMath
E = EllipticCurve("z1")
 
E.isogeny_class()
 

Elliptic curves in class 6762.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6762.z1 6762ba2 \([1, 1, 1, -336533, -75283405]\) \(104453838382375/14904\) \(601430158728\) \([2]\) \(32256\) \(1.6699\)  
6762.z2 6762ba1 \([1, 1, 1, -20973, -1189917]\) \(-25282750375/304704\) \(-12295905467328\) \([2]\) \(16128\) \(1.3234\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 6762.2.a.z

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