Properties

Label 6768.h
Number of curves $2$
Conductor $6768$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("h1")
 
E.isogeny_class()
 

Elliptic curves in class 6768.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6768.h1 6768r2 \([0, 0, 0, -20595, -1137422]\) \(323535264625/59643\) \(178093043712\) \([2]\) \(12288\) \(1.1614\)  
6768.h2 6768r1 \([0, 0, 0, -1155, -21566]\) \(-57066625/34263\) \(-102308769792\) \([2]\) \(6144\) \(0.81485\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 6768.h have rank \(0\).

Complex multiplication

The elliptic curves in class 6768.h do not have complex multiplication.

Modular form 6768.2.a.h

sage: E.q_eigenform(10)
 
\(q - 4 q^{7} + 6 q^{13} + 6 q^{17} - 2 q^{19} + O(q^{20})\) 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.