Properties

Label 236992.q
Number of curves $6$
Conductor $236992$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("q1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 236992.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
236992.q1 236992q6 \([0, 1, 0, -92444513, -342144006113]\) \(2251439055699625/25088\) \(973582993517969408\) \([2]\) \(14598144\) \(3.0206\)  
236992.q2 236992q5 \([0, 1, 0, -5773153, -5356435425]\) \(-548347731625/1835008\) \(-71210641811600048128\) \([2]\) \(7299072\) \(2.6740\)  
236992.q3 236992q4 \([0, 1, 0, -1202593, -416472609]\) \(4956477625/941192\) \(36524574491197571072\) \([2]\) \(4866048\) \(2.4713\)  
236992.q4 236992q2 \([0, 1, 0, -356193, 81650719]\) \(128787625/98\) \(3803058568429568\) \([2]\) \(1622016\) \(1.9220\)  
236992.q5 236992q1 \([0, 1, 0, -17633, 1818271]\) \(-15625/28\) \(-1086588162408448\) \([2]\) \(811008\) \(1.5754\) \(\Gamma_0(N)\)-optimal
236992.q6 236992q3 \([0, 1, 0, 151647, -38097953]\) \(9938375/21952\) \(-851885119328223232\) \([2]\) \(2433024\) \(2.1247\)  

Rank

sage: E.rank()
 

The elliptic curves in class 236992.q have rank \(0\).

Complex multiplication

The elliptic curves in class 236992.q do not have complex multiplication.

Modular form 236992.2.a.q

sage: E.q_eigenform(10)
 
\(q - 2 q^{3} + q^{7} + q^{9} + 4 q^{13} - 6 q^{17} - 2 q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 9 & 18 & 6 \\ 2 & 1 & 6 & 18 & 9 & 3 \\ 3 & 6 & 1 & 3 & 6 & 2 \\ 9 & 18 & 3 & 1 & 2 & 6 \\ 18 & 9 & 6 & 2 & 1 & 3 \\ 6 & 3 & 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.