Properties

Label 104742.t
Number of curves $4$
Conductor $104742$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("t1")
 
E.isogeny_class()
 

Elliptic curves in class 104742.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
104742.t1 104742y4 \([1, -1, 0, -237270800556, 44485157855631312]\) \(13688695234222145601259673233/2003024259937536\) \(216162698739138344921308416\) \([2]\) \(389283840\) \(4.9039\)  
104742.t2 104742y3 \([1, -1, 0, -17042937516, 473972729682384]\) \(5072972674420068408718993/2036482219218784389888\) \(219773420245209566206510271324928\) \([2]\) \(389283840\) \(4.9039\)  
104742.t3 104742y2 \([1, -1, 0, -14830786476, 694949363800272]\) \(3342887139776073669969553/1278380674753560576\) \(137960494137653569726180294656\) \([2, 2]\) \(194641920\) \(4.5573\)  
104742.t4 104742y1 \([1, -1, 0, -790026156, 14177483380944]\) \(-505304979693115442833/512169554353324032\) \(-55272397491825116379812462592\) \([2]\) \(97320960\) \(4.2107\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 104742.t have rank \(0\).

Complex multiplication

The elliptic curves in class 104742.t do not have complex multiplication.

Modular form 104742.2.a.t

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + 2 q^{5} - 4 q^{7} - q^{8} - 2 q^{10} + q^{11} - 2 q^{13} + 4 q^{14} + q^{16} - 2 q^{17} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.