Properties

Label 369600.gh
Number of curves $6$
Conductor $369600$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("gh1")
 
E.isogeny_class()
 

Elliptic curves in class 369600.gh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
369600.gh1 369600gh6 \([0, -1, 0, -7230433, -7480911263]\) \(10206027697760497/5557167\) \(22762156032000000\) \([2]\) \(10485760\) \(2.4672\)  
369600.gh2 369600gh4 \([0, -1, 0, -454433, -115399263]\) \(2533811507137/58110129\) \(238019088384000000\) \([2, 2]\) \(5242880\) \(2.1207\)  
369600.gh3 369600gh2 \([0, -1, 0, -62433, 3376737]\) \(6570725617/2614689\) \(10709766144000000\) \([2, 2]\) \(2621440\) \(1.7741\)  
369600.gh4 369600gh1 \([0, -1, 0, -54433, 4904737]\) \(4354703137/1617\) \(6623232000000\) \([2]\) \(1310720\) \(1.4275\) \(\Gamma_0(N)\)-optimal
369600.gh5 369600gh5 \([0, -1, 0, 49567, -357823263]\) \(3288008303/13504609503\) \(-55314880524288000000\) \([2]\) \(10485760\) \(2.4672\)  
369600.gh6 369600gh3 \([0, -1, 0, 201567, 24232737]\) \(221115865823/190238433\) \(-779216621568000000\) \([2]\) \(5242880\) \(2.1207\)  

Rank

sage: E.rank()
 

The elliptic curves in class 369600.gh have rank \(0\).

Complex multiplication

The elliptic curves in class 369600.gh do not have complex multiplication.

Modular form 369600.2.a.gh

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{7} + q^{9} + q^{11} + 6 q^{13} - 2 q^{17} - 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 8 & 4 & 2 & 1 & 8 & 4 \\ 4 & 2 & 4 & 8 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.