Properties

Label 2184.j
Number of curves $6$
Conductor $2184$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 2184.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2184.j1 2184m5 \([0, 1, 0, -151424, -22730400]\) \(187491149065688834/3549\) \(7268352\) \([2]\) \(4096\) \(1.3043\)  
2184.j2 2184m3 \([0, 1, 0, -9464, -357504]\) \(91557481657828/12595401\) \(12897690624\) \([2, 2]\) \(2048\) \(0.95770\)  
2184.j3 2184m6 \([0, 1, 0, -8624, -422688]\) \(-34639400027234/17130345141\) \(-35082946848768\) \([2]\) \(4096\) \(1.3043\)  
2184.j4 2184m2 \([0, 1, 0, -644, -4704]\) \(115562131792/32867289\) \(8414025984\) \([2, 4]\) \(1024\) \(0.61113\)  
2184.j5 2184m1 \([0, 1, 0, -239, 1290]\) \(94757435392/4179357\) \(66869712\) \([4]\) \(512\) \(0.26455\) \(\Gamma_0(N)\)-optimal
2184.j6 2184m4 \([0, 1, 0, 1696, -29040]\) \(526556774012/674481717\) \(-690669278208\) \([4]\) \(2048\) \(0.95770\)  

Rank

sage: E.rank()
 

The elliptic curves in class 2184.j have rank \(1\).

Complex multiplication

The elliptic curves in class 2184.j do not have complex multiplication.

Modular form 2184.2.a.j

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2 q^{5} + q^{7} + q^{9} - 4 q^{11} + q^{13} - 2 q^{15} + 2 q^{17} - 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.