Properties

Label 229320.j
Number of curves $4$
Conductor $229320$
CM no
Rank $0$
Graph

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

Elliptic curves in class 229320.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
229320.j1 229320bg3 \([0, 0, 0, -2565003, 1580679142]\) \(10625310339698/3855735\) \(677256057966458880\) \([2]\) \(4718592\) \(2.3899\)  
229320.j2 229320bg4 \([0, 0, 0, -1330203, -578492138]\) \(1481943889298/34543665\) \(6067560759651256320\) \([2]\) \(4718592\) \(2.3899\)  
229320.j3 229320bg2 \([0, 0, 0, -183603, 17051902]\) \(7793764996/3080025\) \(270501679957017600\) \([2, 2]\) \(2359296\) \(2.0433\)  
229320.j4 229320bg1 \([0, 0, 0, 36897, 1925602]\) \(253012016/219375\) \(-4816625355360000\) \([2]\) \(1179648\) \(1.6968\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 229320.j have rank \(0\).

Complex multiplication

The elliptic curves in class 229320.j do not have complex multiplication.

Modular form 229320.2.a.j

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.