Properties

Label 182070.j
Number of curves $4$
Conductor $182070$
CM no
Rank $0$
Graph

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

Elliptic curves in class 182070.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
182070.j1 182070dh3 \([1, -1, 0, -289363905, 1891622040525]\) \(152277495831664137649/282362258900400\) \(4968527571751912194020400\) \([2]\) \(56623104\) \(3.6296\)  
182070.j2 182070dh4 \([1, -1, 0, -238176225, -1406989214739]\) \(84917632843343402929/537144431250000\) \(9451748002979458181250000\) \([2]\) \(56623104\) \(3.6296\)  
182070.j3 182070dh2 \([1, -1, 0, -24061905, 8349263325]\) \(87557366190249649/48960807840000\) \(861528465722097159840000\) \([2, 2]\) \(28311552\) \(3.2830\)  
182070.j4 182070dh1 \([1, -1, 0, 5901615, 1032171741]\) \(1291859362462031/773834342400\) \(-13616611799167977062400\) \([2]\) \(14155776\) \(2.9364\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 182070.j have rank \(0\).

Complex multiplication

The elliptic curves in class 182070.j do not have complex multiplication.

Modular form 182070.2.a.j

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} - q^{7} - q^{8} + q^{10} - 2 q^{13} + q^{14} + q^{16} - 8 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.