Properties

Label 349830j
Number of curves $4$
Conductor $349830$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 349830j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
349830.j3 349830j1 \([1, -1, 0, -1018730595, 12524687954325]\) \(-897176485088045307663363/767948742459392000\) \(-100082031344325236883456000\) \([2]\) \(174182400\) \(3.9159\) \(\Gamma_0(N)\)-optimal
349830.j2 349830j2 \([1, -1, 0, -16303036515, 801222385176981]\) \(3677099129012869569042846723/2690674688000000\) \(350659065602985984000000\) \([2]\) \(348364800\) \(4.2624\)  
349830.j4 349830j3 \([1, -1, 0, 1109858205, 54915589284245]\) \(1591383301847324275653/14633798888411156480\) \(-1390299890534788285803457474560\) \([2]\) \(522547200\) \(4.4652\)  
349830.j1 349830j4 \([1, -1, 0, -16655908515, 764725479661781]\) \(5378699555702101965641787/453548482696362123200\) \(43089864132568698316981260590400\) \([2]\) \(1045094400\) \(4.8117\)  

Rank

sage: E.rank()
 

The elliptic curves in class 349830j have rank \(1\).

Complex multiplication

The elliptic curves in class 349830j do not have complex multiplication.

Modular form 349830.2.a.j

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} - 2 q^{7} - q^{8} + q^{10} + 2 q^{14} + q^{16} + 6 q^{17} + 4 q^{19} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.