Properties

Label 7098.k
Number of curves $4$
Conductor $7098$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands for: SageMath
sage: E = EllipticCurve("k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 7098.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7098.k1 7098o3 \([1, 0, 1, -2284377, 1328255164]\) \(124318741396429/51631104\) \(547522009995297792\) \([2]\) \(156000\) \(2.3655\)  
7098.k2 7098o4 \([1, 0, 1, -1932857, 1751063420]\) \(-75306487574989/81352871712\) \(-862706477061653436576\) \([2]\) \(312000\) \(2.7121\)  
7098.k3 7098o1 \([1, 0, 1, -76392, -8122814]\) \(4649101309/6804\) \(72153013733892\) \([2]\) \(31200\) \(1.5608\) \(\Gamma_0(N)\)-optimal
7098.k4 7098o2 \([1, 0, 1, -54422, -12885910]\) \(-1680914269/5786802\) \(-61366138180675146\) \([2]\) \(62400\) \(1.9074\)  

Rank

sage: E.rank()
 

The elliptic curves in class 7098.k have rank \(0\).

Complex multiplication

The elliptic curves in class 7098.k do not have complex multiplication.

Modular form 7098.2.a.k

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - 2q^{5} - q^{6} + q^{7} - q^{8} + q^{9} + 2q^{10} + q^{12} - q^{14} - 2q^{15} + q^{16} + 2q^{17} - q^{18} - 4q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.