↑

Properties

Label 7098h
Number of curves $2$
Conductor $7098$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("h1")
 
E.isogeny_class()
 

Elliptic curves in class 7098h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7098.l2 7098h1 \([1, 0, 1, -14876, -73006]\) \(2640625/1512\) \(208442039675688\) \([]\) \(26208\) \(1.4373\) \(\Gamma_0(N)\)-optimal
7098.l1 7098h2 \([1, 0, 1, -871706, -313330054]\) \(531373116625/2058\) \(283712776225242\) \([]\) \(78624\) \(1.9866\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 7098.2.a.h

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{6} - q^{7} - q^{8} + q^{9} - 3 q^{11} + q^{12} + q^{14} + q^{16} + 3 q^{17} - q^{18} - 5 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.