↑

Properties

Label 858.k
Number of curves $2$
Conductor $858$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 858.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
858.k1 858k1 \([1, 0, 0, -5774401, 5346023177]\) \(-21293376668673906679951249/26211168887701209984\) \(-26211168887701209984\) \([7]\) \(35280\) \(2.6358\) \(\Gamma_0(N)\)-optimal
858.k2 858k2 \([1, 0, 0, 16353089, -335543012233]\) \(483641001192506212470106511/48918776756543177755473774\) \(-48918776756543177755473774\) \([]\) \(246960\) \(3.6088\)  

Rank

sage: E.rank()
 

The elliptic curves in class 858.k have rank \(0\).

Complex multiplication

The elliptic curves in class 858.k do not have complex multiplication.

Modular form 858.2.a.k

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} + q^{7} + q^{8} + q^{9} - q^{10} + q^{11} + q^{12} - q^{13} + q^{14} - q^{15} + q^{16} + 4 q^{17} + q^{18} + 6 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.