Properties

Label 2100k
Number of curves $2$
Conductor $2100$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 2100k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2100.k1 2100k1 \([0, 1, 0, -14133, 641988]\) \(1248870793216/42525\) \(10631250000\) \([2]\) \(2880\) \(1.0156\) \(\Gamma_0(N)\)-optimal
2100.k2 2100k2 \([0, 1, 0, -13508, 701988]\) \(-68150496976/14467005\) \(-57868020000000\) \([2]\) \(5760\) \(1.3622\)  

Rank

sage: E.rank()
 

The elliptic curves in class 2100k have rank \(1\).

Complex multiplication

The elliptic curves in class 2100k do not have complex multiplication.

Modular form 2100.2.a.k

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{7} + q^{9} - 2 q^{11} - 4 q^{13} - 2 q^{17} + 2 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.