Properties

Label 31200.ci
Number of curves $2$
Conductor $31200$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("ci1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 31200.ci

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
31200.ci1 31200cd1 \([0, 1, 0, -358, -2212]\) \(5088448/1053\) \(1053000000\) \([2]\) \(16384\) \(0.44642\) \(\Gamma_0(N)\)-optimal
31200.ci2 31200cd2 \([0, 1, 0, 767, -12337]\) \(778688/1521\) \(-97344000000\) \([2]\) \(32768\) \(0.79299\)  

Rank

sage: E.rank()
 

The elliptic curves in class 31200.ci have rank \(0\).

Complex multiplication

The elliptic curves in class 31200.ci do not have complex multiplication.

Modular form 31200.2.a.ci

sage: E.q_eigenform(10)
 
\(q + q^{3} + 2 q^{7} + q^{9} + 6 q^{11} + q^{13} + 2 q^{17} + 6 q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.