Properties

Label 31200cj
Number of curves $2$
Conductor $31200$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands for: SageMath
sage: E = EllipticCurve("cj1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 31200cj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
31200.bg2 31200cj1 \([0, 1, 0, -4958, -135912]\) \(107850176/117\) \(14625000000\) \([2]\) \(35840\) \(0.86609\) \(\Gamma_0(N)\)-optimal
31200.bg1 31200cj2 \([0, 1, 0, -6208, -63412]\) \(26463592/13689\) \(13689000000000\) \([2]\) \(71680\) \(1.2127\)  

Rank

sage: E.rank()
 

The elliptic curves in class 31200cj have rank \(1\).

Complex multiplication

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

Modular form 31200.2.a.cj

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