Properties

Label 11368g
Number of curves $2$
Conductor $11368$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 11368g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
11368.c2 11368g1 \([0, 1, 0, -104288, -15386960]\) \(-1041220466500/242597383\) \(-29226331660868608\) \([2]\) \(73728\) \(1.8789\) \(\Gamma_0(N)\)-optimal
11368.c1 11368g2 \([0, 1, 0, -1752648, -893633168]\) \(2471097448795250/98942809\) \(23839790153811968\) \([2]\) \(147456\) \(2.2254\)  

Rank

sage: E.rank()
 

The elliptic curves in class 11368g have rank \(0\).

Complex multiplication

The elliptic curves in class 11368g do not have complex multiplication.

Modular form 11368.2.a.g

sage: E.q_eigenform(10)
 
\(q - 2 q^{3} + q^{9} - 4 q^{13} - 2 q^{17} - 6 q^{19} + O(q^{20})\) 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 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.