Properties

Label 243360c
Number of curves $4$
Conductor $243360$
CM no
Rank $2$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 243360c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
243360.c3 243360c1 \([0, 0, 0, -344253, 76200748]\) \(20034997696/455625\) \(102606568070760000\) \([2, 2]\) \(2949120\) \(2.0508\) \(\Gamma_0(N)\)-optimal
243360.c1 243360c2 \([0, 0, 0, -5477628, 4934426848]\) \(1261112198464/675\) \(9728622750412800\) \([2]\) \(5898240\) \(2.3974\)  
243360.c4 243360c3 \([0, 0, 0, 35997, 235373398]\) \(2863288/13286025\) \(-23936060199546892800\) \([2]\) \(5898240\) \(2.3974\)  
243360.c2 243360c4 \([0, 0, 0, -754923, -140550878]\) \(26410345352/10546875\) \(19001216309400000000\) \([2]\) \(5898240\) \(2.3974\)  

Rank

sage: E.rank()
 

The elliptic curves in class 243360c have rank \(2\).

Complex multiplication

The elliptic curves in class 243360c do not have complex multiplication.

Modular form 243360.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{5} - 4 q^{7} - 4 q^{11} - 2 q^{17} + 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.