Properties

Label 243360.cl
Number of curves $4$
Conductor $243360$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("cl1")
 
E.isogeny_class()
 

Elliptic curves in class 243360.cl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
243360.cl1 243360cl4 \([0, 0, 0, -1910883, -1016565082]\) \(428320044872/73125\) \(131741766411840000\) \([2]\) \(4128768\) \(2.2915\)  
243360.cl2 243360cl2 \([0, 0, 0, -815763, 273979082]\) \(33324076232/1285245\) \(2315493286454499840\) \([2]\) \(4128768\) \(2.2915\)  
243360.cl3 243360cl1 \([0, 0, 0, -131313, -12531688]\) \(1111934656/342225\) \(77068933350926400\) \([2, 2]\) \(2064384\) \(1.9450\) \(\Gamma_0(N)\)-optimal
243360.cl4 243360cl3 \([0, 0, 0, 363012, -84505408]\) \(367061696/426465\) \(-6146543853710807040\) \([2]\) \(4128768\) \(2.2915\)  

Rank

sage: E.rank()
 

The elliptic curves in class 243360.cl have rank \(0\).

Complex multiplication

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

Modular form 243360.2.a.cl

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.