Properties

Label 52800.ex
Number of curves $4$
Conductor $52800$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("ex1")
 
E.isogeny_class()
 

Elliptic curves in class 52800.ex

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
52800.ex1 52800db3 \([0, 1, 0, -128833, -17773537]\) \(57736239625/255552\) \(1046740992000000\) \([2]\) \(331776\) \(1.7344\)  
52800.ex2 52800db4 \([0, 1, 0, -64833, -35373537]\) \(-7357983625/127552392\) \(-522454597632000000\) \([2]\) \(663552\) \(2.0809\)  
52800.ex3 52800db1 \([0, 1, 0, -8833, 298463]\) \(18609625/1188\) \(4866048000000\) \([2]\) \(110592\) \(1.1851\) \(\Gamma_0(N)\)-optimal
52800.ex4 52800db2 \([0, 1, 0, 7167, 1274463]\) \(9938375/176418\) \(-722608128000000\) \([2]\) \(221184\) \(1.5316\)  

Rank

sage: E.rank()
 

The elliptic curves in class 52800.ex have rank \(1\).

Complex multiplication

The elliptic curves in class 52800.ex do not have complex multiplication.

Modular form 52800.2.a.ex

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2 q^{7} + q^{9} + q^{11} - 4 q^{13} + 6 q^{17} + 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.