Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("ev1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 52800ev

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
52800.dh4 52800ev1 \([0, -1, 0, 21867, 4565637]\) \(72268906496/606436875\) \(-9702990000000000\) \([2]\) \(221184\) \(1.7490\) \(\Gamma_0(N)\)-optimal
52800.dh3 52800ev2 \([0, -1, 0, -315633, 62953137]\) \(13584145739344/1195803675\) \(306125740800000000\) \([2]\) \(442368\) \(2.0955\)  
52800.dh2 52800ev3 \([0, -1, 0, -1562133, 752609637]\) \(-26348629355659264/24169921875\) \(-386718750000000000\) \([2]\) \(663552\) \(2.2983\)  
52800.dh1 52800ev4 \([0, -1, 0, -24999633, 48119797137]\) \(6749703004355978704/5671875\) \(1452000000000000\) \([2]\) \(1327104\) \(2.6448\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 52800.2.a.ev

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.