Properties

Label 493680br
Number of curves $4$
Conductor $493680$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("br1")
 
E.isogeny_class()
 

Elliptic curves in class 493680br

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
493680.br4 493680br1 \([0, -1, 0, -36258416, 84047206080]\) \(726497538898787209/1038579300\) \(7536257365144780800\) \([2]\) \(33177600\) \(2.8935\) \(\Gamma_0(N)\)-optimal
493680.br3 493680br2 \([0, -1, 0, -36587536, 82443996736]\) \(746461053445307689/27443694341250\) \(199140059508241167360000\) \([2]\) \(66355200\) \(3.2401\)  
493680.br2 493680br3 \([0, -1, 0, -46161056, 34550105856]\) \(1499114720492202169/796539777000000\) \(5779942620700250112000000\) \([2]\) \(99532800\) \(3.4428\)  
493680.br1 493680br4 \([0, -1, 0, -426623776, -3365569130240]\) \(1183430669265454849849/10449720703125000\) \(75826453129416000000000000\) \([2]\) \(199065600\) \(3.7894\)  

Rank

sage: E.rank()
 

The elliptic curves in class 493680br have rank \(0\).

Complex multiplication

The elliptic curves in class 493680br do not have complex multiplication.

Modular form 493680.2.a.br

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} + 2 q^{7} + q^{9} + 4 q^{13} + q^{15} + q^{17} + 2 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.