Properties

Label 352800bg
Number of curves $4$
Conductor $352800$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bg1")
 
E.isogeny_class()
 

Elliptic curves in class 352800bg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
352800.bg3 352800bg1 \([0, 0, 0, -218805825, -1245483421000]\) \(13507798771700416/3544416225\) \(303990830827713225000000\) \([2, 2]\) \(70778880\) \(3.4907\) \(\Gamma_0(N)\)-optimal
352800.bg2 352800bg2 \([0, 0, 0, -245817075, -918566262250]\) \(2394165105226952/854262178245\) \(586134026760673901160000000\) \([2]\) \(141557760\) \(3.8372\)  
352800.bg4 352800bg3 \([0, 0, 0, -192015075, -1561855387750]\) \(-1141100604753992/875529151875\) \(-600725913429909015000000000\) \([2]\) \(141557760\) \(3.8372\)  
352800.bg1 352800bg4 \([0, 0, 0, -3500672700, -79721484136000]\) \(864335783029582144/59535\) \(326789504879040000000\) \([2]\) \(141557760\) \(3.8372\)  

Rank

sage: E.rank()
 

The elliptic curves in class 352800bg have rank \(1\).

Complex multiplication

The elliptic curves in class 352800bg do not have complex multiplication.

Modular form 352800.2.a.bg

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