Properties

Label 352800nz
Number of curves $4$
Conductor $352800$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("nz1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 352800nz

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
352800.nz3 352800nz1 \([0, 0, 0, -775425, -258622000]\) \(601211584/11025\) \(945571484025000000\) \([2, 2]\) \(7077888\) \(2.2440\) \(\Gamma_0(N)\)-optimal
352800.nz2 352800nz2 \([0, 0, 0, -1602300, 389648000]\) \(82881856/36015\) \(197687478260160000000\) \([2]\) \(14155776\) \(2.5906\)  
352800.nz4 352800nz3 \([0, 0, 0, -3675, -750226750]\) \(-8/354375\) \(-243146953035000000000\) \([2]\) \(14155776\) \(2.5906\)  
352800.nz1 352800nz4 \([0, 0, 0, -12351675, -16708473250]\) \(303735479048/105\) \(72043541640000000\) \([2]\) \(14155776\) \(2.5906\)  

Rank

sage: E.rank()
 

The elliptic curves in class 352800nz have rank \(0\).

Complex multiplication

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

Modular form 352800.2.a.nz

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.