Properties

Label 3600k
Number of curves $6$
Conductor $3600$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3600k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3600.v5 3600k1 \([0, 0, 0, 150, 875]\) \(2048/3\) \(-546750000\) \([2]\) \(1024\) \(0.36210\) \(\Gamma_0(N)\)-optimal
3600.v4 3600k2 \([0, 0, 0, -975, 8750]\) \(35152/9\) \(26244000000\) \([2, 2]\) \(2048\) \(0.70867\)  
3600.v3 3600k3 \([0, 0, 0, -5475, -148750]\) \(1556068/81\) \(944784000000\) \([2, 2]\) \(4096\) \(1.0552\)  
3600.v2 3600k4 \([0, 0, 0, -14475, 670250]\) \(28756228/3\) \(34992000000\) \([2]\) \(4096\) \(1.0552\)  
3600.v1 3600k5 \([0, 0, 0, -86475, -9787750]\) \(3065617154/9\) \(209952000000\) \([2]\) \(8192\) \(1.4018\)  
3600.v6 3600k6 \([0, 0, 0, 3525, -589750]\) \(207646/6561\) \(-153055008000000\) \([2]\) \(8192\) \(1.4018\)  

Rank

sage: E.rank()
 

The elliptic curves in class 3600k have rank \(0\).

Complex multiplication

The elliptic curves in class 3600k do not have complex multiplication.

Modular form 3600.2.a.k

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

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.