Properties

Label 3600.l
Number of curves $4$
Conductor $3600$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 3600.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3600.l1 3600bo2 \([0, 0, 0, -18075, -935350]\) \(-349938025/8\) \(-14929920000\) \([]\) \(4320\) \(1.0657\)  
3600.l2 3600bo3 \([0, 0, 0, -10875, 526250]\) \(-121945/32\) \(-37324800000000\) \([]\) \(7200\) \(1.3211\)  
3600.l3 3600bo1 \([0, 0, 0, -75, -2950]\) \(-25/2\) \(-3732480000\) \([]\) \(1440\) \(0.51635\) \(\Gamma_0(N)\)-optimal
3600.l4 3600bo4 \([0, 0, 0, 79125, -3883750]\) \(46969655/32768\) \(-38220595200000000\) \([]\) \(21600\) \(1.8704\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 3600.2.a.l

sage: E.q_eigenform(10)
 
\(q - 2 q^{7} - 3 q^{11} - 4 q^{13} + 3 q^{17} - 5 q^{19} + O(q^{20})\) 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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 15 & 3 & 5 \\ 15 & 1 & 5 & 3 \\ 3 & 5 & 1 & 15 \\ 5 & 3 & 15 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.