Properties

Label 3600.bc
Number of curves $4$
Conductor $3600$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bc1")
 
E.isogeny_class()
 

Elliptic curves in class 3600.bc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3600.bc1 3600bi4 \([0, 0, 0, -451875, -116918750]\) \(-349938025/8\) \(-233280000000000\) \([]\) \(21600\) \(1.8704\)  
3600.bc2 3600bi3 \([0, 0, 0, -1875, -368750]\) \(-25/2\) \(-58320000000000\) \([]\) \(7200\) \(1.3211\)  
3600.bc3 3600bi1 \([0, 0, 0, -435, 4210]\) \(-121945/32\) \(-2388787200\) \([]\) \(1440\) \(0.51635\) \(\Gamma_0(N)\)-optimal
3600.bc4 3600bi2 \([0, 0, 0, 3165, -31070]\) \(46969655/32768\) \(-2446118092800\) \([]\) \(4320\) \(1.0657\)  

Rank

sage: E.rank()
 

The elliptic curves in class 3600.bc have rank \(1\).

Complex multiplication

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

Modular form 3600.2.a.bc

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.