Properties

Label 15600.bf
Number of curves $4$
Conductor $15600$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("bf1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 15600.bf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
15600.bf1 15600f3 \([0, -1, 0, -208008, -36445488]\) \(31103978031362/195\) \(6240000000\) \([2]\) \(73728\) \(1.4851\)  
15600.bf2 15600f4 \([0, -1, 0, -18008, -85488]\) \(20183398562/11567205\) \(370150560000000\) \([2]\) \(73728\) \(1.4851\)  
15600.bf3 15600f2 \([0, -1, 0, -13008, -565488]\) \(15214885924/38025\) \(608400000000\) \([2, 2]\) \(36864\) \(1.1385\)  
15600.bf4 15600f1 \([0, -1, 0, -508, -15488]\) \(-3631696/24375\) \(-97500000000\) \([2]\) \(18432\) \(0.79195\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 15600.bf have rank \(1\).

Complex multiplication

The elliptic curves in class 15600.bf do not have complex multiplication.

Modular form 15600.2.a.bf

sage: E.q_eigenform(10)
 
\(q - q^{3} + 4q^{7} + q^{9} - 4q^{11} - q^{13} - 6q^{17} + O(q^{20})\)  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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.