Properties

Label 15600.bk
Number of curves $4$
Conductor $15600$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("bk1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 15600.bk

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
15600.bk1 15600bd3 \([0, -1, 0, -8295808, -9194021888]\) \(986551739719628473/111045168\) \(7106890752000000\) \([2]\) \(491520\) \(2.4659\)  
15600.bk2 15600bd4 \([0, -1, 0, -935808, 118490112]\) \(1416134368422073/725251155408\) \(46416073946112000000\) \([2]\) \(491520\) \(2.4659\)  
15600.bk3 15600bd2 \([0, -1, 0, -519808, -142757888]\) \(242702053576633/2554695936\) \(163500539904000000\) \([2, 2]\) \(245760\) \(2.1194\)  
15600.bk4 15600bd1 \([0, -1, 0, -7808, -5541888]\) \(-822656953/207028224\) \(-13249806336000000\) \([2]\) \(122880\) \(1.7728\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 15600.bk have rank \(0\).

Complex multiplication

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

Modular form 15600.2.a.bk

sage: E.q_eigenform(10)
 
\(q - q^{3} + 4q^{7} + q^{9} + 4q^{11} - q^{13} - 2q^{17} + 8q^{19} + O(q^{20})\)  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 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.