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Properties

Label 12870.bk
Number of curves $2$
Conductor $12870$
CM no
Rank $0$
Graph

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

Elliptic curves in class 12870.bk

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
12870.bk1 12870bn2 \([1, -1, 1, -105008, -13069573]\) \(175654575624148921/21954418200\) \(16004770867800\) \([2]\) \(61440\) \(1.5563\)  
12870.bk2 12870bn1 \([1, -1, 1, -6008, -239173]\) \(-32894113444921/15289560000\) \(-11146089240000\) \([2]\) \(30720\) \(1.2097\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 12870.bk have rank \(0\).

Complex multiplication

The elliptic curves in class 12870.bk do not have complex multiplication.

Modular form 12870.2.a.bk

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - q^{5} + q^{8} - q^{10} - q^{11} + q^{13} + q^{16} + 4 q^{17} - 2 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.