Properties

Label 3150.bk
Number of curves $2$
Conductor $3150$
CM no
Rank $1$
Graph

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

Elliptic curves in class 3150.bk

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3150.bk1 3150bq1 \([1, -1, 1, -725, -723]\) \(461889917/263424\) \(24004512000\) \([2]\) \(3072\) \(0.68159\) \(\Gamma_0(N)\)-optimal
3150.bk2 3150bq2 \([1, -1, 1, 2875, -7923]\) \(28849701763/16941456\) \(-1543790178000\) \([2]\) \(6144\) \(1.0282\)  

Rank

sage: E.rank()
 

The elliptic curves in class 3150.bk have rank \(1\).

Complex multiplication

The elliptic curves in class 3150.bk do not have complex multiplication.

Modular form 3150.2.a.bk

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{7} + q^{8} - 2q^{11} - 6q^{13} + q^{14} + q^{16} + 4q^{17} - 6q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.