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Properties

Label 32370.bk
Number of curves $2$
Conductor $32370$
CM no
Rank $1$
Graph

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

Elliptic curves in class 32370.bk

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
32370.bk1 32370bk2 \([1, 0, 0, -1546933295, -23418435858105]\) \(409391171678522880998024667047281/10583059885954530\) \(10583059885954530\) \([]\) \(6991712\) \(3.5174\)  
32370.bk2 32370bk1 \([1, 0, 0, -1330145, 291422025]\) \(260267950003303480801681/113901735543570000000\) \(113901735543570000000\) \([7]\) \(998816\) \(2.5444\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 32370.bk have rank \(1\).

Complex multiplication

The elliptic curves in class 32370.bk do not have complex multiplication.

Modular form 32370.2.a.bk

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} + q^{7} + q^{8} + q^{9} + q^{10} - 2 q^{11} + q^{12} + q^{13} + q^{14} + q^{15} + q^{16} - 3 q^{17} + q^{18} - 8 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.