Properties

Label 6930.bm
Number of curves $4$
Conductor $6930$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("bm1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 6930.bm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6930.bm1 6930bk4 \([1, -1, 1, -140837, -15663139]\) \(423783056881319689/99207416000000\) \(72322206264000000\) \([6]\) \(82944\) \(1.9468\)  
6930.bm2 6930bk2 \([1, -1, 1, -131702, -18363571]\) \(346553430870203929/8300600\) \(6051137400\) \([2]\) \(27648\) \(1.3975\)  
6930.bm3 6930bk1 \([1, -1, 1, -8222, -286099]\) \(-84309998289049/414124480\) \(-301896745920\) \([2]\) \(13824\) \(1.0509\) \(\Gamma_0(N)\)-optimal
6930.bm4 6930bk3 \([1, -1, 1, 20443, -1535011]\) \(1296134247276791/2137096192000\) \(-1557943123968000\) \([6]\) \(41472\) \(1.6003\)  

Rank

sage: E.rank()
 

The elliptic curves in class 6930.bm have rank \(0\).

Complex multiplication

The elliptic curves in class 6930.bm do not have complex multiplication.

Modular form 6930.2.a.bm

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

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.