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Properties

Label 96330.bu
Number of curves $4$
Conductor $96330$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("bu1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 96330.bu have rank \(1\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1 - T\)
\(3\)\(1 + T\)
\(5\)\(1 + T\)
\(13\)\(1\)
\(19\)\(1 - T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(7\) \( 1 + 4 T + 7 T^{2}\) 1.7.e
\(11\) \( 1 + 4 T + 11 T^{2}\) 1.11.e
\(17\) \( 1 + 2 T + 17 T^{2}\) 1.17.c
\(23\) \( 1 + 4 T + 23 T^{2}\) 1.23.e
\(29\) \( 1 - 2 T + 29 T^{2}\) 1.29.ac
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 96330.bu do not have complex multiplication.

Modular form 96330.2.a.bu

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

Isogeny matrix

Copy content 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

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 96330.bu

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
96330.bu1 96330ce4 \([1, 1, 1, -3892104226, 93433767506399]\) \(1350880657298392155478632361/408174133300781250000\) \(1970178580183410644531250000\) \([2]\) \(123863040\) \(4.2150\)  
96330.bu2 96330ce3 \([1, 1, 1, -1923240706, -31713126139297]\) \(162991338224782913955132841/4315964092179013950000\) \(20832334323806494144985550000\) \([2]\) \(123863040\) \(4.2150\)  
96330.bu3 96330ce2 \([1, 1, 1, -275490706, 1048098460703]\) \(479053981924423911132841/178891962502500000000\) \(863477334634729522500000000\) \([2, 2]\) \(61931520\) \(3.8684\)  
96330.bu4 96330ce1 \([1, 1, 1, 53532014, 116569335839]\) \(3514830176602998440279/3249744244531200000\) \(-15685894767201396940800000\) \([2]\) \(30965760\) \(3.5218\) \(\Gamma_0(N)\)-optimal