Properties

Label 4080.bb
Number of curves $4$
Conductor $4080$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("bb1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 4080.bb have rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1 - T\)
\(5\)\(1 - T\)
\(17\)\(1 - T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(7\) \( 1 + 7 T^{2}\) 1.7.a
\(11\) \( 1 + 11 T^{2}\) 1.11.a
\(13\) \( 1 + 2 T + 13 T^{2}\) 1.13.c
\(19\) \( 1 - 4 T + 19 T^{2}\) 1.19.ae
\(23\) \( 1 - 8 T + 23 T^{2}\) 1.23.ai
\(29\) \( 1 + 2 T + 29 T^{2}\) 1.29.c
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 4080.bb do not have complex multiplication.

Modular form 4080.2.a.bb

Copy content sage:E.q_eigenform(10)
 
\(q + q^{3} + q^{5} + q^{9} - 2 q^{13} + q^{15} + q^{17} + 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 4080.bb

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4080.bb1 4080o3 \([0, 1, 0, -4000, 27140]\) \(6913728144004/3658971285\) \(3746786595840\) \([4]\) \(6144\) \(1.1042\)  
4080.bb2 4080o2 \([0, 1, 0, -2300, -42900]\) \(5258429611216/47403225\) \(12135225600\) \([2, 2]\) \(3072\) \(0.75759\)  
4080.bb3 4080o1 \([0, 1, 0, -2295, -43092]\) \(83587439220736/6885\) \(110160\) \([2]\) \(1536\) \(0.41102\) \(\Gamma_0(N)\)-optimal
4080.bb4 4080o4 \([0, 1, 0, -680, -100572]\) \(-34008619684/4228250625\) \(-4329728640000\) \([4]\) \(6144\) \(1.1042\)