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Properties

Label 4800.q
Number of curves $6$
Conductor $4800$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("q1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 4800.q have rank \(1\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1 + T\)
\(5\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(7\) \( 1 + 7 T^{2}\) 1.7.a
\(11\) \( 1 + 4 T + 11 T^{2}\) 1.11.e
\(13\) \( 1 + 2 T + 13 T^{2}\) 1.13.c
\(17\) \( 1 + 2 T + 17 T^{2}\) 1.17.c
\(19\) \( 1 - 4 T + 19 T^{2}\) 1.19.ae
\(23\) \( 1 - 8 T + 23 T^{2}\) 1.23.ai
\(29\) \( 1 + 6 T + 29 T^{2}\) 1.29.g
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 4800.q do not have complex multiplication.

Modular form 4800.2.a.q

Copy content sage:E.q_eigenform(10)
 
\(q - q^{3} + q^{9} - 4 q^{11} - 2 q^{13} - 2 q^{17} + 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 8 & 4 \\ 8 & 1 & 4 & 2 & 4 & 8 \\ 2 & 4 & 1 & 2 & 4 & 2 \\ 4 & 2 & 2 & 1 & 2 & 4 \\ 8 & 4 & 4 & 2 & 1 & 8 \\ 4 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 4800.q

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4800.q1 4800c5 \([0, -1, 0, -38433, -2887263]\) \(3065617154/9\) \(18432000000\) \([2]\) \(8192\) \(1.1991\)  
4800.q2 4800c4 \([0, -1, 0, -6433, 200737]\) \(28756228/3\) \(3072000000\) \([2]\) \(4096\) \(0.85251\)  
4800.q3 4800c3 \([0, -1, 0, -2433, -43263]\) \(1556068/81\) \(82944000000\) \([2, 2]\) \(4096\) \(0.85251\)  
4800.q4 4800c2 \([0, -1, 0, -433, 2737]\) \(35152/9\) \(2304000000\) \([2, 2]\) \(2048\) \(0.50594\)  
4800.q5 4800c1 \([0, -1, 0, 67, 237]\) \(2048/3\) \(-48000000\) \([2]\) \(1024\) \(0.15937\) \(\Gamma_0(N)\)-optimal
4800.q6 4800c6 \([0, -1, 0, 1567, -175263]\) \(207646/6561\) \(-13436928000000\) \([2]\) \(8192\) \(1.1991\)