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Properties

Label 248430.fd
Number of curves $6$
Conductor $248430$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("fd1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 248430.fd have rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1 + T\)
\(3\)\(1 - T\)
\(5\)\(1 - T\)
\(7\)\(1\)
\(13\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(11\) \( 1 - 4 T + 11 T^{2}\) 1.11.ae
\(17\) \( 1 - 6 T + 17 T^{2}\) 1.17.ag
\(19\) \( 1 + 4 T + 19 T^{2}\) 1.19.e
\(23\) \( 1 + 8 T + 23 T^{2}\) 1.23.i
\(29\) \( 1 + 10 T + 29 T^{2}\) 1.29.k
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 248430.fd do not have complex multiplication.

Modular form 248430.2.a.fd

Copy content sage:E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} + q^{5} - q^{6} - q^{8} + q^{9} - q^{10} + 4 q^{11} + q^{12} + q^{15} + q^{16} + 6 q^{17} - q^{18} - 4 q^{19} + O(q^{20})\) 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 248430.fd

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
248430.fd1 248430fd5 \([1, 0, 1, -3829217383, 91109816403218]\) \(10934663514379917006241/12996826171875000\) \(7380497957129549560546875000\) \([2]\) \(396361728\) \(4.2587\)  
248430.fd2 248430fd4 \([1, 0, 1, -2756331023, -55698940113022]\) \(4078208988807294650401/359723582400\) \(204275961678997031678400\) \([2]\) \(198180864\) \(3.9121\)  
248430.fd3 248430fd3 \([1, 0, 1, -302505103, 612968613506]\) \(5391051390768345121/2833965225000000\) \(1609321712630954274225000000\) \([2, 2]\) \(198180864\) \(3.9121\)  
248430.fd4 248430fd2 \([1, 0, 1, -172659023, -866185991422]\) \(1002404925316922401/9348917760000\) \(5308962935764021148160000\) \([2, 2]\) \(99090432\) \(3.5656\)  
248430.fd5 248430fd1 \([1, 0, 1, -3064143, -32525399294]\) \(-5602762882081/801531494400\) \(-455165090212232980070400\) \([2]\) \(49545216\) \(3.2190\) \(\Gamma_0(N)\)-optimal
248430.fd6 248430fd6 \([1, 0, 1, 1146669897, 4782534923506]\) \(293623352309352854879/187320324116835000\) \(-106373452348304785346210235000\) \([2]\) \(396361728\) \(4.2587\)