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Properties

Label 95550.m
Number of curves $6$
Conductor $95550$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("m1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 95550.m have rank \(1\).

L-function data

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

Complex multiplication

The elliptic curves in class 95550.m do not have complex multiplication.

Modular form 95550.2.a.m

Copy content sage:E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} - q^{8} + q^{9} - 4 q^{11} - q^{12} + q^{13} + q^{16} - 6 q^{17} - q^{18} + 4 q^{19} + O(q^{20})\) 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 95550.m

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
95550.m1 95550bt6 \([1, 1, 0, -566452275, 5183545015125]\) \(10934663514379917006241/12996826171875000\) \(23891618785858154296875000\) \([2]\) \(56623104\) \(3.7809\)  
95550.m2 95550bt4 \([1, 1, 0, -407741275, -3169190739875]\) \(4078208988807294650401/359723582400\) \(661267496027775000000\) \([2]\) \(28311552\) \(3.4344\)  
95550.m3 95550bt3 \([1, 1, 0, -44749275, 34858108125]\) \(5391051390768345121/2833965225000000\) \(5209580855562890625000000\) \([2, 2]\) \(28311552\) \(3.4344\)  
95550.m4 95550bt2 \([1, 1, 0, -25541275, -49292139875]\) \(1002404925316922401/9348917760000\) \(17185794149160000000000\) \([2, 2]\) \(14155776\) \(3.0878\)  
95550.m5 95550bt1 \([1, 1, 0, -453275, -1850731875]\) \(-5602762882081/801531494400\) \(-1473427793510400000000\) \([2]\) \(7077888\) \(2.7412\) \(\Gamma_0(N)\)-optimal
95550.m6 95550bt5 \([1, 1, 0, 169625725, 272171233125]\) \(293623352309352854879/187320324116835000\) \(-344344512687836264296875000\) \([2]\) \(56623104\) \(3.7809\)