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Properties

Label 99450.dq
Number of curves $8$
Conductor $99450$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("dq1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 99450.dq have rank \(0\).

L-function data

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

Complex multiplication

The elliptic curves in class 99450.dq do not have complex multiplication.

Modular form 99450.2.a.dq

Copy content sage:E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + 4 q^{7} + q^{8} - q^{13} + 4 q^{14} + q^{16} + q^{17} - 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 3 & 4 & 6 & 12 & 12 \\ 2 & 1 & 2 & 6 & 2 & 3 & 6 & 6 \\ 4 & 2 & 1 & 12 & 4 & 6 & 12 & 3 \\ 3 & 6 & 12 & 1 & 12 & 2 & 4 & 4 \\ 4 & 2 & 4 & 12 & 1 & 6 & 3 & 12 \\ 6 & 3 & 6 & 2 & 6 & 1 & 2 & 2 \\ 12 & 6 & 12 & 4 & 3 & 2 & 1 & 4 \\ 12 & 6 & 3 & 4 & 12 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 99450.dq

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
99450.dq1 99450cr8 \([1, -1, 1, -1482975001355, 695102884051264647]\) \(31664865542564944883878115208137569/103216295812500\) \(1175698119489257812500\) \([2]\) \(637009920\) \(5.1282\)  
99450.dq2 99450cr6 \([1, -1, 1, -92685938855, 10860999629389647]\) \(7730680381889320597382223137569/441370202660156250000\) \(5027482464675842285156250000\) \([2, 2]\) \(318504960\) \(4.7816\)  
99450.dq3 99450cr7 \([1, -1, 1, -92517868355, 10902350686786647]\) \(-7688701694683937879808871873249/58423707246780395507812500\) \(-665482540357857942581176757812500\) \([2]\) \(637009920\) \(5.1282\)  
99450.dq4 99450cr5 \([1, -1, 1, -18308984855, 953434712977647]\) \(59589391972023341137821784609/8834417507562311995200\) \(100629536922076960070325000000\) \([2]\) \(212336640\) \(4.5789\)  
99450.dq5 99450cr3 \([1, -1, 1, -5803376855, 169057784545647]\) \(1897660325010178513043539489/14258428094958372000000\) \(162412407519135206062500000000\) \([2]\) \(159252480\) \(4.4351\)  
99450.dq6 99450cr2 \([1, -1, 1, -1250384855, 11970578977647]\) \(18980483520595353274840609/5549773448629762560000\) \(63215388188298389160000000000\) \([2, 2]\) \(106168320\) \(4.2323\)  
99450.dq7 99450cr1 \([1, -1, 1, -471632855, -3796034014353]\) \(1018563973439611524445729/42904970360310988800\) \(488714428010417356800000000\) \([2]\) \(53084160\) \(3.8858\) \(\Gamma_0(N)\)-optimal
99450.dq8 99450cr4 \([1, -1, 1, 3348183145, 79560331441647]\) \(364421318680576777174674911/450962301637624725000000\) \(-5136742467091069133203125000000\) \([2]\) \(212336640\) \(4.5789\)