Elliptic curve isogeny class with LMFDB label 184093.k (Cremona label 184093l)

• Label: 184093.k
• Number of curves: $2$
• Conductor: $184093$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 184093.k have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(7\)	\(1\)
\(13\)	\(1 + T\)
\(17\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 - T + 2 T^{2}\)	1.2.ab
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(11\)	\( 1 - 3 T + 11 T^{2}\)	1.11.ad
\(19\)	\( 1 + 7 T + 19 T^{2}\)	1.19.h
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 - 5 T + 29 T^{2}\)	1.29.af
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 184093.k do not have complex multiplication.

Modular form 184093.2.a.k

Isogeny 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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 184093.k

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
184093.k1	184093l1	\([1, -1, 0, -30977, 2106670]\)	\(-56723625/13\)	\(-753405941197\)	\([]\)	\(264000\)	\(1.2706\)	\(\Gamma_0(N)\)-optimal
184093.k2	184093l2	\([1, -1, 0, 181438, -86838571]\)	\(11397810375/62748517\)	\(-3636546577623150373\)	\([]\)	\(1848000\)	\(2.2435\)