Elliptic curve isogeny class with LMFDB label 327184.ej (Cremona label 327184ej)

• Label: 327184.ej
• Number of curves: $2$
• Conductor: $327184$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 327184.ej have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(11\)	\(1\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - 2 T + 3 T^{2}\)	1.3.ac
\(5\)	\( 1 - 3 T + 5 T^{2}\)	1.5.ad
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 + 3 T + 29 T^{2}\)	1.29.d
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 327184.ej do not have complex multiplication.

Modular form 327184.2.a.ej

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 327184.ej

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
327184.ej1	327184ej2	\([0, -1, 0, -17020384, 27766361856]\)	\(-128667913/4096\)	\(-17358871610420535230464\)	\([]\)	\(26002944\)	\(3.0434\)
327184.ej2	327184ej1	\([0, -1, 0, 974736, 140253632]\)	\(24167/16\)	\(-67808092228205215744\)	\([]\)	\(8667648\)	\(2.4941\)	\(\Gamma_0(N)\)-optimal