Elliptic curve isogeny class with Cremona label 163800j (LMFDB label 163800.et)

• Label: 163800j
• Number of curves: $2$
• Conductor: $163800$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 163800j have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1\)
\(7\)	\(1 + T\)
\(13\)	\(1 - T\)

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
\(19\)	\( 1 - T + 19 T^{2}\)	1.19.ab
\(23\)	\( 1 - T + 23 T^{2}\)	1.23.ab
\(29\)	\( 1 + 3 T + 29 T^{2}\)	1.29.d
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 163800j do not have complex multiplication.

Modular form 163800.2.a.j

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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 163800j

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
163800.et2	163800j1	\([0, 0, 0, -37060995, 86840781550]\)	\(60330571443221291348/417536301\)	\(38961147318912000\)	\([2]\)	\(7225344\)	\(2.7827\)	\(\Gamma_0(N)\)-optimal
163800.et1	163800j2	\([0, 0, 0, -37084395, 86725630150]\)	\(30222460127634675514/79352099523333\)	\(14809006221442497792000\)	\([2]\)	\(14450688\)	\(3.1293\)