Elliptic curve isogeny class with Cremona label 139392s (LMFDB label 139392.bq)

• Label: 139392s
• Number of curves: $2$
• Conductor: $139392$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 139392s have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(11\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(13\)	\( 1 + 6 T + 13 T^{2}\)	1.13.g
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 - 8 T + 19 T^{2}\)	1.19.ai
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 139392s do not have complex multiplication.

Modular form 139392.2.a.s

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 139392s

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
139392.bq2	139392s1	\([0, 0, 0, 1815, -50578]\)	\(4000/9\)	\(-1487771100288\)	\([2]\)	\(163840\)	\(1.0198\)	\(\Gamma_0(N)\)-optimal
139392.bq1	139392s2	\([0, 0, 0, -14520, -553696]\)	\(16000/3\)	\(63478233612288\)	\([2]\)	\(327680\)	\(1.3664\)