Elliptic curve isogeny class with LMFDB label 139392.bv (Cremona label 139392ct)

• Label: 139392.bv
• Number of curves: $2$
• Conductor: $139392$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 139392.bv have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(13\)	\( 1 - 6 T + 13 T^{2}\)	1.13.ag
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 4 T + 29 T^{2}\)	1.29.e
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 139392.2.a.bv

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 139392.bv

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
139392.bv1	139392ct1	\([0, 0, 0, -3630, -69212]\)	\(16000/3\)	\(991847400192\)	\([2]\)	\(163840\)	\(1.0198\)	\(\Gamma_0(N)\)-optimal
139392.bv2	139392ct2	\([0, 0, 0, 7260, -404624]\)	\(4000/9\)	\(-95217350418432\)	\([2]\)	\(327680\)	\(1.3664\)