Elliptic curve isogeny class with Cremona label 371943bf (LMFDB label 371943.bf)

• Label: 371943bf
• Number of curves: $2$
• Conductor: $371943$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 371943bf have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1\)
\(11\)	\(1 - T\)
\(13\)	\(1 - T\)
\(17\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 - T + 2 T^{2}\)	1.2.ab
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(19\)	\( 1 - 6 T + 19 T^{2}\)	1.19.ag
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 10 T + 29 T^{2}\)	1.29.k
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 371943bf do not have complex multiplication.

Modular form 371943.2.a.bf

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 371943bf

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
371943.bf1	371943bf1	\([1, -1, 0, -1089667239507, -93463849214530632]\)	\(8131755985964161964448308988625/4491414222168968491132426977\)	\(79032217286789724021266901490908407577\)	\([2]\)	\(6812467200\)	\(5.9624\)	\(\Gamma_0(N)\)-optimal
371943.bf2	371943bf2	\([1, -1, 0, 4246787202858, -738695623131771255]\)	\(481375691534989591168533139109375/291970430882721534414299079537\)	\(-5137595731194346597694332573222441828137\)	\([2]\)	\(13624934400\)	\(6.3090\)