Elliptic curve isogeny class with Cremona label 6930bi (LMFDB label 6930.bf)

• Label: 6930bi
• Number of curves: $4$
• Conductor: $6930$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 6930bi have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1\)
\(5\)	\(1 - T\)
\(7\)	\(1 - T\)
\(11\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(13\)	\( 1 + 6 T + 13 T^{2}\)	1.13.g
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.ai
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 6930bi do not have complex multiplication.

Modular form 6930.2.a.bi

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 6930bi

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
6930.bf3	6930bi1	\([1, -1, 1, -7772, 265119]\)	\(71210194441849/165580800\)	\(120708403200\)	\([4]\)	\(12288\)	\(1.0070\)	\(\Gamma_0(N)\)-optimal
6930.bf2	6930bi2	\([1, -1, 1, -10652, 53151]\)	\(183337554283129/104587560000\)	\(76244331240000\)	\([2, 2]\)	\(24576\)	\(1.3535\)
6930.bf1	6930bi3	\([1, -1, 1, -109652, -13886049]\)	\(200005594092187129/1027287538200\)	\(748892615347800\)	\([2]\)	\(49152\)	\(1.7001\)
6930.bf4	6930bi4	\([1, -1, 1, 42268, 391839]\)	\(11456208593737991/6725709375000\)	\(-4903042134375000\)	\([2]\)	\(49152\)	\(1.7001\)