Elliptic curve isogeny class with LMFDB label 10350.bj (Cremona label 10350bg)

• Label: 10350.bj
• Number of curves: $4$
• Conductor: $10350$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 10350.bj have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1\)
\(5\)	\(1\)
\(23\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 8 T + 19 T^{2}\)	1.19.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 10350.bj do not have complex multiplication.

Modular form 10350.2.a.bj

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 10350.bj

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
10350.bj1	10350bg3	\([1, -1, 1, -55580, -5028703]\)	\(1666957239793/301806\)	\(3437758968750\)	\([2]\)	\(32768\)	\(1.4090\)
10350.bj2	10350bg4	\([1, -1, 1, -24080, 1397297]\)	\(135559106353/5037138\)	\(57376150031250\)	\([2]\)	\(32768\)	\(1.4090\)
10350.bj3	10350bg2	\([1, -1, 1, -3830, -60703]\)	\(545338513/171396\)	\(1952307562500\)	\([2, 2]\)	\(16384\)	\(1.0625\)
10350.bj4	10350bg1	\([1, -1, 1, 670, -6703]\)	\(2924207/3312\)	\(-37725750000\)	\([2]\)	\(8192\)	\(0.71589\)	\(\Gamma_0(N)\)-optimal