Elliptic curve isogeny class with Cremona label 31850bs (LMFDB label 31850.cb)

• Label: 31850bs
• Number of curves: $4$
• Conductor: $31850$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 31850bs have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(5\)	\(1\)
\(7\)	\(1\)
\(13\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + T + 3 T^{2}\)	1.3.b
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 + T + 23 T^{2}\)	1.23.b
\(29\)	\( 1 - 3 T + 29 T^{2}\)	1.29.ad
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 31850bs do not have complex multiplication.

Modular form 31850.2.a.bs

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 31850bs

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
31850.cb3	31850bs1	\([1, -1, 1, -2450230, -1349948603]\)	\(884984855328729/83492864000\)	\(153482061824000000000\)	\([2]\)	\(1105920\)	\(2.6115\)	\(\Gamma_0(N)\)-optimal
31850.cb2	31850bs2	\([1, -1, 1, -8722230, 8409283397]\)	\(39920686684059609/6492304000000\)	\(11934579270250000000000\)	\([2, 2]\)	\(2211840\)	\(2.9581\)
31850.cb4	31850bs3	\([1, -1, 1, 15777770, 47119283397]\)	\(236293804275620391/658593925444000\)	\(-1210670573977518062500000\)	\([2]\)	\(4423680\)	\(3.3046\)
31850.cb1	31850bs4	\([1, -1, 1, -133574230, 594214867397]\)	\(143378317900125424089/4976562500000\)	\(9148243774414062500000\)	\([2]\)	\(4423680\)	\(3.3046\)