Elliptic curve isogeny class with LMFDB label 210210.bl (Cremona label 210210eb)

• Label: 210210.bl
• Number of curves: $4$
• Conductor: $210210$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 210210.bl have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1 - T\)
\(5\)	\(1 + T\)
\(7\)	\(1\)
\(11\)	\(1 + T\)
\(13\)	\(1 - T\)

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 210210.bl do not have complex multiplication.

Modular form 210210.2.a.bl

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 210210.bl

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
210210.bl1	210210eb3	\([1, 0, 1, -11939954, 15874730456]\)	\(1600086203685293756041/505128060937500\)	\(59427811241235937500\)	\([2]\)	\(11796480\)	\(2.7697\)
210210.bl2	210210eb2	\([1, 0, 1, -847334, 176454632]\)	\(571871738885758921/216522396090000\)	\(25473643377592410000\)	\([2, 2]\)	\(5898240\)	\(2.4232\)
210210.bl3	210210eb1	\([1, 0, 1, -373014, -85749464]\)	\(48787570816576201/1253457004800\)	\(147467963157715200\)	\([2]\)	\(2949120\)	\(2.0766\)	\(\Gamma_0(N)\)-optimal
210210.bl4	210210eb4	\([1, 0, 1, 2656166, 1261138232]\)	\(17615758461429817079/16032362964918300\)	\(-1886191470459673076700\)	\([2]\)	\(11796480\)	\(2.7697\)