Elliptic curve isogeny class with Cremona label 10890c (LMFDB label 10890.f)

• Label: 10890c
• Number of curves: $4$
• Conductor: $10890$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 10890c have rank \(0\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 3 T + 7 T^{2}\)	1.7.d
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(17\)	\( 1 + 8 T + 17 T^{2}\)	1.17.i
\(19\)	\( 1 - 8 T + 19 T^{2}\)	1.19.ai
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 10890c do not have complex multiplication.

Modular form 10890.2.a.c

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 10890c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
10890.f3	10890c1	\([1, -1, 0, -930, -12204]\)	\(-1860867/320\)	\(-15306287040\)	\([2]\)	\(8640\)	\(0.68059\)	\(\Gamma_0(N)\)-optimal
10890.f2	10890c2	\([1, -1, 0, -15450, -735300]\)	\(8527173507/200\)	\(9566429400\)	\([2]\)	\(17280\)	\(1.0272\)
10890.f4	10890c3	\([1, -1, 0, 6330, 51200]\)	\(804357/500\)	\(-17434817581500\)	\([2]\)	\(25920\)	\(1.2299\)
10890.f1	10890c4	\([1, -1, 0, -26340, 436706]\)	\(57960603/31250\)	\(1089676098843750\)	\([2]\)	\(51840\)	\(1.5765\)