Elliptic curve isogeny class with Cremona label 990l (LMFDB label 990.l)

• Label: 990l
• Number of curves: $2$
• Conductor: $990$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 990l have rank \(0\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 5 T + 7 T^{2}\)	1.7.af
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(19\)	\( 1 + 7 T + 19 T^{2}\)	1.19.h
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 - 3 T + 29 T^{2}\)	1.29.ad
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 990l do not have complex multiplication.

Modular form 990.2.a.l

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 990l

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
990.l1	990l1	\([1, -1, 1, -797, -8539]\)	\(-76711450249/851840\)	\(-620991360\)	\([]\)	\(840\)	\(0.50212\)	\(\Gamma_0(N)\)-optimal
990.l2	990l2	\([1, -1, 1, 2668, -45961]\)	\(2882081488391/2883584000\)	\(-2102132736000\)	\([3]\)	\(2520\)	\(1.0514\)