Elliptic curve isogeny class with Cremona label 109520e (LMFDB label 109520.u)

• Label: 109520e
• Number of curves: $2$
• Conductor: $109520$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 109520e have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1 - T\)
\(37\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 2 T + 3 T^{2}\)	1.3.c
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(11\)	\( 1 - 5 T + 11 T^{2}\)	1.11.af
\(13\)	\( 1 - T + 13 T^{2}\)	1.13.ab
\(17\)	\( 1 + 4 T + 17 T^{2}\)	1.17.e
\(19\)	\( 1 - 5 T + 19 T^{2}\)	1.19.af
\(23\)	\( 1 + T + 23 T^{2}\)	1.23.b
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 109520e do not have complex multiplication.

Modular form 109520.2.a.e

Isogeny matrix

The \((i,j)\)-th 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.

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

Isogeny graph

The vertices are labelled with Cremona labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 109520e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
109520.u2	109520e1	\([0, -1, 0, -219496, -5063424]\)	\(8788/5\)	\(665404107750794240\)	\([2]\)	\(1960704\)	\(2.1098\)	\(\Gamma_0(N)\)-optimal
109520.u1	109520e2	\([0, -1, 0, -2245616, 1290032480]\)	\(4705274/25\)	\(6654041077507942400\)	\([2]\)	\(3921408\)	\(2.4564\)