Elliptic curve isogeny class with Cremona label 283920cu (LMFDB label 283920.cu)

• Label: 283920cu
• Number of curves: $4$
• Conductor: $283920$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 283920cu have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 - 8 T + 19 T^{2}\)	1.19.ai
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 283920cu do not have complex multiplication.

Modular form 283920.2.a.cu

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 283920cu

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
283920.cu4	283920cu1	\([0, -1, 0, -77120, -1890240]\)	\(2565726409/1404585\)	\(27769501774909440\)	\([2]\)	\(2752512\)	\(1.8460\)	\(\Gamma_0(N)\)-optimal
283920.cu2	283920cu2	\([0, -1, 0, -739600, 243492352]\)	\(2263054145689/16769025\)	\(331533847720857600\)	\([2, 2]\)	\(5505024\)	\(2.1925\)
283920.cu1	283920cu3	\([0, -1, 0, -11812480, 15630366400]\)	\(9219915604149769/511875\)	\(10120080821760000\)	\([4]\)	\(11010048\)	\(2.5391\)
283920.cu3	283920cu4	\([0, -1, 0, -266400, 550504512]\)	\(-105756712489/6558605235\)	\(-129667624041451991040\)	\([2]\)	\(11010048\)	\(2.5391\)