Elliptic curve isogeny class with Cremona label 383040dd (LMFDB label 383040.dd)

• Label: 383040dd
• Number of curves: $4$
• Conductor: $383040$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 383040dd have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1 + T\)
\(7\)	\(1 + T\)
\(19\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.ai
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 383040dd do not have complex multiplication.

Modular form 383040.2.a.dd

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 383040dd

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
383040.dd4	383040dd1	\([0, 0, 0, 1993812, -11195971792]\)	\(4586790226340951/286015269335040\)	\(-54658369151367685079040\)	\([2]\)	\(24772608\)	\(3.0426\)	\(\Gamma_0(N)\)-optimal
383040.dd3	383040dd2	\([0, 0, 0, -64545708, -192103618768]\)	\(155617476551393929129/6633105589454400\)	\(1267606218266970056294400\)	\([2, 2]\)	\(49545216\)	\(3.3891\)
383040.dd2	383040dd3	\([0, 0, 0, -171796908, 611808475952]\)	\(2934284984699764805929/851931751022747640\)	\(162806692969338117700976640\)	\([2]\)	\(99090432\)	\(3.7357\)
383040.dd1	383040dd4	\([0, 0, 0, -1021926828, -12574105119952]\)	\(617611911727813844500009/1197723879765000\)	\(228888597849357680640000\)	\([2]\)	\(99090432\)	\(3.7357\)