Elliptic curve isogeny class with Cremona label 43680ce (LMFDB label 43680.cd)

• Label: 43680ce
• Number of curves: $4$
• Conductor: $43680$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 43680ce have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 43680ce do not have complex multiplication.

Modular form 43680.2.a.ce

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 43680ce

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
43680.cd3	43680ce1	\([0, 1, 0, -390, -1512]\)	\(102766285504/46580625\)	\(2981160000\)	\([2, 2]\)	\(24576\)	\(0.51309\)	\(\Gamma_0(N)\)-optimal
43680.cd4	43680ce2	\([0, 1, 0, 1360, -9912]\)	\(542939080312/404852175\)	\(-207284313600\)	\([4]\)	\(49152\)	\(0.85966\)
43680.cd2	43680ce3	\([0, 1, 0, -3120, 65100]\)	\(6562309703048/106640625\)	\(54600000000\)	\([2]\)	\(49152\)	\(0.85966\)
43680.cd1	43680ce4	\([0, 1, 0, -5265, -148737]\)	\(3941317078336/2340975\)	\(9588633600\)	\([2]\)	\(49152\)	\(0.85966\)