Elliptic curve isogeny class with Cremona label 43681c (LMFDB label 43681.h)

• Label: 43681c
• Number of curves: $2$
• Conductor: $43681$
• CM: \(\Q(\sqrt{-11}) \)
• Rank: $2$

Rank

The elliptic curves in class 43681c have rank \(2\).

L-function data

Bad L-factors:

Prime	L-Factor
\(11\)	\(1\)
\(19\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + T + 2 T^{2}\)	1.2.b
\(3\)	\( 1 + 2 T + 3 T^{2}\)	1.3.c
\(5\)	\( 1 - T + 5 T^{2}\)	1.5.ab
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(13\)	\( 1 + T + 13 T^{2}\)	1.13.b
\(17\)	\( 1 + 5 T + 17 T^{2}\)	1.17.f
\(23\)	\( 1 - 2 T + 23 T^{2}\)	1.23.ac
\(29\)	\( 1 + 9 T + 29 T^{2}\)	1.29.j
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

Each elliptic curve in class 43681c has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-11}) \).

Modular form 43681.2.a.c

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.

\(\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 43681c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
43681.h2	43681c1	\([0, 1, 1, -2647, -54675]\)	\(-32768\)	\(-62618067611\)	\([]\)	\(28800\)	\(0.84915\)	\(\Gamma_0(N)\)-optimal	\(-11\)
43681.h1	43681c2	\([0, 1, 1, -320327, 71490832]\)	\(-32768\)	\(-110931726475010771\)	\([]\)	\(316800\)	\(2.0481\)		\(-11\)