Elliptic curve isogeny class with LMFDB label 2116.d (Cremona label 2116c)

• Label: 2116.d
• Number of curves: $2$
• Conductor: $2116$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 2116.d have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(23\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - T + 3 T^{2}\)	1.3.ab
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 + T + 13 T^{2}\)	1.13.b
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(29\)	\( 1 + 3 T + 29 T^{2}\)	1.29.d
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 2116.d do not have complex multiplication.

Modular form 2116.2.a.d

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 LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

Elliptic curves in class 2116.d

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
2116.d1	2116c2	\([0, 1, 0, -9698, 446045]\)	\(-42592000/12167\)	\(-28818442583408\)	\([]\)	\(3168\)	\(1.2978\)
2116.d2	2116c1	\([0, 1, 0, 882, -4663]\)	\(32000/23\)	\(-54477207152\)	\([]\)	\(1056\)	\(0.74848\)	\(\Gamma_0(N)\)-optimal