Elliptic curve isogeny class with LMFDB label 361998.dc (Cremona label 361998dc)

• Label: 361998.dc
• Number of curves: $2$
• Conductor: $361998$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 361998.dc have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1\)
\(7\)	\(1 + T\)
\(13\)	\(1\)
\(17\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(11\)	\( 1 - 6 T + 11 T^{2}\)	1.11.ag
\(19\)	\( 1 - 6 T + 19 T^{2}\)	1.19.ag
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.ai
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 361998.dc do not have complex multiplication.

Modular form 361998.2.a.dc

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 LMFDB numbering.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 361998.dc

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
361998.dc1	361998dc2	\([1, -1, 1, -122180, -16407309]\)	\(125939845703125/509796\)	\(816495900948\)	\([2]\)	\(1843200\)	\(1.4965\)
361998.dc2	361998dc1	\([1, -1, 1, -7520, -263181]\)	\(-29360639125/1959216\)	\(-3137905815408\)	\([2]\)	\(921600\)	\(1.1499\)	\(\Gamma_0(N)\)-optimal