Elliptic curve isogeny class with Cremona label 379200cj (LMFDB label 379200.cj)

• Label: 379200cj
• Number of curves: $2$
• Conductor: $379200$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 379200cj have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(5\)	\(1\)
\(79\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(11\)	\( 1 + 6 T + 11 T^{2}\)	1.11.g
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 2 T + 23 T^{2}\)	1.23.c
\(29\)	\( 1 + 4 T + 29 T^{2}\)	1.29.e
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 379200cj do not have complex multiplication.

Modular form 379200.2.a.cj

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 379200cj

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
379200.cj1	379200cj1	\([0, -1, 0, -2008, 13762]\)	\(895841344/444375\)	\(444375000000\)	\([2]\)	\(442368\)	\(0.92800\)	\(\Gamma_0(N)\)-optimal
379200.cj2	379200cj2	\([0, -1, 0, 7367, 98137]\)	\(690807104/468075\)	\(-29956800000000\)	\([2]\)	\(884736\)	\(1.2746\)