Elliptic curve isogeny class with Cremona label 78400cw (LMFDB label 78400.cp)

• Label: 78400cw
• Number of curves: $2$
• Conductor: $78400$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 78400cw have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1\)
\(7\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + T + 3 T^{2}\)	1.3.b
\(11\)	\( 1 + 5 T + 11 T^{2}\)	1.11.f
\(13\)	\( 1 - 3 T + 13 T^{2}\)	1.13.ad
\(17\)	\( 1 + 5 T + 17 T^{2}\)	1.17.f
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 - 2 T + 23 T^{2}\)	1.23.ac
\(29\)	\( 1 + 3 T + 29 T^{2}\)	1.29.d
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 78400cw do not have complex multiplication.

Modular form 78400.2.a.cw

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 78400cw

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
78400.cp2	78400cw1	\([0, 1, 0, -233, -7337]\)	\(-64\)	\(-21952000000\)	\([2]\)	\(65536\)	\(0.66568\)	\(\Gamma_0(N)\)-optimal
78400.cp1	78400cw2	\([0, 1, 0, -7233, -238337]\)	\(238328\)	\(175616000000\)	\([2]\)	\(131072\)	\(1.0123\)