Elliptic curve isogeny class with Cremona label 218400bi (LMFDB label 218400.s)

• Label: 218400bi
• Number of curves: $2$
• Conductor: $218400$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 218400bi have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(5\)	\(1\)
\(7\)	\(1 - T\)
\(13\)	\(1 + T\)

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 218400bi do not have complex multiplication.

Modular form 218400.2.a.bi

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 Cremona numbering.

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

Isogeny graph

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

Elliptic curves in class 218400bi

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
218400.s2	218400bi1	\([0, -1, 0, -225958, 16567912]\)	\(10207015805888/4966786461\)	\(620848307625000000\)	\([2]\)	\(2119680\)	\(2.1076\)	\(\Gamma_0(N)\)-optimal
218400.s1	218400bi2	\([0, -1, 0, -2972208, 1971897912]\)	\(2903764922264296/2326273677\)	\(2326273677000000000\)	\([2]\)	\(4239360\)	\(2.4542\)