Elliptic curve isogeny class with Cremona label 88200bo (LMFDB label 88200.eh)

• Label: 88200bo
• Number of curves: $2$
• Conductor: $88200$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 88200bo have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + 3 T + 11 T^{2}\)	1.11.d
\(13\)	\( 1 + T + 13 T^{2}\)	1.13.b
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 + 7 T + 19 T^{2}\)	1.19.h
\(23\)	\( 1 + 5 T + 23 T^{2}\)	1.23.f
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 88200bo do not have complex multiplication.

Modular form 88200.2.a.bo

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 88200bo

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
88200.eh2	88200bo1	\([0, 0, 0, -3675, -4716250]\)	\(-4/7\)	\(-9605805552000000\)	\([2]\)	\(368640\)	\(1.7457\)	\(\Gamma_0(N)\)-optimal
88200.eh1	88200bo2	\([0, 0, 0, -444675, -112761250]\)	\(3543122/49\)	\(134481277728000000\)	\([2]\)	\(737280\)	\(2.0923\)