Elliptic curve isogeny class with Cremona label 95550bo (LMFDB label 95550.cr)

• Label: 95550bo
• Number of curves: $2$
• Conductor: $95550$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 95550bo have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + T + 11 T^{2}\)	1.11.b
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 - 3 T + 29 T^{2}\)	1.29.ad
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 95550bo do not have complex multiplication.

Modular form 95550.2.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 95550bo

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
95550.cr1	95550bo1	\([1, 1, 0, -45688850, -118886527500]\)	\(16728308209329751/16376256\)	\(10325640605553000000\)	\([2]\)	\(7741440\)	\(2.9421\)	\(\Gamma_0(N)\)-optimal
95550.cr2	95550bo2	\([1, 1, 0, -45345850, -120758964500]\)	\(-16354376146655191/523792501128\)	\(-330264324063537010875000\)	\([2]\)	\(15482880\)	\(3.2886\)