Elliptic curve isogeny class with Cremona label 115885o (LMFDB label 115885.g)

• Label: 115885o
• Number of curves: $2$
• Conductor: $115885$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 115885o have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(5\)	\(1 - T\)
\(7\)	\(1\)
\(11\)	\(1 - T\)
\(43\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 - T + 2 T^{2}\)	1.2.ab
\(3\)	\( 1 - 2 T + 3 T^{2}\)	1.3.ac
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(17\)	\( 1 + 8 T + 17 T^{2}\)	1.17.i
\(19\)	\( 1 + 8 T + 19 T^{2}\)	1.19.i
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 115885o do not have complex multiplication.

Modular form 115885.2.a.o

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 115885o

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
115885.g2	115885o1	\([0, -1, 1, -2025, -33279]\)	\(7809531904/286165\)	\(33667026085\)	\([]\)	\(77760\)	\(0.78946\)	\(\Gamma_0(N)\)-optimal
115885.g1	115885o2	\([0, -1, 1, -23585, 1391298]\)	\(12332795428864/109322125\)	\(12861638684125\)	\([]\)	\(233280\)	\(1.3388\)