Elliptic curve isogeny class with LMFDB label 34848.bi (Cremona label 34848m)

• Label: 34848.bi
• Number of curves: $2$
• Conductor: $34848$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 34848.bi have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(11\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 - 2 T + 23 T^{2}\)	1.23.ac
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 34848.bi do not have complex multiplication.

Modular form 34848.2.a.bi

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 LMFDB numbering.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 34848.bi

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
34848.bi1	34848m1	\([0, 0, 0, -107085, 13485692]\)	\(1643032000/297\)	\(24548223154752\)	\([2]\)	\(92160\)	\(1.5729\)	\(\Gamma_0(N)\)-optimal
34848.bi2	34848m2	\([0, 0, 0, -96195, 16336694]\)	\(-148877000/88209\)	\(-58326578215690752\)	\([2]\)	\(184320\)	\(1.9195\)