Elliptic curve isogeny class with LMFDB label 296208.fr (Cremona label 296208fr)

• Label: 296208.fr
• Number of curves: $2$
• Conductor: $296208$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 296208.fr have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(11\)	\(1\)
\(17\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 4 T + 5 T^{2}\)	1.5.ae
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 296208.fr do not have complex multiplication.

Modular form 296208.2.a.fr

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 296208.fr

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
296208.fr1	296208fr2	\([0, 0, 0, -23285767923, 1367678295964530]\)	\(9776604686860471347243/147962546281\)	\(21132902427062159273177088\)	\([2]\)	\(442368000\)	\(4.4089\)
296208.fr2	296208fr1	\([0, 0, 0, -1456719363, 21328067929410]\)	\(2393558463315519963/9284733153971\)	\(1326101535394935089898590208\)	\([2]\)	\(221184000\)	\(4.0623\)	\(\Gamma_0(N)\)-optimal