Elliptic curve isogeny class with Cremona label 247744r (LMFDB label 247744.r)

• Label: 247744r
• Number of curves: $2$
• Conductor: $247744$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 247744r have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(7\)	\(1\)
\(79\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + T + 3 T^{2}\)	1.3.b
\(5\)	\( 1 - T + 5 T^{2}\)	1.5.ab
\(11\)	\( 1 + 2 T + 11 T^{2}\)	1.11.c
\(13\)	\( 1 + T + 13 T^{2}\)	1.13.b
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 - 10 T + 29 T^{2}\)	1.29.ak
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 247744r do not have complex multiplication.

Modular form 247744.2.a.r

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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 247744r

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
247744.r2	247744r1	\([0, -1, 0, -1317185, -576316607]\)	\(8194759433281/82837504\)	\(2554789759050317824\)	\([]\)	\(3041280\)	\(2.3501\)	\(\Gamma_0(N)\)-optimal
247744.r1	247744r2	\([0, -1, 0, -73319745, 241663125313]\)	\(1413378216646643521/49232902384\)	\(1518390930984197423104\)	\([]\)	\(15206400\)	\(3.1548\)