Elliptic curve isogeny class with Cremona label 24882bj (LMFDB label 24882.bi)

• Label: 24882bj
• Number of curves: $2$
• Conductor: $24882$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 24882bj have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1 - T\)
\(11\)	\(1 + T\)
\(13\)	\(1 - T\)
\(29\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(7\)	\( 1 + T + 7 T^{2}\)	1.7.b
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 - 9 T + 23 T^{2}\)	1.23.aj
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 24882bj do not have complex multiplication.

Modular form 24882.2.a.bj

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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 24882bj

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
24882.bi2	24882bj1	\([1, 0, 0, 411779, 8250737]\)	\(7721758769769063671471/4497774542859970944\)	\(-4497774542859970944\)	\([7]\)	\(482944\)	\(2.2686\)	\(\Gamma_0(N)\)-optimal
24882.bi1	24882bj2	\([1, 0, 0, -163046131, -801348432313]\)	\(-479352730263827621784814619569/214316023050990383094\)	\(-214316023050990383094\)	\([]\)	\(3380608\)	\(3.2416\)