Elliptic curve isogeny class with Cremona label 252300j (LMFDB label 252300.j)

• Label: 252300j
• Number of curves: $2$
• Conductor: $252300$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 252300j have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(5\)	\(1\)
\(29\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + T + 7 T^{2}\)	1.7.b
\(11\)	\( 1 + 6 T + 11 T^{2}\)	1.11.g
\(13\)	\( 1 - 5 T + 13 T^{2}\)	1.13.af
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 + 5 T + 19 T^{2}\)	1.19.f
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 252300j do not have complex multiplication.

Modular form 252300.2.a.j

Isogeny matrix

The \((i,j)\)-th 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, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 252300j

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
252300.j2	252300j1	\([0, -1, 0, -280333, -83461463]\)	\(-40960/27\)	\(-1606022966700000000\)	\([]\)	\(4354560\)	\(2.1943\)	\(\Gamma_0(N)\)-optimal
252300.j1	252300j2	\([0, -1, 0, -25510333, -49584721463]\)	\(-30866268160/3\)	\(-178446996300000000\)	\([]\)	\(13063680\)	\(2.7436\)