Elliptic curve isogeny class with Cremona label 119952ct (LMFDB label 119952.gr)

• Label: 119952ct
• Number of curves: $2$
• Conductor: $119952$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 119952ct have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(7\)	\(1\)
\(17\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + T + 5 T^{2}\)	1.5.b
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 + T + 13 T^{2}\)	1.13.b
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.ai
\(29\)	\( 1 + 5 T + 29 T^{2}\)	1.29.f
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 119952ct do not have complex multiplication.

Modular form 119952.2.a.ct

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 119952ct

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
119952.gr2	119952ct1	\([0, 0, 0, 12789, -2824262]\)	\(17779581/275128\)	\(-3579700920090624\)	\([]\)	\(552960\)	\(1.6651\)	\(\Gamma_0(N)\)-optimal
119952.gr1	119952ct2	\([0, 0, 0, -1186731, -497852838]\)	\(-19486825371/11662\)	\(-110614616407056384\)	\([]\)	\(1658880\)	\(2.2144\)