Elliptic curve isogeny class with LMFDB label 374400.kg (Cremona label 374400kg)

• Label: 374400.kg
• Number of curves: $2$
• Conductor: $374400$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 374400.kg have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1\)
\(13\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 - 2 T + 23 T^{2}\)	1.23.ac
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 374400.kg do not have complex multiplication.

Modular form 374400.2.a.kg

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 374400.kg

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
374400.kg1	374400kg2	\([0, 0, 0, -79785300, -211296602000]\)	\(601942297084171232/141650616290625\)	\(13217702307310800000000000\)	\([2]\)	\(68812800\)	\(3.5320\)
374400.kg2	374400kg1	\([0, 0, 0, 11620950, -20623164500]\)	\(59519748892520576/97453916015625\)	\(-284175619101562500000000\)	\([2]\)	\(34406400\)	\(3.1854\)	\(\Gamma_0(N)\)-optimal