Elliptic curve isogeny class with LMFDB label 369600.kf (Cremona label 369600kf)

• Label: 369600.kf
• Number of curves: $4$
• Conductor: $369600$
• CM: no
• Rank: $2$

Rank

The elliptic curves in class 369600.kf have rank \(2\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(5\)	\(1\)
\(7\)	\(1 - T\)
\(11\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 369600.kf do not have complex multiplication.

Modular form 369600.2.a.kf

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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 369600.kf

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
369600.kf1	369600kf3	\([0, -1, 0, -82433, 9136737]\)	\(120993582536/6237\)	\(3193344000000\)	\([2]\)	\(1310720\)	\(1.4687\)
369600.kf2	369600kf4	\([0, -1, 0, -26433, -1531263]\)	\(3989418056/307461\)	\(157420032000000\)	\([2]\)	\(1310720\)	\(1.4687\)
369600.kf3	369600kf2	\([0, -1, 0, -5433, 127737]\)	\(277167808/53361\)	\(3415104000000\)	\([2, 2]\)	\(655360\)	\(1.1221\)
369600.kf4	369600kf1	\([0, -1, 0, 692, 11362]\)	\(36594368/79233\)	\(-79233000000\)	\([2]\)	\(327680\)	\(0.77553\)	\(\Gamma_0(N)\)-optimal