Elliptic curve isogeny class with LMFDB label 72600.ek (Cremona label 72600ed)

• Label: 72600.ek
• Number of curves: $4$
• Conductor: $72600$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 72600.ek have rank \(0\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 72600.ek do not have complex multiplication.

Modular form 72600.2.a.ek

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 72600.ek

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
72600.ek1	72600ed4	\([0, 1, 0, -31945008, 69484201488]\)	\(127191074376964/495\)	\(14030763120000000\)	\([2]\)	\(2949120\)	\(2.7345\)
72600.ek2	72600ed2	\([0, 1, 0, -1997508, 1084111488]\)	\(124386546256/245025\)	\(1736306936100000000\)	\([2, 2]\)	\(1474560\)	\(2.3879\)
72600.ek3	72600ed3	\([0, 1, 0, -1332008, 1818823488]\)	\(-9220796644/45106875\)	\(-1278553289310000000000\)	\([2]\)	\(2949120\)	\(2.7345\)
72600.ek4	72600ed1	\([0, 1, 0, -167383, 4337738]\)	\(1171019776/658845\)	\(291796026761250000\)	\([2]\)	\(737280\)	\(2.0413\)	\(\Gamma_0(N)\)-optimal