Elliptic curve isogeny class with Cremona label 273600jh (LMFDB label 273600.jh)

• Label: 273600jh
• Number of curves: $4$
• Conductor: $273600$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 273600jh have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1\)
\(19\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 273600jh do not have complex multiplication.

Modular form 273600.2.a.jh

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 273600jh

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
273600.jh3	273600jh1	\([0, 0, 0, -446700, -114226000]\)	\(3301293169/22800\)	\(68080435200000000\)	\([2]\)	\(2359296\)	\(2.0635\)	\(\Gamma_0(N)\)-optimal
273600.jh2	273600jh2	\([0, 0, 0, -734700, 51086000]\)	\(14688124849/8122500\)	\(24253655040000000000\)	\([2, 2]\)	\(4718592\)	\(2.4101\)
273600.jh1	273600jh3	\([0, 0, 0, -8942700, 10278254000]\)	\(26487576322129/44531250\)	\(132969600000000000000\)	\([2]\)	\(9437184\)	\(2.7567\)
273600.jh4	273600jh4	\([0, 0, 0, 2865300, 403886000]\)	\(871257511151/527800050\)	\(-1576002504499200000000\)	\([2]\)	\(9437184\)	\(2.7567\)