Elliptic curve isogeny class with Cremona label 187200ef (LMFDB label 187200.hj)

• Label: 187200ef
• Number of curves: $4$
• Conductor: $187200$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 187200ef have rank \(0\).

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 \(\mathbb{F}_p\)
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 - 6 T + 19 T^{2}\)	1.19.ag
\(23\)	\( 1 + 2 T + 23 T^{2}\)	1.23.c
\(29\)	\( 1 + 4 T + 29 T^{2}\)	1.29.e
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 187200ef do not have complex multiplication.

Modular form 187200.2.a.ef

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 187200ef

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
187200.hj3	187200ef1	\([0, 0, 0, -1441453575, -21064400476000]\)	\(454357982636417669333824/3003024375\)	\(2189204769375000000\)	\([2]\)	\(41287680\)	\(3.5782\)	\(\Gamma_0(N)\)-optimal
187200.hj2	187200ef2	\([0, 0, 0, -1441481700, -21063537376000]\)	\(7099759044484031233216/577161945398025\)	\(26928067724490254400000000\)	\([2, 2]\)	\(82575360\)	\(3.9247\)
187200.hj1	187200ef3	\([0, 0, 0, -1540346700, -18008806606000]\)	\(1082883335268084577352/251301565117746585\)	\(93797806577068677358080000000\)	\([2]\)	\(165150720\)	\(4.2713\)
187200.hj4	187200ef4	\([0, 0, 0, -1343066700, -24063029746000]\)	\(-717825640026599866952/254764560814329735\)	\(-95090362794826944929280000000\)	\([2]\)	\(165150720\)	\(4.2713\)