Elliptic curve isogeny class with Cremona label 154800cy (LMFDB label 154800.em)

• Label: 154800cy
• Number of curves: $4$
• Conductor: $154800$
• CM: no
• Rank: $2$

Rank

The elliptic curves in class 154800cy have rank \(2\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1\)
\(43\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(11\)	\( 1 + 6 T + 11 T^{2}\)	1.11.g
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 + 4 T + 17 T^{2}\)	1.17.e
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 154800cy do not have complex multiplication.

Modular form 154800.2.a.cy

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 154800cy

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
154800.em4	154800cy1	\([0, 0, 0, -387075, 27477250]\)	\(137467988281/72562500\)	\(3385476000000000000\)	\([2]\)	\(2211840\)	\(2.2471\)	\(\Gamma_0(N)\)-optimal
154800.em3	154800cy2	\([0, 0, 0, -4887075, 4153977250]\)	\(276670733768281/336980250\)	\(15722150544000000000\)	\([2]\)	\(4423680\)	\(2.5936\)
154800.em2	154800cy3	\([0, 0, 0, -17937075, -29239172750]\)	\(13679527032530281/381633600\)	\(17805497241600000000\)	\([2]\)	\(6635520\)	\(2.7964\)
154800.em1	154800cy4	\([0, 0, 0, -18657075, -26764532750]\)	\(15393836938735081/2275690697640\)	\(106174625189091840000000\)	\([2]\)	\(13271040\)	\(3.1429\)