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

• Label: 273600mp
• Number of curves: $2$
• Conductor: $273600$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 273600mp have rank \(0\).

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 \(\mathbb{F}_p\)
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 273600.2.a.mp

Isogeny matrix

The \((i,j)\)-th 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.

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

Isogeny graph

The vertices are labelled with Cremona labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 273600mp

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
273600.mp2	273600mp1	\([0, 0, 0, -54540, 4957200]\)	\(-27818127/361\)	\(-232835088384000\)	\([2]\)	\(786432\)	\(1.5656\)	\(\Gamma_0(N)\)-optimal
273600.mp1	273600mp2	\([0, 0, 0, -875340, 315219600]\)	\(115003963647/19\)	\(12254478336000\)	\([2]\)	\(1572864\)	\(1.9122\)