Elliptic curve isogeny class with Cremona label 25536cm (LMFDB label 25536.bk)

• Label: 25536cm
• Number of curves: $4$
• Conductor: $25536$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 25536cm have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(7\)	\(1 + T\)
\(19\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 25536cm do not have complex multiplication.

Modular form 25536.2.a.cm

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 25536cm

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
25536.bk4	25536cm1	\([0, -1, 0, -17437, 352957]\)	\(572616640141312/280535480757\)	\(287268332295168\)	\([2]\)	\(98304\)	\(1.4676\)	\(\Gamma_0(N)\)-optimal
25536.bk2	25536cm2	\([0, -1, 0, -148657, -21770735]\)	\(22174957026242512/278654127129\)	\(4565469218881536\)	\([2, 2]\)	\(196608\)	\(1.8142\)
25536.bk3	25536cm3	\([0, -1, 0, -25537, -56859935]\)	\(-28104147578308/21301741002339\)	\(-1396030898329288704\)	\([2]\)	\(393216\)	\(2.1607\)
25536.bk1	25536cm4	\([0, -1, 0, -2371297, -1404697343]\)	\(22501000029889239268/3620708343\)	\(237286741966848\)	\([2]\)	\(393216\)	\(2.1607\)