Elliptic curve isogeny class with LMFDB label 25536.ce (Cremona label 25536bj)

• Label: 25536.ce
• Number of curves: $4$
• Conductor: $25536$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 25536.ce have rank \(1\).

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 \(\mathbb{F}_p\)
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 - 6 T + 13 T^{2}\)	1.13.ag
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 25536.2.a.ce

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 LMFDB 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 LMFDB labels.

Elliptic curves in class 25536.ce

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
25536.ce1	25536bj4	\([0, 1, 0, -12929, -473889]\)	\(1823652903746/328593657\)	\(43069427810304\)	\([2]\)	\(81920\)	\(1.3352\)
25536.ce2	25536bj2	\([0, 1, 0, -3809, 82431]\)	\(93280467172/7800849\)	\(511236440064\)	\([2, 2]\)	\(40960\)	\(0.98860\)
25536.ce3	25536bj1	\([0, 1, 0, -3729, 86415]\)	\(350104249168/2793\)	\(45760512\)	\([2]\)	\(20480\)	\(0.64202\)	\(\Gamma_0(N)\)-optimal
25536.ce4	25536bj3	\([0, 1, 0, 4031, 385055]\)	\(55251546334/517244049\)	\(-67796211990528\)	\([4]\)	\(81920\)	\(1.3352\)