Elliptic curve isogeny class with LMFDB label 88725.cf (Cremona label 88725bm)

• Label: 88725.cf
• Number of curves: $4$
• Conductor: $88725$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 88725.cf have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1 - T\)
\(5\)	\(1\)
\(7\)	\(1 + T\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 - T + 2 T^{2}\)	1.2.ab
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 23 T^{2}\)	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 88725.cf do not have complex multiplication.

Modular form 88725.2.a.cf

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 88725.cf

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
88725.cf1	88725bm4	\([1, 0, 1, -71290626, 231676651273]\)	\(531301262949272089/4740474375\)	\(357521318398740234375\)	\([2]\)	\(7741440\)	\(3.1096\)
88725.cf2	88725bm2	\([1, 0, 1, -4556751, 3446798773]\)	\(138742439989609/12224619225\)	\(921967220262547265625\)	\([2, 2]\)	\(3870720\)	\(2.7630\)
88725.cf3	88725bm1	\([1, 0, 1, -986626, -316112977]\)	\(1408317602329/242911305\)	\(18320101143371015625\)	\([2]\)	\(1935360\)	\(2.4165\)	\(\Gamma_0(N)\)-optimal
88725.cf4	88725bm3	\([1, 0, 1, 5055124, 16057578773]\)	\(189425802193991/1586486902455\)	\(-119651082174248688984375\)	\([2]\)	\(7741440\)	\(3.1096\)