Elliptic curve isogeny class with LMFDB label 9675.s (Cremona label 9675m)

• Label: 9675.s
• Number of curves: $4$
• Conductor: $9675$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 9675.s have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 - T + 2 T^{2}\)	1.2.ab
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 9675.s do not have complex multiplication.

Modular form 9675.2.a.s

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 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, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 9675.s

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
9675.s1	9675m3	\([1, -1, 0, -55017, -4892234]\)	\(1616855892553/22851963\)	\(260298141046875\)	\([2]\)	\(30720\)	\(1.5709\)
9675.s2	9675m2	\([1, -1, 0, -6642, 90391]\)	\(2845178713/1347921\)	\(15353662640625\)	\([2, 2]\)	\(15360\)	\(1.2243\)
9675.s3	9675m1	\([1, -1, 0, -5517, 159016]\)	\(1630532233/1161\)	\(13224515625\)	\([2]\)	\(7680\)	\(0.87770\)	\(\Gamma_0(N)\)-optimal
9675.s4	9675m4	\([1, -1, 0, 23733, 667516]\)	\(129784785047/92307627\)	\(-1051441563796875\)	\([2]\)	\(30720\)	\(1.5709\)