Elliptic curve isogeny class with LMFDB label 9280.h (Cremona label 9280a)

• Label: 9280.h
• Number of curves: $4$
• Conductor: $9280$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 9280.h have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1 + T\)
\(29\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(7\)	\( 1 + 7 T^{2}\)	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
\(19\)	\( 1 - 8 T + 19 T^{2}\)	1.19.ai
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 9280.h do not have complex multiplication.

Modular form 9280.2.a.h

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 9280.h

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
9280.h1	9280a3	\([0, 0, 0, -3308, -60368]\)	\(61085802564/11328125\)	\(742400000000\)	\([2]\)	\(8192\)	\(0.99598\)
9280.h2	9280a2	\([0, 0, 0, -988, 11088]\)	\(6509904336/525625\)	\(8611840000\)	\([2, 2]\)	\(4096\)	\(0.64940\)
9280.h3	9280a1	\([0, 0, 0, -968, 11592]\)	\(97960237056/725\)	\(742400\)	\([2]\)	\(2048\)	\(0.30283\)	\(\Gamma_0(N)\)-optimal
9280.h4	9280a4	\([0, 0, 0, 1012, 50288]\)	\(1748981916/17682025\)	\(-1158809190400\)	\([2]\)	\(8192\)	\(0.99598\)