Elliptic curve isogeny class with Cremona label 33282y (LMFDB label 33282.s)

• Label: 33282y
• Number of curves: $2$
• Conductor: $33282$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 33282y have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1\)
\(43\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + T + 5 T^{2}\)	1.5.b
\(7\)	\( 1 - T + 7 T^{2}\)	1.7.ab
\(11\)	\( 1 + 3 T + 11 T^{2}\)	1.11.d
\(13\)	\( 1 + T + 13 T^{2}\)	1.13.b
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 - T + 19 T^{2}\)	1.19.ab
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + T + 29 T^{2}\)	1.29.b
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 33282y do not have complex multiplication.

Modular form 33282.2.a.y

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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 33282y

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
33282.s2	33282y1	\([1, -1, 1, -283244, -55164193]\)	\(294937/16\)	\(136331168037938064\)	\([]\)	\(433440\)	\(2.0438\)	\(\Gamma_0(N)\)-optimal
33282.s1	33282y2	\([1, -1, 1, -3861059, 2907266627]\)	\(747081097/4096\)	\(34900779017712144384\)	\([3]\)	\(1300320\)	\(2.5931\)