Elliptic curve isogeny class with Cremona label 33856be (LMFDB label 33856.bg)

• Label: 33856be
• Number of curves: $2$
• Conductor: $33856$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 33856be have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(23\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - T + 3 T^{2}\)	1.3.ab
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(11\)	\( 1 - 6 T + 11 T^{2}\)	1.11.ag
\(13\)	\( 1 - T + 13 T^{2}\)	1.13.ab
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(29\)	\( 1 + 9 T + 29 T^{2}\)	1.29.j
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 33856be do not have complex multiplication.

Modular form 33856.2.a.be

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 Cremona numbering.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 33856be

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
33856.bg2	33856be1	\([0, 1, 0, 3527, 40831]\)	\(32000/23\)	\(-3486541257728\)	\([]\)	\(33792\)	\(1.0951\)	\(\Gamma_0(N)\)-optimal
33856.bg1	33856be2	\([0, 1, 0, -38793, -3607153]\)	\(-42592000/12167\)	\(-1844380325338112\)	\([]\)	\(101376\)	\(1.6444\)