Elliptic curve isogeny class with Cremona label 233289f (LMFDB label 233289.f)

• Label: 233289f
• Number of curves: $2$
• Conductor: $233289$
• CM: no
• Rank: $2$

Rank

The elliptic curves in class 233289f have rank \(2\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1\)
\(7\)	\(1\)
\(23\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + 2 T + 2 T^{2}\)	1.2.c
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(11\)	\( 1 + 2 T + 11 T^{2}\)	1.11.c
\(13\)	\( 1 + T + 13 T^{2}\)	1.13.b
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 - T + 19 T^{2}\)	1.19.ab
\(29\)	\( 1 + 4 T + 29 T^{2}\)	1.29.e
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 233289f do not have complex multiplication.

Modular form 233289.2.a.f

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.

\(\left(\begin{array}{rr} 1 & 13 \\ 13 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 233289f

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
233289.f2	233289f1	\([0, 0, 1, -11109, -489722]\)	\(-28672/3\)	\(-15863969972907\)	\([]\)	\(608256\)	\(1.2720\)	\(\Gamma_0(N)\)-optimal
233289.f1	233289f2	\([0, 0, 1, -4343619, 3487180828]\)	\(-1713910976512/1594323\)	\(-8430764066371668987\)	\([]\)	\(7907328\)	\(2.5544\)