Elliptic curve isogeny class with Cremona label 235200ok (LMFDB label 235200.ok)

• Label: 235200ok
• Number of curves: $2$
• Conductor: $235200$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 235200ok have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(5\)	\(1\)
\(7\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 - 6 T + 11 T^{2}\)	1.11.ag
\(13\)	\( 1 - 6 T + 13 T^{2}\)	1.13.ag
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 8 T + 29 T^{2}\)	1.29.ai
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 235200ok do not have complex multiplication.

Modular form 235200.2.a.ok

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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

Elliptic curves in class 235200ok

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
235200.ok1	235200ok1	\([0, -1, 0, -83772033, -168274884063]\)	\(393349474783/153600000\)	\(25388294288179200000000000\)	\([2]\)	\(72253440\)	\(3.5734\)	\(\Gamma_0(N)\)-optimal
235200.ok2	235200ok2	\([0, -1, 0, 267459967, -1212487620063]\)	\(12801408679457/11250000000\)	\(-1859494210560000000000000000\)	\([2]\)	\(144506880\)	\(3.9200\)