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

• Label: 235200hr
• Number of curves: $2$
• Conductor: $235200$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 235200hr have rank \(0\).

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 \(\mathbb{F}_p\)
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 - T + 13 T^{2}\)	1.13.ab
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 - 5 T + 19 T^{2}\)	1.19.af
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 235200.2.a.hr

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 235200hr

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
235200.hr2	235200hr1	\([0, -1, 0, 467, 7687]\)	\(229376/675\)	\(-33075000000\)	\([]\)	\(165888\)	\(0.70190\)	\(\Gamma_0(N)\)-optimal
235200.hr1	235200hr2	\([0, -1, 0, -20533, 1141687]\)	\(-19539165184/46875\)	\(-2296875000000\)	\([]\)	\(497664\)	\(1.2512\)