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

• Label: 235200.hs
• Number of curves: $4$
• Conductor: $235200$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 235200.hs 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 \(\mathbb{F}_p\)
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 235200.2.a.hs

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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 235200.hs

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
235200.hs1	235200hs3	\([0, -1, 0, -2353633, 1390595137]\)	\(23937672968/45\)	\(2710632960000000\)	\([2]\)	\(3538944\)	\(2.2166\)
235200.hs2	235200hs4	\([0, -1, 0, -393633, -66664863]\)	\(111980168/32805\)	\(1976051427840000000\)	\([2]\)	\(3538944\)	\(2.2166\)
235200.hs3	235200hs2	\([0, -1, 0, -148633, 21290137]\)	\(48228544/2025\)	\(15247310400000000\)	\([2, 2]\)	\(1769472\)	\(1.8700\)
235200.hs4	235200hs1	\([0, -1, 0, 4492, 1230762]\)	\(85184/5625\)	\(-661775625000000\)	\([2]\)	\(884736\)	\(1.5234\)	\(\Gamma_0(N)\)-optimal