Elliptic curve isogeny class with LMFDB label 283920.hh (Cremona label 283920hh)

• Label: 283920.hh
• Number of curves: $4$
• Conductor: $283920$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 283920.hh have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(5\)	\(1 - T\)
\(7\)	\(1 + T\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 10 T + 29 T^{2}\)	1.29.k
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 283920.hh do not have complex multiplication.

Modular form 283920.2.a.hh

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 283920.hh

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
283920.hh1	283920hh3	\([0, 1, 0, -4221000, 3336471828]\)	\(841356017734178/1404585\)	\(13884750887454720\)	\([2]\)	\(6881280\)	\(2.3596\)
283920.hh2	283920hh4	\([0, 1, 0, -692280, -153261900]\)	\(3711757787138/1124589375\)	\(11116908782703360000\)	\([2]\)	\(6881280\)	\(2.3596\)
283920.hh3	283920hh2	\([0, 1, 0, -266400, 50990148]\)	\(423026849956/16769025\)	\(82883461930214400\)	\([2, 2]\)	\(3440640\)	\(2.0131\)
283920.hh4	283920hh1	\([0, 1, 0, 7380, 2914380]\)	\(35969456/2985255\)	\(-3688769459531520\)	\([2]\)	\(1720320\)	\(1.6665\)	\(\Gamma_0(N)\)-optimal