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

• Label: 283920he
• Number of curves: $4$
• Conductor: $283920$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 283920he have rank \(0\).

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.g
\(19\)	\( 1 + 8 T + 19 T^{2}\)	1.19.i
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 283920.2.a.he

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 283920he

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
283920.he4	283920he1	\([0, 1, 0, -1946997680, -16752013318572]\)	\(41285728533151645510969/17760741842188800000\)	\(351140694304987052192563200000\)	\([2]\)	\(464486400\)	\(4.3656\)	\(\Gamma_0(N)\)-optimal
283920.he2	283920he2	\([0, 1, 0, -26660259760, -1674804307485100]\)	\(105997782562506306791694649/51649016225625000000\)	\(1021132539326434429440000000000\)	\([2, 2]\)	\(928972800\)	\(4.7122\)
283920.he3	283920he3	\([0, 1, 0, -22218453040, -2251171370749612]\)	\(-61354313914516350666047929/75227254486083984375000\)	\(-1487288684538759375000000000000000\)	\([2]\)	\(1857945600\)	\(5.0588\)
283920.he1	283920he4	\([0, 1, 0, -426514259760, -107213388658685100]\)	\(434014578033107719741685694649/103121648659575000\)	\(2038777863556606141132800000\)	\([2]\)	\(1857945600\)	\(5.0588\)