Elliptic curve isogeny class with LMFDB label 286650.he (Cremona label 286650he)

• Label: 286650.he
• Number of curves: $4$
• Conductor: $286650$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 286650.he have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 8 T + 19 T^{2}\)	1.19.i
\(23\)	\( 1 + 4 T + 23 T^{2}\)	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 286650.he do not have complex multiplication.

Modular form 286650.2.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 LMFDB 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 LMFDB labels.

Elliptic curves in class 286650.he

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
286650.he1	286650he4	\([1, -1, 0, -3648723568317, -1667548926470833659]\)	\(4008766897254067912673785886329/1423480510711669921875000000\)	\(1907600026919357478618621826171875000000\)	\([2]\)	\(15854469120\)	\(6.2383\)
286650.he2	286650he2	\([1, -1, 0, -1542327640317, 718254102190582341]\)	\(302773487204995438715379645049/8911747415025000000000000\)	\(11942593861226115125390625000000000000\)	\([2, 2]\)	\(7927234560\)	\(5.8917\)
286650.he3	286650he1	\([1, -1, 0, -1531263832317, 729328254851062341]\)	\(296304326013275547793071733369/268420373544960000000\)	\(359708972442534973440000000000000\)	\([2]\)	\(3963617280\)	\(5.5451\)	\(\Gamma_0(N)\)-optimal
286650.he4	286650he3	\([1, -1, 0, 387047359683, 2395311227815582341]\)	\(4784981304203817469820354951/1852343836482910078035000000\)	\(-2482317900209335627888582066171875000000\)	\([2]\)	\(15854469120\)	\(6.2383\)