Elliptic curve isogeny class with Cremona label 35490bl (LMFDB label 35490.bp)

• Label: 35490bl
• Number of curves: $4$
• Conductor: $35490$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 35490bl have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + 3 T + 11 T^{2}\)	1.11.d
\(17\)	\( 1 + T + 17 T^{2}\)	1.17.b
\(19\)	\( 1 - 5 T + 19 T^{2}\)	1.19.af
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 - 3 T + 29 T^{2}\)	1.29.ad
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 35490bl do not have complex multiplication.

Modular form 35490.2.a.bl

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 35490bl

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
35490.bp3	35490bl1	\([1, 0, 1, -5060878, -4382567824]\)	\(2969894891179808929/22997520\)	\(111004636513680\)	\([2]\)	\(860160\)	\(2.2871\)	\(\Gamma_0(N)\)-optimal
35490.bp2	35490bl2	\([1, 0, 1, -5064258, -4376421632]\)	\(2975849362756797409/8263842596100\)	\(39887989817438844900\)	\([2, 2]\)	\(1720320\)	\(2.6337\)
35490.bp4	35490bl3	\([1, 0, 1, -3064988, -7866347344]\)	\(-659704930833045889/5156082432978750\)	\(-24887425092243727308750\)	\([2]\)	\(3440640\)	\(2.9803\)
35490.bp1	35490bl4	\([1, 0, 1, -7117608, -493126112]\)	\(8261629364934163009/4759323790524030\)	\(22972346906015502720270\)	\([2]\)	\(3440640\)	\(2.9803\)