Elliptic curve isogeny class with Cremona label 105840ek (LMFDB label 105840.gi)

• Label: 105840ek
• Number of curves: $2$
• Conductor: $105840$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 105840ek have rank \(0\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + 5 T + 11 T^{2}\)	1.11.f
\(13\)	\( 1 + 6 T + 13 T^{2}\)	1.13.g
\(17\)	\( 1 + 5 T + 17 T^{2}\)	1.17.f
\(19\)	\( 1 + 6 T + 19 T^{2}\)	1.19.g
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 105840ek do not have complex multiplication.

Modular form 105840.2.a.ek

Isogeny matrix

The \((i,j)\)-th 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 105840ek

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
105840.gi1	105840ek1	\([0, 0, 0, -1617, -36701]\)	\(-9199872/6125\)	\(-311299254000\)	\([]\)	\(82944\)	\(0.90612\)	\(\Gamma_0(N)\)-optimal
105840.gi2	105840ek2	\([0, 0, 0, 13083, 539539]\)	\(541416192/588245\)	\(-269074623187440\)	\([]\)	\(248832\)	\(1.4554\)