Elliptic curve isogeny class with LMFDB label 26208.i (Cremona label 26208k)

• Label: 26208.i
• Number of curves: $4$
• Conductor: $26208$
• CM: no
• Rank: $2$

Rank

The elliptic curves in class 26208.i have rank \(2\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 8 T + 23 T^{2}\)	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 26208.i do not have complex multiplication.

Modular form 26208.2.a.i

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 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, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 26208.i

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
26208.i1	26208k4	\([0, 0, 0, -4476, 115040]\)	\(3321287488/7371\)	\(22009688064\)	\([2]\)	\(24576\)	\(0.86724\)
26208.i2	26208k3	\([0, 0, 0, -3891, -92986]\)	\(17454600584/93639\)	\(34950569472\)	\([2]\)	\(24576\)	\(0.86724\)
26208.i3	26208k1	\([0, 0, 0, -381, 380]\)	\(131096512/74529\)	\(3477225024\)	\([2, 2]\)	\(12288\)	\(0.52066\)	\(\Gamma_0(N)\)-optimal
26208.i4	26208k2	\([0, 0, 0, 1509, 3026]\)	\(1018108216/599781\)	\(-223867058688\)	\([2]\)	\(24576\)	\(0.86724\)