Elliptic curve isogeny class with Cremona label 26588c (LMFDB label 26588.b)

• Label: 26588c
• Number of curves: $2$
• Conductor: $26588$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 26588c have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(17\)	\(1\)
\(23\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - 3 T + 3 T^{2}\)	1.3.ad
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(13\)	\( 1 + T + 13 T^{2}\)	1.13.b
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(29\)	\( 1 + T + 29 T^{2}\)	1.29.b
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 26588c do not have complex multiplication.

Modular form 26588.2.a.c

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 26588c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
26588.b2	26588c1	\([0, -1, 0, 482, 1841]\)	\(32000/23\)	\(-8882625392\)	\([]\)	\(9216\)	\(0.59734\)	\(\Gamma_0(N)\)-optimal
26588.b1	26588c2	\([0, -1, 0, -5298, -179651]\)	\(-42592000/12167\)	\(-4698908832368\)	\([]\)	\(27648\)	\(1.1466\)