Elliptic curve isogeny class with LMFDB label 26928.r (Cremona label 26928bd)

• Label: 26928.r
• Number of curves: $2$
• Conductor: $26928$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 26928.r have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(11\)	\(1 + T\)
\(17\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 - 2 T + 23 T^{2}\)	1.23.ac
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 26928.r do not have complex multiplication.

Modular form 26928.2.a.r

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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 26928.r

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
26928.r1	26928bd2	\([0, 0, 0, -26211, 1633250]\)	\(666940371553/37026\)	\(110559043584\)	\([2]\)	\(36864\)	\(1.1844\)
26928.r2	26928bd1	\([0, 0, 0, -1731, 22466]\)	\(192100033/38148\)	\(113909317632\)	\([2]\)	\(18432\)	\(0.83787\)	\(\Gamma_0(N)\)-optimal