Elliptic curve isogeny class with Cremona label 26010bn (LMFDB label 26010.bn)

• Label: 26010bn
• Number of curves: $2$
• Conductor: $26010$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 26010bn have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1\)
\(5\)	\(1 + T\)
\(17\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(13\)	\( 1 - T + 13 T^{2}\)	1.13.ab
\(19\)	\( 1 + 7 T + 19 T^{2}\)	1.19.h
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 + 3 T + 29 T^{2}\)	1.29.d
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 26010bn do not have complex multiplication.

Modular form 26010.2.a.bn

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.

\(\left(\begin{array}{rr} 1 & 13 \\ 13 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 26010bn

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
26010.bn2	26010bn1	\([1, -1, 1, -1253, -24803]\)	\(-60698457/40960\)	\(-146701393920\)	\([]\)	\(34944\)	\(0.84324\)	\(\Gamma_0(N)\)-optimal
26010.bn1	26010bn2	\([1, -1, 1, -1134983, 465711481]\)	\(-45145776875761017/2441406250\)	\(-8744084472656250\)	\([]\)	\(454272\)	\(2.1257\)