Elliptic curve isogeny class with Cremona label 26b (LMFDB label 26.b)

• Label: 26b
• Number of curves: $2$
• Conductor: $26$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 26b have rank $0$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1 - T$
$13$	$1 + T$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$3$	$1 + 3 T + 3 T^{2}$	1.3.d
$5$	$1 + T + 5 T^{2}$	1.5.b
$7$	$1 - T + 7 T^{2}$	1.7.ab
$11$	$1 + 2 T + 11 T^{2}$	1.11.c
$17$	$1 + 3 T + 17 T^{2}$	1.17.d
$19$	$1 - 6 T + 19 T^{2}$	1.19.ag
$23$	$1 + 4 T + 23 T^{2}$	1.23.e
$29$	$1 - 2 T + 29 T^{2}$	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 26b do not have complex multiplication.

Modular form 26.2.a.b

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.

$\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 26b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
26.b2	26b1	$[1, -1, 1, -3, 3]$	$-2146689/1664$	$-1664$	$[7]$	$2$	$-0.68316$	$\Gamma_0(N)$-optimal
26.b1	26b2	$[1, -1, 1, -213, -1257]$	$-1064019559329/125497034$	$-125497034$	$[]$	$14$	$0.28979$