Elliptic curve isogeny class with Cremona label 11a (LMFDB label 11.a)

• Label: 11a
• Number of curves: $3$
• Conductor: $11$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 11a have rank $0$.

L-function data

Bad L-factors:

Prime	L-Factor
$11$	$1 - T$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$2$	$1 + 2 T + 2 T^{2}$	1.2.c
$3$	$1 + T + 3 T^{2}$	1.3.b
$5$	$1 - T + 5 T^{2}$	1.5.ab
$7$	$1 + 2 T + 7 T^{2}$	1.7.c
$13$	$1 - 4 T + 13 T^{2}$	1.13.ae
$17$	$1 + 2 T + 17 T^{2}$	1.17.c
$19$	$1 + 19 T^{2}$	1.19.a
$23$	$1 + T + 23 T^{2}$	1.23.b
$29$	$1 + 29 T^{2}$	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 11a do not have complex multiplication.

Modular form 11.2.a.a

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.

$\left(\begin{array}{rrr} 1 & 5 & 5 \\ 5 & 1 & 25 \\ 5 & 25 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 11a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
11.a2	11a1	$[0, -1, 1, -10, -20]$	$-122023936/161051$	$-161051$	$[5]$	$1$	$-0.30801$	$\Gamma_0(N)$-optimal
11.a1	11a2	$[0, -1, 1, -7820, -263580]$	$-52893159101157376/11$	$-11$	$[]$	$5$	$0.49671$
11.a3	11a3	$[0, -1, 1, 0, 0]$	$-4096/11$	$-11$	$[5]$	$5$	$-1.1127$