Elliptic curve isogeny class with Cremona label 20691r (LMFDB label 20691.a)

• Label: 20691r
• Number of curves: $2$
• Conductor: $20691$
• CM: no
• Rank: $0$

Elliptic curves in class 20691r

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
20691.a2	20691r1	$[0, 0, 1, 21417, -1377918]$	$841232384/1121931$	$-1448937949928139$	$[]$	$129600$	$1.5949$	$\Gamma_0(N)$-optimal
20691.a1	20691r2	$[0, 0, 1, -4781073, -4023806328]$	$-9358714467168256/22284891$	$-28780222919156379$	$[]$	$648000$	$2.3997$

Rank

The elliptic curves in class 20691r have rank $0$.

L-function data

Bad L-factors:

Prime	L-Factor
$3$	$1$
$11$	$1$
$19$	$1 + T$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$2$	$1 - 2 T + 2 T^{2}$	1.2.ac
$5$	$1 + 5 T^{2}$	1.5.a
$7$	$1 - 2 T + 7 T^{2}$	1.7.ac
$13$	$1 - 5 T + 13 T^{2}$	1.13.af
$17$	$1 + 3 T + 17 T^{2}$	1.17.d
$23$	$1 + 6 T + 23 T^{2}$	1.23.g
$29$	$1 - 8 T + 29 T^{2}$	1.29.ai
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 20691r do not have complex multiplication.

Modular form 20691.2.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 Cremona numbering.

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

Isogeny graph

The vertices are labelled with Cremona labels.