Elliptic curve isogeny class with Cremona label 209814r (LMFDB label 209814.dj)

• Label: 209814r
• Number of curves: $2$
• Conductor: $209814$
• CM: no
• Rank: $0$

Elliptic curves in class 209814r

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
209814.dj1	209814r1	$[1, 0, 0, -88151, -6402747]$	$1771561/612$	$26169839635627908$	$[2]$	$3317760$	$1.8520$	$\Gamma_0(N)$-optimal
209814.dj2	209814r2	$[1, 0, 0, 261539, -44518957]$	$46268279/46818$	$-2001992732125534962$	$[2]$	$6635520$	$2.1986$

Rank

The elliptic curves in class 209814r have rank $0$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1 + T$
$3$	$1 + T$
$11$	$1$
$17$	$1$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$5$	$1 - 2 T + 5 T^{2}$	1.5.ac
$7$	$1 + 4 T + 7 T^{2}$	1.7.e
$13$	$1 - 4 T + 13 T^{2}$	1.13.ae
$19$	$1 - 8 T + 19 T^{2}$	1.19.ai
$23$	$1 + 23 T^{2}$	1.23.a
$29$	$1 + 29 T^{2}$	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 209814r do not have complex multiplication.

Modular form 209814.2.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.

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

Isogeny graph

The vertices are labelled with Cremona labels.