Elliptic curve isogeny class with Cremona label 107800r (LMFDB label 107800.n)

• Label: 107800r
• Number of curves: $2$
• Conductor: $107800$
• CM: no
• Rank: $1$

Elliptic curves in class 107800r

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
107800.n2	107800r1	$[0, 1, 0, 53492, 643488]$	$35969456/21175$	$-9964870300000000$	$[2]$	$589824$	$1.7592$	$\Gamma_0(N)$-optimal
107800.n1	107800r2	$[0, 1, 0, -216008, 4955488]$	$592143556/336875$	$634128110000000000$	$[2]$	$1179648$	$2.1058$

Rank

The elliptic curves in class 107800r have rank $1$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1$
$5$	$1$
$7$	$1$
$11$	$1 - T$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$3$	$1 + 2 T + 3 T^{2}$	1.3.c
$13$	$1 - 6 T + 13 T^{2}$	1.13.ag
$17$	$1 + 2 T + 17 T^{2}$	1.17.c
$19$	$1 + 4 T + 19 T^{2}$	1.19.e
$23$	$1 - 6 T + 23 T^{2}$	1.23.ag
$29$	$1 + 2 T + 29 T^{2}$	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 107800r do not have complex multiplication.

Modular form 107800.2.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.