Elliptic curve isogeny class with LMFDB label 119700.by (Cremona label 119700bk)

• Label: 119700.by
• Number of curves: $2$
• Conductor: $119700$
• CM: no
• Rank: $1$

Elliptic curves in class 119700.by

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
119700.by1	119700bk2	$[0, 0, 0, -330375, 51250750]$	$1367595682000/402300927$	$1173109503132000000$	$[2]$	$1990656$	$2.1730$
119700.by2	119700bk1	$[0, 0, 0, 55500, 5331625]$	$103737344000/127413867$	$-23221177260750000$	$[2]$	$995328$	$1.8264$	$\Gamma_0(N)$-optimal

Rank

The elliptic curves in class 119700.by have rank $1$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1$
$3$	$1$
$5$	$1$
$7$	$1 - T$
$19$	$1 - T$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$11$	$1 - 2 T + 11 T^{2}$	1.11.ac
$13$	$1 + 6 T + 13 T^{2}$	1.13.g
$17$	$1 + 8 T + 17 T^{2}$	1.17.i
$23$	$1 + 2 T + 23 T^{2}$	1.23.c
$29$	$1 + 6 T + 29 T^{2}$	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 119700.by do not have complex multiplication.

Modular form 119700.2.a.by

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 LMFDB numbering.

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

Isogeny graph

The vertices are labelled with LMFDB labels.