Elliptic curve isogeny class with LMFDB label 110670.i (Cremona label 110670j)

• Label: 110670.i
• Number of curves: $2$
• Conductor: $110670$
• CM: no
• Rank: $1$

Elliptic curves in class 110670.i

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
110670.i1	110670j2	$[1, 1, 0, -38019667, -81933755981]$	$6077831506811167772920660921/618308289484887346301250$	$618308289484887346301250$	$[2]$	$22937600$	$3.3009$
110670.i2	110670j1	$[1, 1, 0, 2986583, -6228017231]$	$2946098419096782416239079/18468116719344435937500$	$-18468116719344435937500$	$[2]$	$11468800$	$2.9544$	$\Gamma_0(N)$-optimal

Rank

The elliptic curves in class 110670.i have rank $1$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1 + T$
$3$	$1 + T$
$5$	$1 - T$
$7$	$1 + T$
$17$	$1 + T$
$31$	$1 - T$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$11$	$1 - 2 T + 11 T^{2}$	1.11.ac
$13$	$1 - 4 T + 13 T^{2}$	1.13.ae
$19$	$1 - 6 T + 19 T^{2}$	1.19.ag
$23$	$1 + 8 T + 23 T^{2}$	1.23.i
$29$	$1 - 4 T + 29 T^{2}$	1.29.ae
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 110670.i do not have complex multiplication.

Modular form 110670.2.a.i

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.