Elliptic curve isogeny class with LMFDB label 82110.u (Cremona label 82110s)

• Label: 82110.u
• Number of curves: $2$
• Conductor: $82110$
• CM: no
• Rank: $2$

Elliptic curves in class 82110.u

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
82110.u1	82110s2	$[1, 0, 1, -142605354, -648136131428]$	$320723808872496523935142301209/4135958612138279753487360$	$4135958612138279753487360$	$[2]$	$23961600$	$3.5318$
82110.u2	82110s1	$[1, 0, 1, -16832554, 10611485852]$	$527440803339012896847466009/256574315980928345702400$	$256574315980928345702400$	$[2]$	$11980800$	$3.1853$	$\Gamma_0(N)$-optimal

Rank

The elliptic curves in class 82110.u have rank $2$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1 + T$
$3$	$1 - T$
$5$	$1 + T$
$7$	$1 + T$
$17$	$1 - T$
$23$	$1 - T$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$11$	$1 + 2 T + 11 T^{2}$	1.11.c
$13$	$1 + 4 T + 13 T^{2}$	1.13.e
$19$	$1 + 4 T + 19 T^{2}$	1.19.e
$29$	$1 - 2 T + 29 T^{2}$	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 82110.u do not have complex multiplication.

Modular form 82110.2.a.u

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.