Elliptic curve isogeny class with LMFDB label 82110.d (Cremona label 82110b)

• Label: 82110.d
• Number of curves: $2$
• Conductor: $82110$
• CM: no
• Rank: $1$

Elliptic curves in class 82110.d

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
82110.d1	82110b2	$[1, 1, 0, -3584833, -2613965123]$	$5094841618754165781496729/674331960579480$	$674331960579480$	$[2]$	$2242560$	$2.2597$
82110.d2	82110b1	$[1, 1, 0, -223433, -41149563]$	$-1233583919615644207129/14314037777726400$	$-14314037777726400$	$[2]$	$1121280$	$1.9132$	$\Gamma_0(N)$-optimal

Rank

The elliptic curves in class 82110.d have rank $1$.

L-function data

Bad L-factors:

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

Good L-factors:

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

See L-function page for more information

Complex multiplication

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

Modular form 82110.2.a.d

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.