Elliptic curve isogeny class with Cremona label 10608x (LMFDB label 10608.l)

• Label: 10608x
• Number of curves: $2$
• Conductor: $10608$
• CM: no
• Rank: $2$

Elliptic curves in class 10608x

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
10608.l2	10608x1	$[0, 1, 0, -4200, 103284]$	$2000852317801/2094417$	$8578732032$	$[2]$	$18432$	$0.82332$	$\Gamma_0(N)$-optimal
10608.l1	10608x2	$[0, 1, 0, -5240, 47124]$	$3885442650361/1996623837$	$8178171236352$	$[2]$	$36864$	$1.1699$

Rank

The elliptic curves in class 10608x have rank $2$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1$
$3$	$1 - T$
$13$	$1 + T$
$17$	$1 - T$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$5$	$1 + 5 T^{2}$	1.5.a
$7$	$1 - 2 T + 7 T^{2}$	1.7.ac
$11$	$1 - 2 T + 11 T^{2}$	1.11.ac
$19$	$1 - 8 T + 19 T^{2}$	1.19.ai
$23$	$1 + 23 T^{2}$	1.23.a
$29$	$1 + 6 T + 29 T^{2}$	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 10608x do not have complex multiplication.

Modular form 10608.2.a.x

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.