Elliptic curve isogeny class with LMFDB label 68450.s (Cremona label 68450e)

• Label: 68450.s
• Number of curves: $3$
• Conductor: $68450$
• CM: no
• Rank: $1$

Elliptic curves in class 68450.s

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
68450.s1	68450e1	$[1, 1, 0, -1831750, 953472750]$	$-16954786009/370$	$-14833105802031250$	$[]$	$1181952$	$2.2190$	$\Gamma_0(N)$-optimal
68450.s2	68450e2	$[1, 1, 0, -633875, 2176503125]$	$-702595369/50653000$	$-2030652184298078125000$	$[]$	$3545856$	$2.7683$
68450.s3	68450e3	$[1, 1, 0, 5697750, -58360163500]$	$510273943271/37000000000$	$-1483310580203125000000000$	$[]$	$10637568$	$3.3176$

Rank

The elliptic curves in class 68450.s have rank $1$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1 + T$
$5$	$1$
$37$	$1$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$3$	$1 - 2 T + 3 T^{2}$	1.3.ac
$7$	$1 - T + 7 T^{2}$	1.7.ab
$11$	$1 - 3 T + 11 T^{2}$	1.11.ad
$13$	$1 + 4 T + 13 T^{2}$	1.13.e
$17$	$1 - 3 T + 17 T^{2}$	1.17.ad
$19$	$1 + 2 T + 19 T^{2}$	1.19.c
$23$	$1 - 6 T + 23 T^{2}$	1.23.ag
$29$	$1 + 3 T + 29 T^{2}$	1.29.d
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 68450.s do not have complex multiplication.

Modular form 68450.2.a.s

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.

$\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with LMFDB labels.