Elliptic curve isogeny class with Cremona label 2550v (LMFDB label 2550.u)

• Label: 2550v
• Number of curves: $4$
• Conductor: $2550$
• CM: no
• Rank: $1$

Elliptic curves in class 2550v

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
2550.u2	2550v1	$[1, 1, 1, -6388, 193781]$	$1845026709625/793152$	$12393000000$	$[2]$	$3456$	$0.89684$	$\Gamma_0(N)$-optimal
2550.u3	2550v2	$[1, 1, 1, -5388, 257781]$	$-1107111813625/1228691592$	$-19198306125000$	$[2]$	$6912$	$1.2434$
2550.u1	2550v3	$[1, 1, 1, -18763, -755719]$	$46753267515625/11591221248$	$181112832000000$	$[2]$	$10368$	$1.4461$
2550.u4	2550v4	$[1, 1, 1, 45237, -4723719]$	$655215969476375/1001033261568$	$-15641144712000000$	$[2]$	$20736$	$1.7927$

Rank

The elliptic curves in class 2550v have rank $1$.

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$7$	$1 + T + 7 T^{2}$	1.7.b
$11$	$1 + 3 T + 11 T^{2}$	1.11.d
$13$	$1 - 4 T + 13 T^{2}$	1.13.ae
$19$	$1 + 5 T + 19 T^{2}$	1.19.f
$23$	$1 + 8 T + 23 T^{2}$	1.23.i
$29$	$1 + 4 T + 29 T^{2}$	1.29.e
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 2550v do not have complex multiplication.

Modular form 2550.2.a.v

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.

$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with Cremona labels.