Elliptic curve isogeny class with Cremona label 20280s (LMFDB label 20280.n)

• Label: 20280s
• Number of curves: $4$
• Conductor: $20280$
• CM: no
• Rank: $1$

Elliptic curves in class 20280s

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
20280.n4	20280s1	$[0, -1, 0, 14140, 452100]$	$253012016/219375$	$-271073593440000$	$[4]$	$64512$	$1.4570$	$\Gamma_0(N)$-optimal
20280.n3	20280s2	$[0, -1, 0, -70360, 4068700]$	$7793764996/3080025$	$15223493007590400$	$[2, 2]$	$129024$	$1.8036$
20280.n2	20280s3	$[0, -1, 0, -509760, -137066580]$	$1481943889298/34543665$	$341474658539489280$	$[2]$	$258048$	$2.1501$
20280.n1	20280s4	$[0, -1, 0, -982960, 375314380]$	$10625310339698/3855735$	$38115115826411520$	$[2]$	$258048$	$2.1501$

Rank

The elliptic curves in class 20280s have rank $1$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1$
$3$	$1 - T$
$5$	$1 + T$
$13$	$1$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$7$	$1 + 4 T + 7 T^{2}$	1.7.e
$11$	$1 + 11 T^{2}$	1.11.a
$17$	$1 - 2 T + 17 T^{2}$	1.17.ac
$19$	$1 + 19 T^{2}$	1.19.a
$23$	$1 + 23 T^{2}$	1.23.a
$29$	$1 + 2 T + 29 T^{2}$	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 20280s do not have complex multiplication.

Modular form 20280.2.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 Cremona numbering.

$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with Cremona labels.