Elliptic curve isogeny class with LMFDB label 1872.c (Cremona label 1872r)

• Label: 1872.c
• Number of curves: $4$
• Conductor: $1872$
• CM: no
• Rank: $0$

Elliptic curves in class 1872.c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
1872.c1	1872r4	$[0, 0, 0, -2986491, 1986506026]$	$986551739719628473/111045168$	$331579094925312$	$[4]$	$30720$	$2.2105$
1872.c2	1872r3	$[0, 0, 0, -336891, -25526486]$	$1416134368422073/725251155408$	$2165588346029801472$	$[2]$	$30720$	$2.2105$
1872.c3	1872r2	$[0, 0, 0, -187131, 30873130]$	$242702053576633/2554695936$	$7628281189761024$	$[2, 2]$	$15360$	$1.8640$
1872.c4	1872r1	$[0, 0, 0, -2811, 1197610]$	$-822656953/207028224$	$-618182964412416$	$[2]$	$7680$	$1.5174$	$\Gamma_0(N)$-optimal

Rank

The elliptic curves in class 1872.c have rank $0$.

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$5$	$1 + 2 T + 5 T^{2}$	1.5.c
$7$	$1 + 4 T + 7 T^{2}$	1.7.e
$11$	$1 + 4 T + 11 T^{2}$	1.11.e
$17$	$1 + 2 T + 17 T^{2}$	1.17.c
$19$	$1 - 8 T + 19 T^{2}$	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 1872.c do not have complex multiplication.

Modular form 1872.2.a.c

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.