Elliptic curve isogeny class with LMFDB label 880.h (Cremona label 880i)

• Label: 880.h
• Number of curves: $4$
• Conductor: $880$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 880.h have rank $0$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1$
$5$	$1 - T$
$11$	$1 - T$

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 880.h do not have complex multiplication.

Modular form 880.2.a.h

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.

Elliptic curves in class 880.h

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
880.h1	880i3	$[0, 0, 0, -947, -11214]$	$22930509321/6875$	$28160000$	$[2]$	$256$	$0.40748$
880.h2	880i4	$[0, 0, 0, -467, 3794]$	$2749884201/73205$	$299847680$	$[4]$	$256$	$0.40748$
880.h3	880i2	$[0, 0, 0, -67, -126]$	$8120601/3025$	$12390400$	$[2, 2]$	$128$	$0.060908$
880.h4	880i1	$[0, 0, 0, 13, -14]$	$59319/55$	$-225280$	$[2]$	$64$	$-0.28567$	$\Gamma_0(N)$-optimal