Elliptic curve isogeny class with LMFDB label 23520.h (Cremona label 23520bc)

• Label: 23520.h
• Number of curves: $4$
• Conductor: $23520$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 23520.h have rank $1$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1$
$3$	$1 + T$
$5$	$1 + T$
$7$	$1$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$11$	$1 + 11 T^{2}$	1.11.a
$13$	$1 + 2 T + 13 T^{2}$	1.13.c
$17$	$1 - 2 T + 17 T^{2}$	1.17.ac
$19$	$1 + 4 T + 19 T^{2}$	1.19.e
$23$	$1 - 8 T + 23 T^{2}$	1.23.ai
$29$	$1 + 2 T + 29 T^{2}$	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 23520.h do not have complex multiplication.

Modular form 23520.2.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 23520.h

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
23520.h1	23520bc4	$[0, -1, 0, -691896, 221748696]$	$608119035935048/826875$	$49807880640000$	$[2]$	$147456$	$1.9025$
23520.h2	23520bc3	$[0, -1, 0, -109776, -9315900]$	$2428799546888/778248135$	$46878778795322880$	$[2]$	$147456$	$1.9025$
23520.h3	23520bc1	$[0, -1, 0, -43626, 3411360]$	$1219555693504/43758225$	$329479130433600$	$[2, 2]$	$73728$	$1.5559$	$\Gamma_0(N)$-optimal
23520.h4	23520bc2	$[0, -1, 0, 16399, 12018945]$	$1012048064/130203045$	$-62743584936775680$	$[2]$	$147456$	$1.9025$