Elliptic curve isogeny class with Cremona label 58800gb (LMFDB label 58800.m)

• Label: 58800gb
• Number of curves: $6$
• Conductor: $58800$
• CM: no
• Rank: $1$

Elliptic curves in class 58800gb

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
58800.m6	58800gb1	$[0, -1, 0, 19192, -231888]$	$103823/63$	$-474360768000000$	$[2]$	$196608$	$1.5053$	$\Gamma_0(N)$-optimal
58800.m5	58800gb2	$[0, -1, 0, -78808, -1799888]$	$7189057/3969$	$29884728384000000$	$[2, 2]$	$393216$	$1.8519$
58800.m3	58800gb3	$[0, -1, 0, -764808, 256136112]$	$6570725617/45927$	$345808999872000000$	$[2]$	$786432$	$2.1985$
58800.m2	58800gb4	$[0, -1, 0, -960808, -361655888]$	$13027640977/21609$	$162705743424000000$	$[2, 2]$	$786432$	$2.1985$
58800.m4	58800gb5	$[0, -1, 0, -666808, -587447888]$	$-4354703137/17294403$	$-130218829987008000000$	$[2]$	$1572864$	$2.5450$
58800.m1	58800gb6	$[0, -1, 0, -15366808, -23180759888]$	$53297461115137/147$	$1106841792000000$	$[2]$	$1572864$	$2.5450$

Rank

The elliptic curves in class 58800gb have rank $1$.

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$11$	$1 + 3 T + 11 T^{2}$	1.11.d
$13$	$1 - T + 13 T^{2}$	1.13.ab
$17$	$1 + 17 T^{2}$	1.17.a
$19$	$1 + 7 T + 19 T^{2}$	1.19.h
$23$	$1 + 5 T + 23 T^{2}$	1.23.f
$29$	$1 + 29 T^{2}$	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 58800gb do not have complex multiplication.

Modular form 58800.2.a.gb

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.

$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with Cremona labels.