Elliptic curve isogeny class with LMFDB label 55800.bd (Cremona label 55800bn)

• Label: 55800.bd
• Number of curves: $4$
• Conductor: $55800$
• CM: no
• Rank: $1$

Elliptic curves in class 55800.bd

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
55800.bd1	55800bn4	$[0, 0, 0, -1494075, -702882250]$	$15811147933922/1016955$	$23723526240000000$	$[2]$	$589824$	$2.1996$
55800.bd2	55800bn3	$[0, 0, 0, -504075, 129347750]$	$607199886722/41558445$	$969475404960000000$	$[2]$	$589824$	$2.1996$
55800.bd3	55800bn2	$[0, 0, 0, -99075, -9567250]$	$9220796644/1946025$	$22698435600000000$	$[2, 2]$	$294912$	$1.8531$
55800.bd4	55800bn1	$[0, 0, 0, 13425, -904750]$	$91765424/174375$	$-508477500000000$	$[2]$	$147456$	$1.5065$	$\Gamma_0(N)$-optimal

Rank

The elliptic curves in class 55800.bd have rank $1$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1$
$3$	$1$
$5$	$1$
$31$	$1 + T$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$7$	$1 + 7 T^{2}$	1.7.a
$11$	$1 + 11 T^{2}$	1.11.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.ae
$29$	$1 + 2 T + 29 T^{2}$	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 55800.bd do not have complex multiplication.

Modular form 55800.2.a.bd

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.