Elliptic curve isogeny class with Cremona label 3800a (LMFDB label 3800.e)

• Label: 3800a
• Number of curves: $4$
• Conductor: $3800$
• CM: no
• Rank: $1$

Elliptic curves in class 3800a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
3800.e4	3800a1	$[0, 0, 0, -50, 2625]$	$-55296/11875$	$-2968750000$	$[2]$	$1536$	$0.49689$	$\Gamma_0(N)$-optimal
3800.e3	3800a2	$[0, 0, 0, -3175, 68250]$	$884901456/9025$	$36100000000$	$[2, 2]$	$3072$	$0.84346$
3800.e2	3800a3	$[0, 0, 0, -5675, -54250]$	$1263284964/651605$	$10425680000000$	$[2]$	$6144$	$1.1900$
3800.e1	3800a4	$[0, 0, 0, -50675, 4390750]$	$899466517764/95$	$1520000000$	$[4]$	$6144$	$1.1900$

Rank

The elliptic curves in class 3800a have rank $1$.

Complex multiplication

The elliptic curves in class 3800a do not have complex multiplication.

Modular form 3800.2.a.a

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.