Elliptic curve isogeny class with Cremona label 4400c (LMFDB label 4400.r)

• Label: 4400c
• Number of curves: $4$
• Conductor: $4400$
• CM: no
• Rank: $0$

Elliptic curves in class 4400c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
4400.r3	4400c1	$[0, 0, 0, -126050, -17225125]$	$885956203616256/15125$	$3781250000$	$[2]$	$13824$	$1.3797$	$\Gamma_0(N)$-optimal
4400.r2	4400c2	$[0, 0, 0, -126175, -17189250]$	$55537159171536/228765625$	$915062500000000$	$[2, 2]$	$27648$	$1.7263$
4400.r1	4400c3	$[0, 0, 0, -188675, 1623250]$	$46424454082884/26794860125$	$428717762000000000$	$[4]$	$55296$	$2.0728$
4400.r4	4400c4	$[0, 0, 0, -65675, -33705750]$	$-1957960715364/29541015625$	$-472656250000000000$	$[2]$	$55296$	$2.0728$

Rank

The elliptic curves in class 4400c have rank $0$.

Complex multiplication

The elliptic curves in class 4400c do not have complex multiplication.

Modular form 4400.2.a.c

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.