Elliptic curve isogeny class with Cremona label 880c (LMFDB label 880.g)

• Label: 880c
• Number of curves: $4$
• Conductor: $880$
• CM: no
• Rank: $1$

Elliptic curves in class 880c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
880.g3	880c1	$[0, 0, 0, -5042, -137801]$	$885956203616256/15125$	$242000$	$[2]$	$576$	$0.57496$	$\Gamma_0(N)$-optimal
880.g2	880c2	$[0, 0, 0, -5047, -137514]$	$55537159171536/228765625$	$58564000000$	$[2, 2]$	$1152$	$0.92153$
880.g1	880c3	$[0, 0, 0, -7547, 12986]$	$46424454082884/26794860125$	$27437936768000$	$[4]$	$2304$	$1.2681$
880.g4	880c4	$[0, 0, 0, -2627, -269646]$	$-1957960715364/29541015625$	$-30250000000000$	$[4]$	$2304$	$1.2681$

Rank

The elliptic curves in class 880c have rank $1$.

Complex multiplication

The elliptic curves in class 880c do not have complex multiplication.

Modular form 880.2.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.