Elliptic curve isogeny class with Cremona label 122018f (LMFDB label 122018.j)

• Label: 122018f
• Number of curves: $4$
• Conductor: $122018$
• CM: no
• Rank: $0$

Elliptic curves in class 122018f

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
122018.j4	122018f1	$[1, -1, 0, 232597, -14656459]$	$6128487/3952$	$-897426016167377008$	$[2]$	$2056320$	$2.1338$	$\Gamma_0(N)$-optimal
122018.j3	122018f2	$[1, -1, 0, -987583, -119835975]$	$469097433/244036$	$55416056498335530244$	$[2, 2]$	$4112640$	$2.4804$
122018.j2	122018f3	$[1, -1, 0, -8918753, 10166891515]$	$345505073913/3388346$	$769430630611504862234$	$[2]$	$8225280$	$2.8269$
122018.j1	122018f4	$[1, -1, 0, -12579293, -17152694649]$	$969417177273/1085318$	$246455619689965910822$	$[2]$	$8225280$	$2.8269$

Rank

The elliptic curves in class 122018f have rank $0$.

Complex multiplication

The elliptic curves in class 122018f do not have complex multiplication.

Modular form 122018.2.a.f

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.