Elliptic curve isogeny class with Cremona label 8670r (LMFDB label 8670.r)

• Label: 8670r
• Number of curves: $4$
• Conductor: $8670$
• CM: no
• Rank: $1$

Elliptic curves in class 8670r

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
8670.r4	8670r1	$[1, 1, 1, 1150, -1153]$	$6967871/4080$	$-98481281520$	$[4]$	$9216$	$0.79883$	$\Gamma_0(N)$-optimal
8670.r3	8670r2	$[1, 1, 1, -4630, -15025]$	$454756609/260100$	$6278181696900$	$[2, 2]$	$18432$	$1.1454$
8670.r1	8670r3	$[1, 1, 1, -53760, -4810113]$	$711882749089/1721250$	$41546790641250$	$[2]$	$36864$	$1.4920$
8670.r2	8670r4	$[1, 1, 1, -47980, 4007855]$	$506071034209/2505630$	$60479817013470$	$[2]$	$36864$	$1.4920$

Rank

The elliptic curves in class 8670r have rank $1$.

Complex multiplication

The elliptic curves in class 8670r do not have complex multiplication.

Modular form 8670.2.a.r

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.