Elliptic curve isogeny class with Cremona label 630e (LMFDB label 630.d)

• Label: 630e
• Number of curves: $4$
• Conductor: $630$
• CM: no
• Rank: $1$

Elliptic curves in class 630e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
630.d4	630e1	$[1, -1, 0, 21, 53]$	$1367631/2800$	$-2041200$	$[2]$	$128$	$-0.10485$	$\Gamma_0(N)$-optimal
630.d3	630e2	$[1, -1, 0, -159, 665]$	$611960049/122500$	$89302500$	$[2, 2]$	$256$	$0.24172$
630.d2	630e3	$[1, -1, 0, -789, -7777]$	$74565301329/5468750$	$3986718750$	$[2]$	$512$	$0.58829$
630.d1	630e4	$[1, -1, 0, -2409, 46115]$	$2121328796049/120050$	$87516450$	$[2]$	$512$	$0.58829$

Rank

The elliptic curves in class 630e have rank $1$.

Complex multiplication

The elliptic curves in class 630e do not have complex multiplication.

Modular form 630.2.a.e

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.