Elliptic curve isogeny class with Cremona label 630c (LMFDB label 630.a)

• Label: 630c
• Number of curves: $8$
• Conductor: $630$
• CM: no
• Rank: $0$

Elliptic curves in class 630c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
630.a7	630c1	$[1, -1, 0, 1890, -24300]$	$1023887723039/928972800$	$-677221171200$	$[2]$	$1024$	$0.95744$	$\Gamma_0(N)$-optimal
630.a6	630c2	$[1, -1, 0, -9630, -210924]$	$135487869158881/51438240000$	$37498476960000$	$[2, 2]$	$2048$	$1.3040$
630.a4	630c3	$[1, -1, 0, -135630, -19186524]$	$378499465220294881/120530818800$	$87866966905200$	$[2]$	$4096$	$1.6506$
630.a5	630c4	$[1, -1, 0, -67950, 6682500]$	$47595748626367201/1215506250000$	$886104056250000$	$[2, 2]$	$4096$	$1.6506$
630.a2	630c5	$[1, -1, 0, -1080450, 432540000]$	$191342053882402567201/129708022500$	$94557148402500$	$[2, 2]$	$8192$	$1.9972$
630.a8	630c6	$[1, -1, 0, 11430, 21304296]$	$226523624554079/269165039062500$	$-196221313476562500$	$[2]$	$8192$	$1.9972$
630.a1	630c7	$[1, -1, 0, -17287200, 27669604050]$	$783736670177727068275201/360150$	$262549350$	$[2]$	$16384$	$2.3437$
630.a3	630c8	$[1, -1, 0, -1073700, 438205950]$	$-187778242790732059201/4984939585440150$	$-3634020957785869350$	$[2]$	$16384$	$2.3437$

Rank

The elliptic curves in class 630c have rank $0$.

Complex multiplication

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

Modular form 630.2.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.

$\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 4 & 8 & 8 & 16 & 16 \\ 2 & 1 & 2 & 2 & 4 & 4 & 8 & 8 \\ 4 & 2 & 1 & 4 & 8 & 8 & 16 & 16 \\ 4 & 2 & 4 & 1 & 2 & 2 & 4 & 4 \\ 8 & 4 & 8 & 2 & 1 & 4 & 2 & 2 \\ 8 & 4 & 8 & 2 & 4 & 1 & 8 & 8 \\ 16 & 8 & 16 & 4 & 2 & 8 & 1 & 4 \\ 16 & 8 & 16 & 4 & 2 & 8 & 4 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with Cremona labels.