Elliptic curve search results

Results (12 matches)

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Label	Class	Class size	Class degree	Base field	Field degree	Field signature	Conductor	Conductor norm	Discriminant norm	Root analytic conductor	Bad primes	Rank	Torsion	CM	CM	Sato-Tate	$\Q$-curve	Base change	Semistable	Potentially good	Nonmax $\ell$	mod-$\ell$ images	$Ш_{\textrm{an}}$	Tamagawa	Regulator	Period	Leading coeff	j-invariant	Weierstrass coefficients	Weierstrass equation
512.1-a1	512.1-a	$4$	$4$	$\Q(\sqrt{3})$	$2$	$[2, 0]$	512.1	$2^{9}$	$- 2^{17}$	$1.47247$	$(a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$2$	2B	$1$	$1$	$1$	$18.70900640$	1.350206235	$-2002968 a + 3470040$	$\bigl[0$ , $-a$ , $0$ , $3064 a - 5306$ , $-119716 a + 207354\bigr]$	${y}^2={x}^{3}-a{x}^{2}+\left(3064a-5306\right){x}-119716a+207354$
512.1-b1	512.1-b	$4$	$4$	$\Q(\sqrt{3})$	$2$	$[2, 0]$	512.1	$2^{9}$	$- 2^{17}$	$1.47247$	$(a+1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$2$	2B	$1$	$2^{2}$	$0.648148600$	$5.952999858$	2.227664748	$-2002968 a + 3470040$	$\bigl[0$ , $-a$ , $0$ , $220 a - 380$ , $2464 a - 4268\bigr]$	${y}^2={x}^{3}-a{x}^{2}+\left(220a-380\right){x}+2464a-4268$
512.1-g1	512.1-g	$4$	$4$	$\Q(\sqrt{3})$	$2$	$[2, 0]$	512.1	$2^{9}$	$- 2^{17}$	$1.47247$	$(a+1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$2$	2B	$1$	$1$	$2.592594401$	$5.952999858$	2.227664748	$-2002968 a + 3470040$	$\bigl[0$ , $a$ , $0$ , $3064 a - 5306$ , $119716 a - 207354\bigr]$	${y}^2={x}^{3}+a{x}^{2}+\left(3064a-5306\right){x}+119716a-207354$
512.1-h1	512.1-h	$4$	$4$	$\Q(\sqrt{3})$	$2$	$[2, 0]$	512.1	$2^{9}$	$- 2^{17}$	$1.47247$	$(a+1)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$2$	2B	$1$	$2^{2}$	$1$	$18.70900640$	1.350206235	$-2002968 a + 3470040$	$\bigl[0$ , $a$ , $0$ , $220 a - 380$ , $-2464 a + 4268\bigr]$	${y}^2={x}^{3}+a{x}^{2}+\left(220a-380\right){x}-2464a+4268$
1024.1-c1	1024.1-c	$4$	$4$	$\Q(\sqrt{3})$	$2$	$[2, 0]$	1024.1	$2^{10}$	$- 2^{23}$	$1.75107$	$(a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$2$	2B	$1$	$2^{2}$	$1$	$5.276710919$	1.523255234	$-2002968 a + 3470040$	$\bigl[0$ , $-a$ , $0$ , $1642 a - 2843$ , $48607 a - 84190\bigr]$	${y}^2={x}^{3}-a{x}^{2}+\left(1642a-2843\right){x}+48607a-84190$
1024.1-d1	1024.1-d	$4$	$4$	$\Q(\sqrt{3})$	$2$	$[2, 0]$	1024.1	$2^{10}$	$- 2^{23}$	$1.75107$	$(a+1)$	$1$	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$2$	2B	$1$	$2^{2}$	$1.741115149$	$10.55342183$	2.652162765	$-2002968 a + 3470040$	$\bigl[0$ , $-a$ , $0$ , $118 a - 203$ , $-849 a + 1470\bigr]$	${y}^2={x}^{3}-a{x}^{2}+\left(118a-203\right){x}-849a+1470$
1024.1-q1	1024.1-q	$4$	$4$	$\Q(\sqrt{3})$	$2$	$[2, 0]$	1024.1	$2^{10}$	$- 2^{23}$	$1.75107$	$(a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$2$	2B	$1$	$2$	$1$	$10.55342183$	1.523255234	$-2002968 a + 3470040$	$\bigl[0$ , $a$ , $0$ , $10 a - 11$ , $-23 a + 38\bigr]$	${y}^2={x}^{3}+a{x}^{2}+\left(10a-11\right){x}-23a+38$
1024.1-r1	1024.1-r	$4$	$4$	$\Q(\sqrt{3})$	$2$	$[2, 0]$	1024.1	$2^{10}$	$- 2^{23}$	$1.75107$	$(a+1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$2$	2B	$1$	$2$	$1.741115149$	$5.276710919$	2.652162765	$-2002968 a + 3470040$	$\bigl[0$ , $a$ , $0$ , $118 a - 203$ , $849 a - 1470\bigr]$	${y}^2={x}^{3}+a{x}^{2}+\left(118a-203\right){x}+849a-1470$
4608.1-a1	4608.1-a	$4$	$4$	$\Q(\sqrt{3})$	$2$	$[2, 0]$	4608.1	$2^{9} \cdot 3^{2}$	$- 2^{17} \cdot 3^{6}$	$2.55039$	$(a+1), (a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$2$	2B	$4$	$2$	$1$	$4.308416424$	2.487465382	$-2002968 a + 3470040$	$\bigl[0$ , $0$ , $0$ , $660 a - 1143$ , $12144 a - 21034\bigr]$	${y}^2={x}^{3}+\left(660a-1143\right){x}+12144a-21034$
4608.1-f1	4608.1-f	$4$	$4$	$\Q(\sqrt{3})$	$2$	$[2, 0]$	4608.1	$2^{9} \cdot 3^{2}$	$- 2^{17} \cdot 3^{6}$	$2.55039$	$(a+1), (a)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$2$	2B	$1$	$2^{2}$	$1.442267495$	$4.308416424$	3.587590466	$-2002968 a + 3470040$	$\bigl[0$ , $0$ , $0$ , $9192 a - 15921$ , $631254 a - 1093364\bigr]$	${y}^2={x}^{3}+\left(9192a-15921\right){x}+631254a-1093364$
4608.1-bb1	4608.1-bb	$4$	$4$	$\Q(\sqrt{3})$	$2$	$[2, 0]$	4608.1	$2^{9} \cdot 3^{2}$	$- 2^{17} \cdot 3^{6}$	$2.55039$	$(a+1), (a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$2$	2B	$1$	$2^{2}$	$1$	$8.616832848$	2.487465382	$-2002968 a + 3470040$	$\bigl[0$ , $0$ , $0$ , $9192 a - 15921$ , $-631254 a + 1093364\bigr]$	${y}^2={x}^{3}+\left(9192a-15921\right){x}-631254a+1093364$
4608.1-be1	4608.1-be	$4$	$4$	$\Q(\sqrt{3})$	$2$	$[2, 0]$	4608.1	$2^{9} \cdot 3^{2}$	$- 2^{17} \cdot 3^{6}$	$2.55039$	$(a+1), (a)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$2$	2B	$1$	$2$	$1.442267495$	$8.616832848$	3.587590466	$-2002968 a + 3470040$	$\bigl[0$ , $0$ , $0$ , $660 a - 1143$ , $-12144 a + 21034\bigr]$	${y}^2={x}^{3}+\left(660a-1143\right){x}-12144a+21034$

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  *The rank, regulator and analytic order of Ш are not known for all curves in the database; curves for which these are unknown will not appear in searches specifying one of these quantities.