Elliptic curve search results

Results (5 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
98.1-a9	98.1-a	$12$	$36$	\(\Q(\sqrt{2}) \)	$2$	$[2, 0]$	98.1	\( 2 \cdot 7^{2} \)	\( 2^{3} \cdot 7^{15} \)	$0.79523$	$(a), (-2a+1), (2a+1)$	0	$\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓		$2, 3$	2B, 3Cs.1.1	$1$	\( 2^{2} \cdot 3^{2} \)	$1$	$1.962857973$	0.693975091	\( \frac{392127492092318125}{55365148804} a + \frac{138814532776321000}{13841287201} \)	\( \bigl[1\) , \( 0\) , \( 1\) , \( -130 a - 356\) , \( -2000 a - 2038\bigr] \)	${y}^2+{x}{y}+{y}={x}^{3}+\left(-130a-356\right){x}-2000a-2038$
686.1-d9	686.1-d	$12$	$36$	\(\Q(\sqrt{2}) \)	$2$	$[2, 0]$	686.1	\( 2 \cdot 7^{3} \)	\( 2^{3} \cdot 7^{21} \)	$1.29349$	$(a), (-2a+1), (2a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 3$	2B, 3Cs	$1$	\( 2^{2} \cdot 3 \)	$1$	$1.985259457$	2.105685636	\( \frac{392127492092318125}{55365148804} a + \frac{138814532776321000}{13841287201} \)	\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -2593 a - 4241\) , \( 94830 a + 138943\bigr] \)	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-2593a-4241\right){x}+94830a+138943$
686.2-d9	686.2-d	$12$	$36$	\(\Q(\sqrt{2}) \)	$2$	$[2, 0]$	686.2	\( 2 \cdot 7^{3} \)	\( 2^{3} \cdot 7^{21} \)	$1.29349$	$(a), (-2a+1), (2a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 3$	2B, 3Cs	$4$	\( 2^{2} \cdot 3 \)	$1$	$0.496314864$	2.105685636	\( \frac{392127492092318125}{55365148804} a + \frac{138814532776321000}{13841287201} \)	\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 251 a - 2161\) , \( 5169 a - 37057\bigr] \)	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(251a-2161\right){x}+5169a-37057$
784.1-a9	784.1-a	$12$	$36$	\(\Q(\sqrt{2}) \)	$2$	$[2, 0]$	784.1	\( 2^{4} \cdot 7^{2} \)	\( 2^{15} \cdot 7^{15} \)	$1.33740$	$(a), (-2a+1), (2a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 3$	2B, 3Cs	$1$	\( 2^{3} \)	$1$	$1.756927026$	1.242335014	\( \frac{392127492092318125}{55365148804} a + \frac{138814532776321000}{13841287201} \)	\( \bigl[a\) , \( -1\) , \( 0\) , \( -520 a - 1422\) , \( 16000 a + 16302\bigr] \)	${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-520a-1422\right){x}+16000a+16302$
4802.1-z9	4802.1-z	$12$	$36$	\(\Q(\sqrt{2}) \)	$2$	$[2, 0]$	4802.1	\( 2 \cdot 7^{4} \)	\( 2^{3} \cdot 7^{27} \)	$2.10397$	$(a), (-2a+1), (2a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 3$	2B, 3Cs	$1$	\( 2^{4} \)	$1$	$0.501979150$	0.709905722	\( \frac{392127492092318125}{55365148804} a + \frac{138814532776321000}{13841287201} \)	\( \bigl[1\) , \( 1\) , \( 0\) , \( -6370 a - 17420\) , \( 679630 a + 681528\bigr] \)	${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(-6370a-17420\right){x}+679630a+681528$

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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.