Elliptic curve search results

Results (18 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
3844.2-a2	3844.2-a	$4$	$4$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	3844.2	\( 2^{2} \cdot 31^{2} \)	\( 2^{2} \cdot 31^{8} \)	$1.21869$	$(-6a+1), (6a-5), (2)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2B	$1$	\( 2^{2} \)	$1$	$1.241295225$	1.433324264	\( \frac{3196010817}{1847042} \)	\( \bigl[1\) , \( -1\) , \( 1\) , \( -31\) , \( 5\bigr] \)	${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-31{x}+5$
1922.1-a2	1922.1-a	$4$	$4$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	1922.1	\( 2 \cdot 31^{2} \)	\( 2^{2} \cdot 31^{8} \)	$1.18333$	$(a+1), (31)$	$1$	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2B	$1$	\( 2^{3} \)	$1.604379946$	$1.241295225$	1.991509166	\( \frac{3196010817}{1847042} \)	\( \bigl[1\) , \( -1\) , \( 1\) , \( -31\) , \( 5\bigr] \)	${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-31{x}+5$
3844.2-a2	3844.2-a	$4$	$4$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	3844.2	\( 2^{2} \cdot 31^{2} \)	\( 2^{2} \cdot 31^{8} \)	$1.86159$	$(a), (-a+1), (31)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2B	$4$	\( 2^{2} \)	$1$	$1.241295225$	3.753323965	\( \frac{3196010817}{1847042} \)	\( \bigl[1\) , \( -1\) , \( 1\) , \( -31\) , \( 5\bigr] \)	${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-31{x}+5$
1922.1-a2	1922.1-a	$4$	$4$	\(\Q(\sqrt{-2}) \)	$2$	$[0, 1]$	1922.1	\( 2 \cdot 31^{2} \)	\( 2^{2} \cdot 31^{8} \)	$1.67349$	$(a), (31)$	$1$	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2B	$1$	\( 2^{3} \)	$4.039244295$	$1.241295225$	3.545358913	\( \frac{3196010817}{1847042} \)	\( \bigl[1\) , \( -1\) , \( 1\) , \( -31\) , \( 5\bigr] \)	${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-31{x}+5$
3844.2-c2	3844.2-c	$4$	$4$	\(\Q(\sqrt{-11}) \)	$2$	$[0, 1]$	3844.2	\( 2^{2} \cdot 31^{2} \)	\( 2^{2} \cdot 31^{8} \)	$2.33362$	$(-3a+4), (3a+1), (2)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2B	$1$	\( 2^{2} \)	$1$	$1.241295225$	0.748529184	\( \frac{3196010817}{1847042} \)	\( \bigl[1\) , \( -1\) , \( 1\) , \( -31\) , \( 5\bigr] \)	${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-31{x}+5$
3844.1-a2	3844.1-a	$4$	$4$	\(\Q(\sqrt{-19}) \)	$2$	$[0, 1]$	3844.1	\( 2^{2} \cdot 31^{2} \)	\( 2^{2} \cdot 31^{8} \)	$3.06698$	$(2), (31)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2B	$1$	\( 2^{2} \)	$2.393195134$	$1.241295225$	2.726066130	\( \frac{3196010817}{1847042} \)	\( \bigl[1\) , \( -1\) , \( 1\) , \( -31\) , \( 5\bigr] \)	${y}^2+{x}{y}+{y}={x}^3-{x}^2-31{x}+5$
124.2-a2	124.2-a	$6$	$8$	\(\Q(\sqrt{-31}) \)	$2$	$[0, 1]$	124.2	\( 2^{2} \cdot 31 \)	\( 2^{2} \cdot 31^{8} \)	$1.66026$	$(2,a), (2,a+1), (-2a+1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2B	$1$	\( 2 \)	$9.445571402$	$1.241295225$	4.211651901	\( \frac{3196010817}{1847042} \)	\( \bigl[1\) , \( -1\) , \( 1\) , \( -31\) , \( 5\bigr] \)	${y}^2+{x}{y}+{y}={x}^3-{x}^2-31{x}+5$
3844.2-a2	3844.2-a	$4$	$4$	\(\Q(\sqrt{-43}) \)	$2$	$[0, 1]$	3844.2	\( 2^{2} \cdot 31^{2} \)	\( 2^{2} \cdot 31^{8} \)	$4.61390$	$(a+4), (a-5), (2)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2B	$1$	\( 2^{2} \)	$1$	$1.241295225$	0.378591494	\( \frac{3196010817}{1847042} \)	\( \bigl[1\) , \( -1\) , \( 1\) , \( -31\) , \( 5\bigr] \)	${y}^2+{x}{y}+{y}={x}^3-{x}^2-31{x}+5$
3844.1-a2	3844.1-a	$4$	$4$	\(\Q(\sqrt{-67}) \)	$2$	$[0, 1]$	3844.1	\( 2^{2} \cdot 31^{2} \)	\( 2^{2} \cdot 31^{8} \)	$5.75933$	$(2), (31)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2B	$1$	\( 2^{2} \)	$10.88498062$	$1.241295225$	6.602757320	\( \frac{3196010817}{1847042} \)	\( \bigl[1\) , \( -1\) , \( 1\) , \( -31\) , \( 5\bigr] \)	${y}^2+{x}{y}+{y}={x}^3-{x}^2-31{x}+5$
3844.1-a2	3844.1-a	$4$	$4$	\(\Q(\sqrt{-163}) \)	$2$	$[0, 1]$	3844.1	\( 2^{2} \cdot 31^{2} \)	\( 2^{2} \cdot 31^{8} \)	$8.98314$	$(2), (31)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2B	$1$	\( 2^{2} \)	$13.81268877$	$1.241295225$	5.371795862	\( \frac{3196010817}{1847042} \)	\( \bigl[1\) , \( -1\) , \( 1\) , \( -31\) , \( 5\bigr] \)	${y}^2+{x}{y}+{y}={x}^3-{x}^2-31{x}+5$
62.1-a2	62.1-a	$4$	$4$	\(\Q(\sqrt{-62}) \)	$2$	$[0, 1]$	62.1	\( 2 \cdot 31 \)	\( 2^{2} \cdot 31^{8} \)	$3.94877$	$(2,a), (31,a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2B	$16$	\( 2^{2} \)	$1$	$1.241295225$	2.522314420	\( \frac{3196010817}{1847042} \)	\( \bigl[1\) , \( -1\) , \( 1\) , \( -31\) , \( 5\bigr] \)	${y}^2+{x}{y}+{y}={x}^3-{x}^2-31{x}+5$
62.1-c2	62.1-c	$4$	$4$	\(\Q(\sqrt{-93}) \)	$2$	$[0, 1]$	62.1	\( 2 \cdot 31 \)	\( 2^{2} \cdot 31^{8} \)	$4.83624$	$(2,a+1), (31,a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2B	$4$	\( 2^{2} \)	$1$	$1.241295225$	0.514865275	\( \frac{3196010817}{1847042} \)	\( \bigl[1\) , \( -1\) , \( 1\) , \( -31\) , \( 5\bigr] \)	${y}^2+{x}{y}+{y}={x}^3-{x}^2-31{x}+5$
62.1-d2	62.1-d	$4$	$4$	\(\Q(\sqrt{-186}) \)	$2$	$[0, 1]$	62.1	\( 2 \cdot 31 \)	\( 2^{2} \cdot 31^{8} \)	$6.83948$	$(2,a), (31,a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2B	$4$	\( 2^{2} \)	$1$	$2.482590450$	0.364064727	\( \frac{3196010817}{1847042} \)	\( \bigl[1\) , \( -1\) , \( 1\) , \( -31\) , \( 5\bigr] \)	${y}^2+{x}{y}+{y}={x}^3-{x}^2-31{x}+5$
62.1-d2	62.1-d	$4$	$4$	\(\Q(\sqrt{-217}) \)	$2$	$[0, 1]$	62.1	\( 2 \cdot 31 \)	\( 2^{2} \cdot 31^{8} \)	$7.38748$	$(2,a+1), (31,a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2B	$16$	\( 2^{2} \)	$1$	$2.482590450$	1.348233768	\( \frac{3196010817}{1847042} \)	\( \bigl[1\) , \( -1\) , \( 1\) , \( -31\) , \( 5\bigr] \)	${y}^2+{x}{y}+{y}={x}^3-{x}^2-31{x}+5$
3844.1-c2	3844.1-c	$4$	$4$	\(\Q(\sqrt{5}) \)	$2$	$[2, 0]$	3844.1	\( 2^{2} \cdot 31^{2} \)	\( 2^{2} \cdot 31^{8} \)	$1.57333$	$(5a-2), (5a-3), (2)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2B	$1$	\( 2^{2} \)	$0.522741163$	$4.917223407$	2.299067034	\( \frac{3196010817}{1847042} \)	\( \bigl[1\) , \( -1\) , \( 1\) , \( -31\) , \( 5\bigr] \)	${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-31{x}+5$
1922.1-c3	1922.1-c	$6$	$8$	\(\Q(\sqrt{2}) \)	$2$	$[2, 0]$	1922.1	\( 2 \cdot 31^{2} \)	\( 2^{2} \cdot 31^{8} \)	$1.67349$	$(a), (-4a-1), (4a-1)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2Cs	$1$	\( 2^{3} \)	$2.036836915$	$4.917223407$	3.541043031	\( \frac{3196010817}{1847042} \)	\( \bigl[1\) , \( -1\) , \( 1\) , \( -31\) , \( 5\bigr] \)	${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-31{x}+5$
1922.1-a2	1922.1-a	$4$	$4$	\(\Q(\sqrt{3}) \)	$2$	$[2, 0]$	1922.1	\( 2 \cdot 31^{2} \)	\( 2^{2} \cdot 31^{8} \)	$2.04959$	$(a+1), (31)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2B	$1$	\( 2^{3} \)	$1$	$4.917223407$	2.838960258	\( \frac{3196010817}{1847042} \)	\( \bigl[1\) , \( -1\) , \( 1\) , \( -31\) , \( 5\bigr] \)	${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-31{x}+5$
124.1-c2	124.1-c	$4$	$4$	\(\Q(\sqrt{93}) \)	$2$	$[2, 0]$	124.1	\( 2^{2} \cdot 31 \)	\( 2^{2} \cdot 31^{8} \)	$2.87565$	$(3a-17), (2)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2B	$1$	\( 2 \)	$9.111184694$	$4.917223407$	4.645723052	\( \frac{3196010817}{1847042} \)	\( \bigl[1\) , \( -1\) , \( 1\) , \( -31\) , \( 5\bigr] \)	${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-31{x}+5$

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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.