Elliptic curve search results

Results (7 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
15876.3-e6	15876.3-e	$6$	$18$	\(\Q(\sqrt{-11}) \)	$2$	$[0, 1]$	15876.3	\( 2^{2} \cdot 3^{4} \cdot 7^{2} \)	\( 2^{18} \cdot 3^{12} \cdot 7^{4} \)	$3.32675$	$(-a), (a-1), (2), (7)$	$1$	$\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2, 3$	2B, 3B.1.1	$1$	\( 2^{3} \cdot 3^{2} \)	$15.73689502$	$0.145902855$	5.538300100	\( \frac{2251439055699625}{25088} \)	\( \bigl[1\) , \( -1\) , \( 1\) , \( -24575\) , \( 1488935\bigr] \)	${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-24575{x}+1488935$
98.2-a6	98.2-a	$6$	$18$	\(\Q(\sqrt{-33}) \)	$2$	$[0, 1]$	98.2	\( 2 \cdot 7^{2} \)	\( 2^{18} \cdot 7^{4} \)	$3.23022$	$(2,a+1), (7,a+3), (7,a+4)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3Cs	$1$	\( 2^{3} \)	$15.73689502$	$0.437708567$	4.796308581	\( \frac{2251439055699625}{25088} \)	\( \bigl[a\) , \( -1\) , \( 0\) , \( -2702\) , \( 63308\bigr] \)	${y}^2+a{x}{y}={x}^3-{x}^2-2702{x}+63308$
28.2-a6	28.2-a	$6$	$18$	\(\Q(\sqrt{-231}) \)	$2$	$[0, 1]$	28.2	\( 2^{2} \cdot 7 \)	\( 2^{18} \cdot 7^{16} \)	$3.12417$	$(2,a), (2,a+1), (7,a+3)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3Cs	$4$	\( 2 \)	$15.73689502$	$0.437708567$	3.625668490	\( \frac{2251439055699625}{25088} \)	\( \bigl[1\) , \( 1\) , \( 0\) , \( -133795\) , \( 18781197\bigr] \)	${y}^2+{x}{y}={x}^3+{x}^2-133795{x}+18781197$
98.2-a6	98.2-a	$6$	$18$	\(\Q(\sqrt{-66}) \)	$2$	$[0, 1]$	98.2	\( 2 \cdot 7^{2} \)	\( 2^{30} \cdot 7^{4} \)	$4.56822$	$(2,a), (7,a+2), (7,a+5)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3Cs	$1$	\( 2^{3} \)	$15.73689502$	$0.437708567$	3.391502322	\( \frac{2251439055699625}{25088} \)	\( \bigl[a\) , \( 1\) , \( a\) , \( -10809\) , \( 495655\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^3+{x}^2-10809{x}+495655$
98.1-b6	98.1-b	$6$	$18$	\(\Q(\sqrt{-165}) \)	$2$	$[0, 1]$	98.1	\( 2 \cdot 7^{2} \)	\( 2^{18} \cdot 5^{12} \cdot 7^{4} \)	$7.22299$	$(2,a+1), (7)$	$2$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3Cs	$4$	\( 2^{2} \)	$16.16604968$	$0.875417135$	8.813876630	\( \frac{2251439055699625}{25088} \)	\( \bigl[a\) , \( 1\) , \( 0\) , \( -67723\) , \( 7778223\bigr] \)	${y}^2+a{x}{y}={x}^3+{x}^2-67723{x}+7778223$
14.1-a6	14.1-a	$6$	$18$	\(\Q(\sqrt{-462}) \)	$2$	$[0, 1]$	14.1	\( 2 \cdot 7 \)	\( 2^{18} \cdot 7^{4} \cdot 47^{12} \)	$7.43056$	$(2,a), (7,a)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3Cs	$4$	\( 2^{2} \)	$15.73689502$	$0.875417135$	2.563734776	\( \frac{2251439055699625}{25088} \)	\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 207557 a + 4064904\) , \( -92674518 a + 5268121598\bigr] \)	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3-a{x}^2+\left(207557a+4064904\right){x}-92674518a+5268121598$
196.1-b6	196.1-b	$6$	$18$	\(\Q(\sqrt{33}) \)	$2$	$[2, 0]$	196.1	\( 2^{2} \cdot 7^{2} \)	\( 2^{18} \cdot 7^{4} \)	$1.92070$	$(-a-2), (-a+3), (7)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3B.1.2	$1$	\( 2 \)	$15.73689502$	$0.436190660$	1.194918927	\( \frac{2251439055699625}{25088} \)	\( \bigl[1\) , \( 0\) , \( 1\) , \( -2731\) , \( -55146\bigr] \)	${y}^2+{x}{y}+{y}={x}^{3}-2731{x}-55146$

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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.