Elliptic curve search results

Results (8 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
14.1-a6	14.1-a	$6$	$18$	\(\Q(\sqrt{-105}) \)	$2$	$[0, 1]$	14.1	\( 2 \cdot 7 \)	\( 2^{18} \cdot 7^{16} \)	$3.54238$	$(2,a+1), (7,a)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3Cs	$4$	\( 2^{2} \)	$7.014414334$	$0.437708567$	2.397020788	\( \frac{2251439055699625}{25088} \)	\( \bigl[a\) , \( 1\) , \( 0\) , \( -133583\) , \( -17711429\bigr] \)	${y}^2+a{x}{y}={x}^3+{x}^2-133583{x}-17711429$
14.1-b6	14.1-b	$6$	$18$	\(\Q(\sqrt{-105}) \)	$2$	$[0, 1]$	14.1	\( 2 \cdot 7 \)	\( 2^{18} \cdot 7^{4} \)	$3.54238$	$(2,a+1), (7,a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3Cs.1.1	$4$	\( 2^{3} \)	$1$	$0.437708567$	0.341727858	\( \frac{2251439055699625}{25088} \)	\( \bigl[1\) , \( 0\) , \( 1\) , \( -2731\) , \( -55146\bigr] \)	${y}^2+{x}{y}+{y}={x}^3-2731{x}-55146$
14.1-c6	14.1-c	$6$	$18$	\(\Q(\sqrt{-105}) \)	$2$	$[0, 1]$	14.1	\( 2 \cdot 7 \)	\( 2^{18} \cdot 7^{4} \)	$3.54238$	$(2,a+1), (7,a)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3Cs	$4$	\( 2^{2} \)	$13.06298536$	$0.437708567$	4.463986012	\( \frac{2251439055699625}{25088} \)	\( \bigl[a\) , \( -1\) , \( 0\) , \( -2483\) , \( 78971\bigr] \)	${y}^2+a{x}{y}={x}^3-{x}^2-2483{x}+78971$
14.1-d6	14.1-d	$6$	$18$	\(\Q(\sqrt{-105}) \)	$2$	$[0, 1]$	14.1	\( 2 \cdot 7 \)	\( 2^{18} \cdot 7^{16} \)	$3.54238$	$(2,a+1), (7,a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3Cs	$36$	\( 2^{3} \)	$1$	$0.437708567$	3.075550725	\( \frac{2251439055699625}{25088} \)	\( \bigl[1\) , \( 1\) , \( 0\) , \( -133795\) , \( 18781197\bigr] \)	${y}^2+{x}{y}={x}^3+{x}^2-133795{x}+18781197$
14.1-e6	14.1-e	$6$	$18$	\(\Q(\sqrt{-105}) \)	$2$	$[0, 1]$	14.1	\( 2 \cdot 7 \)	\( 2^{18} \cdot 3^{12} \cdot 7^{4} \)	$3.54238$	$(2,a+1), (7,a)$	$2$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3Cs	$4$	\( 2^{2} \cdot 3^{2} \)	$1.316293928$	$0.437708567$	8.096657497	\( \frac{2251439055699625}{25088} \)	\( \bigl[a\) , \( 0\) , \( 0\) , \( -24345\) , \( -1268433\bigr] \)	${y}^2+a{x}{y}={x}^3-24345{x}-1268433$
14.1-f6	14.1-f	$6$	$18$	\(\Q(\sqrt{-105}) \)	$2$	$[0, 1]$	14.1	\( 2 \cdot 7 \)	\( 2^{18} \cdot 5^{12} \cdot 7^{4} \)	$3.54238$	$(2,a+1), (7,a)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3Cs	$4$	\( 2^{3} \cdot 3^{2} \)	$1.027270605$	$0.437708567$	6.318845715	\( \frac{2251439055699625}{25088} \)	\( \bigl[a\) , \( 1\) , \( a\) , \( -67998\) , \( 7438753\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^3+{x}^2-67998{x}+7438753$
14.1-g6	14.1-g	$6$	$18$	\(\Q(\sqrt{-105}) \)	$2$	$[0, 1]$	14.1	\( 2 \cdot 7 \)	\( 2^{18} \cdot 5^{12} \cdot 7^{4} \)	$3.54238$	$(2,a+1), (7,a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3Cs	$16$	\( 2^{2} \cdot 3^{2} \)	$1$	$0.437708567$	6.151101451	\( \frac{2251439055699625}{25088} \)	\( \bigl[1\) , \( 1\) , \( 1\) , \( -68263\) , \( -6893219\bigr] \)	${y}^2+{x}{y}+{y}={x}^3+{x}^2-68263{x}-6893219$
14.1-h6	14.1-h	$6$	$18$	\(\Q(\sqrt{-105}) \)	$2$	$[0, 1]$	14.1	\( 2 \cdot 7 \)	\( 2^{18} \cdot 3^{12} \cdot 7^{4} \)	$3.54238$	$(2,a+1), (7,a)$	$1$	$\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3Cs.1.1	$4$	\( 2^{3} \cdot 3^{2} \)	$16.19450614$	$0.437708567$	11.06822780	\( \frac{2251439055699625}{25088} \)	\( \bigl[1\) , \( -1\) , \( 1\) , \( -24575\) , \( 1488935\bigr] \)	${y}^2+{x}{y}+{y}={x}^3-{x}^2-24575{x}+1488935$

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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.