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-a2	14.1-a	$6$	$18$	\(\Q(\sqrt{-105}) \)	$2$	$[0, 1]$	14.1	\( 2 \cdot 7 \)	\( 2^{4} \cdot 7^{14} \)	$3.54238$	$(2,a+1), (7,a)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3Cs	$4$	\( 2^{2} \)	$0.389689685$	$7.878754216$	2.397020788	\( -\frac{15625}{28} \)	\( \bigl[a\) , \( 1\) , \( 0\) , \( 187\) , \( -281\bigr] \)	${y}^2+a{x}{y}={x}^3+{x}^2+187{x}-281$
14.1-b2	14.1-b	$6$	$18$	\(\Q(\sqrt{-105}) \)	$2$	$[0, 1]$	14.1	\( 2 \cdot 7 \)	\( 2^{4} \cdot 7^{2} \)	$3.54238$	$(2,a+1), (7,a)$	0	$\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3Cs.1.1	$4$	\( 2^{2} \)	$1$	$7.878754216$	0.341727858	\( -\frac{15625}{28} \)	\( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( 0\bigr] \)	${y}^2+{x}{y}+{y}={x}^3-{x}$
14.1-c2	14.1-c	$6$	$18$	\(\Q(\sqrt{-105}) \)	$2$	$[0, 1]$	14.1	\( 2 \cdot 7 \)	\( 2^{4} \cdot 7^{2} \)	$3.54238$	$(2,a+1), (7,a)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3Cs	$4$	\( 2^{2} \)	$0.725721409$	$7.878754216$	4.463986012	\( -\frac{15625}{28} \)	\( \bigl[a\) , \( -1\) , \( 0\) , \( 247\) , \( -745\bigr] \)	${y}^2+a{x}{y}={x}^3-{x}^2+247{x}-745$
14.1-d2	14.1-d	$6$	$18$	\(\Q(\sqrt{-105}) \)	$2$	$[0, 1]$	14.1	\( 2 \cdot 7 \)	\( 2^{4} \cdot 7^{14} \)	$3.54238$	$(2,a+1), (7,a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3Cs	$4$	\( 2^{2} \)	$1$	$7.878754216$	3.075550725	\( -\frac{15625}{28} \)	\( \bigl[1\) , \( 1\) , \( 0\) , \( -25\) , \( -111\bigr] \)	${y}^2+{x}{y}={x}^3+{x}^2-25{x}-111$
14.1-e2	14.1-e	$6$	$18$	\(\Q(\sqrt{-105}) \)	$2$	$[0, 1]$	14.1	\( 2 \cdot 7 \)	\( 2^{4} \cdot 3^{12} \cdot 7^{2} \)	$3.54238$	$(2,a+1), (7,a)$	$2$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3Cs	$1$	\( 2^{3} \)	$1.316293928$	$7.878754216$	8.096657497	\( -\frac{15625}{28} \)	\( \bigl[a\) , \( 0\) , \( 0\) , \( 225\) , \( -621\bigr] \)	${y}^2+a{x}{y}={x}^3+225{x}-621$
14.1-f2	14.1-f	$6$	$18$	\(\Q(\sqrt{-105}) \)	$2$	$[0, 1]$	14.1	\( 2 \cdot 7 \)	\( 2^{4} \cdot 5^{12} \cdot 7^{2} \)	$3.54238$	$(2,a+1), (7,a)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3Cs	$1$	\( 2^{3} \)	$2.054541211$	$7.878754216$	6.318845715	\( -\frac{15625}{28} \)	\( \bigl[a\) , \( 1\) , \( a\) , \( 252\) , \( -497\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^3+{x}^2+252{x}-497$
14.1-g2	14.1-g	$6$	$18$	\(\Q(\sqrt{-105}) \)	$2$	$[0, 1]$	14.1	\( 2 \cdot 7 \)	\( 2^{4} \cdot 5^{12} \cdot 7^{2} \)	$3.54238$	$(2,a+1), (7,a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3Cs	$4$	\( 2^{3} \)	$1$	$7.878754216$	6.151101451	\( -\frac{15625}{28} \)	\( \bigl[1\) , \( 1\) , \( 1\) , \( -13\) , \( 31\bigr] \)	${y}^2+{x}{y}+{y}={x}^3+{x}^2-13{x}+31$
14.1-h2	14.1-h	$6$	$18$	\(\Q(\sqrt{-105}) \)	$2$	$[0, 1]$	14.1	\( 2 \cdot 7 \)	\( 2^{4} \cdot 3^{12} \cdot 7^{2} \)	$3.54238$	$(2,a+1), (7,a)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3Cs.1.1	$1$	\( 2^{3} \)	$3.598779144$	$7.878754216$	11.06822780	\( -\frac{15625}{28} \)	\( \bigl[1\) , \( -1\) , \( 1\) , \( -5\) , \( -7\bigr] \)	${y}^2+{x}{y}+{y}={x}^3-{x}^2-5{x}-7$

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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.