Elliptic curve search results

Results (4 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
98.2-a3	98.2-a	$6$	$18$	\(\Q(\sqrt{-17}) \)	$2$	$[0, 1]$	98.2	\( 2 \cdot 7^{2} \)	\( 2^{12} \cdot 7^{6} \)	$2.31846$	$(2,a+1), (7,a+2), (7,a+5)$	$1$	$\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3Cs.1.1	$1$	\( 2 \cdot 3^{2} \)	$1.687975075$	$2.626251405$	1.075171804	\( \frac{9938375}{21952} \)	\( \bigl[1\) , \( 0\) , \( 1\) , \( 4\) , \( -6\bigr] \)	${y}^2+{x}{y}+{y}={x}^3+4{x}-6$
98.1-d3	98.1-d	$6$	$18$	\(\Q(\sqrt{-85}) \)	$2$	$[0, 1]$	98.1	\( 2 \cdot 7^{2} \)	\( 2^{12} \cdot 5^{12} \cdot 7^{6} \)	$5.18423$	$(2,a+1), (7)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3Cs	$1$	\( 2^{2} \cdot 3^{2} \)	$1.687975075$	$2.626251405$	8.654966070	\( \frac{9938375}{21952} \)	\( \bigl[1\) , \( 1\) , \( 1\) , \( 112\) , \( -719\bigr] \)	${y}^2+{x}{y}+{y}={x}^3+{x}^2+112{x}-719$
98.1-e3	98.1-e	$6$	$18$	\(\Q(\sqrt{-221}) \)	$2$	$[0, 1]$	98.1	\( 2 \cdot 7^{2} \)	\( 2^{12} \cdot 7^{6} \cdot 13^{12} \)	$8.35932$	$(2,a+1), (7)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3Cs	$1$	\( 2^{2} \cdot 3^{2} \)	$1.687975075$	$5.252502811$	5.367582097	\( \frac{9938375}{21952} \)	\( \bigl[1\) , \( 0\) , \( 0\) , \( 757\) , \( -13391\bigr] \)	${y}^2+{x}{y}={x}^3+757{x}-13391$
14.1-f3	14.1-f	$6$	$18$	\(\Q(\sqrt{-357}) \)	$2$	$[0, 1]$	14.1	\( 2 \cdot 7 \)	\( 2^{12} \cdot 7^{6} \cdot 17^{12} \)	$6.53183$	$(2,a+1), (7,a)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3Cs	$1$	\( 2^{3} \cdot 3^{2} \)	$1.687975075$	$5.252502811$	8.446382019	\( \frac{9938375}{21952} \)	\( \bigl[a\) , \( 1\) , \( a\) , \( 4069\) , \( -33359\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^3+{x}^2+4069{x}-33359$

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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.