Elliptic curve search results

Results (5 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
539.1-b1	539.1-b	$3$	$9$	\(\Q(\sqrt{-11}) \)	$2$	$[0, 1]$	539.1	\( 7^{2} \cdot 11 \)	\( 7^{4} \cdot 11^{2} \)	$1.42801$	$(-2a+1), (7)$	0	$\Z/3\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2Cn, 3B.1.1	$4$	\( 2^{2} \)	$1$	$1.803987222$	1.933947068	\( -\frac{78843215872}{539} \)	\( \bigl[0\) , \( 1\) , \( 1\) , \( -89\) , \( 295\bigr] \)	${y}^2+{y}={x}^{3}+{x}^{2}-89{x}+295$
13475.1-b1	13475.1-b	$3$	$9$	\(\Q(\sqrt{-11}) \)	$2$	$[0, 1]$	13475.1	\( 5^{2} \cdot 7^{2} \cdot 11 \)	\( 5^{6} \cdot 7^{4} \cdot 11^{2} \)	$3.19313$	$(-a-1), (-2a+1), (7)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 3$	2Cn, 3B	$1$	\( 2^{2} \)	$1$	$0.806767612$	1.945996699	\( -\frac{78843215872}{539} \)	\( \bigl[0\) , \( a + 1\) , \( 1\) , \( -267 a + 178\) , \( 1181 a - 3248\bigr] \)	${y}^2+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-267a+178\right){x}+1181a-3248$
13475.3-b1	13475.3-b	$3$	$9$	\(\Q(\sqrt{-11}) \)	$2$	$[0, 1]$	13475.3	\( 5^{2} \cdot 7^{2} \cdot 11 \)	\( 5^{6} \cdot 7^{4} \cdot 11^{2} \)	$3.19313$	$(a-2), (-2a+1), (7)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 3$	2Cn, 3B	$1$	\( 2^{2} \)	$1$	$0.806767612$	1.945996699	\( -\frac{78843215872}{539} \)	\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( 269 a - 90\) , \( -1449 a - 1977\bigr] \)	${y}^2+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(269a-90\right){x}-1449a-1977$
26411.1-b1	26411.1-b	$3$	$9$	\(\Q(\sqrt{-11}) \)	$2$	$[0, 1]$	26411.1	\( 7^{4} \cdot 11 \)	\( 7^{16} \cdot 11^{2} \)	$3.77817$	$(-2a+1), (7)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2, 3$	2Cn, 3B	$1$	\( 2^{3} \)	$0.380901696$	$0.257712460$	0.947113353	\( -\frac{78843215872}{539} \)	\( \bigl[0\) , \( -1\) , \( 1\) , \( -4377\) , \( -110013\bigr] \)	${y}^2+{y}={x}^{3}-{x}^{2}-4377{x}-110013$
43659.3-a1	43659.3-a	$3$	$9$	\(\Q(\sqrt{-11}) \)	$2$	$[0, 1]$	43659.3	\( 3^{4} \cdot 7^{2} \cdot 11 \)	\( 3^{12} \cdot 7^{4} \cdot 11^{2} \)	$4.28404$	$(-a), (a-1), (-2a+1), (7)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2, 3$	2Cn, 3B.1.2	$1$	\( 2^{2} \)	$0.745116266$	$0.601329074$	2.161523128	\( -\frac{78843215872}{539} \)	\( \bigl[0\) , \( 0\) , \( 1\) , \( -804\) , \( -8775\bigr] \)	${y}^2+{y}={x}^{3}-804{x}-8775$

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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.