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
3400.4-b2	3400.4-b	$6$	$8$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	3400.4	$2^{3} \cdot 5^{2} \cdot 17$	$2^{4} \cdot 5^{8} \cdot 17^{2}$	$1.36470$	$(a+1), (-a-2), (2a+1), (a-4)$	0	$\Z/2\Z\oplus\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2Cs	$1$	$2^{6}$	$1$	$1.789627193$	1.789627193	$-\frac{18495673728}{180625} a - \frac{897072368}{36125}$	$\bigl[i + 1$ , $1$ , $i + 1$ , $-34 i - 8$ , $-84 i + 34\bigr]$	${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+{x}^{2}+\left(-34i-8\right){x}-84i+34$
34000.4-a2	34000.4-a	$6$	$8$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	34000.4	$2^{4} \cdot 5^{3} \cdot 17$	$2^{4} \cdot 5^{14} \cdot 17^{2}$	$2.42682$	$(a+1), (-a-2), (2a+1), (a-4)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2Cs	$1$	$2^{4}$	$1$	$0.800345611$	0.800345611	$-\frac{18495673728}{180625} a - \frac{897072368}{36125}$	$\bigl[i + 1$ , $i + 1$ , $0$ , $134 i - 109$ , $-854 i + 98\bigr]$	${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(i+1\right){x}^{2}+\left(134i-109\right){x}-854i+98$
34000.6-b2	34000.6-b	$6$	$8$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	34000.6	$2^{4} \cdot 5^{3} \cdot 17$	$2^{4} \cdot 5^{14} \cdot 17^{2}$	$2.42682$	$(a+1), (-a-2), (2a+1), (a-4)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2Cs	$1$	$2^{4}$	$2.292065342$	$0.800345611$	3.668888877	$-\frac{18495673728}{180625} a - \frac{897072368}{36125}$	$\bigl[i + 1$ , $-i$ , $0$ , $67 i + 158$ , $693 i - 474\bigr]$	${y}^2+\left(i+1\right){x}{y}={x}^{3}-i{x}^{2}+\left(67i+158\right){x}+693i-474$
57800.6-b2	57800.6-b	$6$	$8$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	57800.6	$2^{3} \cdot 5^{2} \cdot 17^{2}$	$2^{4} \cdot 5^{8} \cdot 17^{8}$	$2.77109$	$(a+1), (-a-2), (2a+1), (a-4)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2Cs	$1$	$2^{6}$	$1.151803464$	$0.434048349$	3.999507146	$-\frac{18495673728}{180625} a - \frac{897072368}{36125}$	$\bigl[i + 1$ , $i - 1$ , $0$ , $433 i + 390$ , $1769 i - 5508\bigr]$	${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(i-1\right){x}^{2}+\left(433i+390\right){x}+1769i-5508$
85000.6-d2	85000.6-d	$6$	$8$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	85000.6	$2^{3} \cdot 5^{4} \cdot 17$	$2^{4} \cdot 5^{20} \cdot 17^{2}$	$3.05157$	$(a+1), (-a-2), (2a+1), (a-4)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2Cs	$1$	$2^{6}$	$1$	$0.357925438$	1.431701754	$-\frac{18495673728}{180625} a - \frac{897072368}{36125}$	$\bigl[i + 1$ , $-i - 1$ , $0$ , $-833 i - 206$ , $-8571 i + 3828\bigr]$	${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(-833i-206\right){x}-8571i+3828$

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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.