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
1690.6-a2	1690.6-a	$4$	$10$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	1690.6	\( 2 \cdot 5 \cdot 13^{2} \)	\( 2^{2} \cdot 5^{5} \cdot 13^{3} \)	$1.14588$	$(a+1), (2a+1), (2a+3)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 5$	2B, 5B	$1$	\( 2^{2} \cdot 5 \)	$0.037103590$	$3.214267043$	1.192608490	\( \frac{10462207}{6250} a - \frac{2706038}{3125} \)	\( \bigl[i\) , \( i\) , \( i + 1\) , \( -3 i + 4\) , \( -3 i - 2\bigr] \)	${y}^2+i{x}{y}+\left(i+1\right){y}={x}^{3}+i{x}^{2}+\left(-3i+4\right){x}-3i-2$
8450.9-b2	8450.9-b	$4$	$10$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	8450.9	\( 2 \cdot 5^{2} \cdot 13^{2} \)	\( 2^{2} \cdot 5^{11} \cdot 13^{9} \)	$1.71349$	$(a+1), (2a+1), (2a+3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 5$	2B, 5B	$1$	\( 2^{4} \)	$1$	$0.398680759$	1.594723038	\( \frac{10462207}{6250} a - \frac{2706038}{3125} \)	\( \bigl[1\) , \( 1\) , \( 0\) , \( 86 i - 277\) , \( 498 i - 2511\bigr] \)	${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(86i-277\right){x}+498i-2511$
13520.6-a2	13520.6-a	$4$	$10$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	13520.6	\( 2^{4} \cdot 5 \cdot 13^{2} \)	\( 2^{14} \cdot 5^{5} \cdot 13^{9} \)	$1.92714$	$(a+1), (2a+1), (2a+3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 5$	2B, 5B	$1$	\( 2^{3} \)	$1$	$0.445738639$	0.891477279	\( \frac{10462207}{6250} a - \frac{2706038}{3125} \)	\( \bigl[i + 1\) , \( -i - 1\) , \( 0\) , \( -136 i - 188\) , \( 1704 i + 672\bigr] \)	${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(-136i-188\right){x}+1704i+672$
42250.6-l2	42250.6-l	$4$	$10$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	42250.6	\( 2 \cdot 5^{3} \cdot 13^{2} \)	\( 2^{2} \cdot 5^{11} \cdot 13^{9} \)	$2.56227$	$(a+1), (-a-2), (2a+1), (2a+3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 5$	2B, 5B	$1$	\( 2^{3} \cdot 5 \)	$1$	$0.398680759$	3.986807596	\( \frac{10462207}{6250} a - \frac{2706038}{3125} \)	\( \bigl[i\) , \( i + 1\) , \( 0\) , \( -290 i - 5\) , \( -1350 i + 2175\bigr] \)	${y}^2+i{x}{y}={x}^{3}+\left(i+1\right){x}^{2}+\left(-290i-5\right){x}-1350i+2175$
67600.9-f2	67600.9-f	$4$	$10$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	67600.9	\( 2^{4} \cdot 5^{2} \cdot 13^{2} \)	\( 2^{14} \cdot 5^{11} \cdot 13^{3} \)	$2.88174$	$(a+1), (2a+1), (2a+3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 5$	2B, 5B	$1$	\( 2^{4} \)	$1$	$0.718731960$	2.874927842	\( \frac{10462207}{6250} a - \frac{2706038}{3125} \)	\( \bigl[i + 1\) , \( i + 1\) , \( i + 1\) , \( -89 i + 8\) , \( 130 i - 339\bigr] \)	${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(i+1\right){x}^{2}+\left(-89i+8\right){x}+130i-339$

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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.