Elliptic curve search results

Results (9 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
650.4-a4	650.4-a	$8$	$12$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	650.4	\( 2 \cdot 5^{2} \cdot 13 \)	\( 2^{3} \cdot 5^{14} \cdot 13^{4} \)	$0.90240$	$(a+1), (-a-2), (2a+1), (2a+3)$	0	$\Z/12\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B.1.1	$1$	\( 2^{5} \cdot 3^{2} \)	$1$	$0.723212322$	1.446424644	\( \frac{20122730162024161}{27891601562500} a + \frac{104798752060117927}{27891601562500} \)	\( \bigl[1\) , \( 0\) , \( i + 1\) , \( -109 i + 9\) , \( 170 i - 274\bigr] \)	${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+\left(-109i+9\right){x}+170i-274$
16250.6-a4	16250.6-a	$8$	$12$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	16250.6	\( 2 \cdot 5^{4} \cdot 13 \)	\( 2^{3} \cdot 5^{26} \cdot 13^{4} \)	$2.01782$	$(a+1), (-a-2), (2a+1), (2a+3)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B	$1$	\( 2^{4} \)	$1.965455703$	$0.144642464$	2.274306853	\( \frac{20122730162024161}{27891601562500} a + \frac{104798752060117927}{27891601562500} \)	\( \bigl[i\) , \( -1\) , \( i + 1\) , \( -2713 i + 238\) , \( -21313 i + 34250\bigr] \)	${y}^2+i{x}{y}+\left(i+1\right){y}={x}^{3}-{x}^{2}+\left(-2713i+238\right){x}-21313i+34250$
26000.4-f4	26000.4-f	$8$	$12$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	26000.4	\( 2^{4} \cdot 5^{3} \cdot 13 \)	\( 2^{15} \cdot 5^{20} \cdot 13^{4} \)	$2.26940$	$(a+1), (-a-2), (2a+1), (2a+3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B	$1$	\( 2^{5} \)	$1$	$0.161715191$	1.293721531	\( \frac{20122730162024161}{27891601562500} a + \frac{104798752060117927}{27891601562500} \)	\( \bigl[i + 1\) , \( 1\) , \( 0\) , \( -1150 i + 1850\) , \( -21384 i - 19388\bigr] \)	${y}^2+\left(i+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-1150i+1850\right){x}-21384i-19388$
26000.6-f4	26000.6-f	$8$	$12$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	26000.6	\( 2^{4} \cdot 5^{3} \cdot 13 \)	\( 2^{15} \cdot 5^{20} \cdot 13^{4} \)	$2.26940$	$(a+1), (-a-2), (2a+1), (2a+3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B	$1$	\( 2^{6} \)	$1$	$0.161715191$	2.587443063	\( \frac{20122730162024161}{27891601562500} a + \frac{104798752060117927}{27891601562500} \)	\( \bigl[i + 1\) , \( -1\) , \( 0\) , \( -1454 i - 1622\) , \( -26840 i - 10620\bigr] \)	${y}^2+\left(i+1\right){x}{y}={x}^{3}-{x}^{2}+\left(-1454i-1622\right){x}-26840i-10620$
42250.6-e4	42250.6-e	$8$	$12$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	42250.6	\( 2 \cdot 5^{3} \cdot 13^{2} \)	\( 2^{3} \cdot 5^{20} \cdot 13^{10} \)	$2.56227$	$(a+1), (-a-2), (2a+1), (2a+3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B	$1$	\( 2^{5} \cdot 3 \)	$1$	$0.089703448$	2.152882762	\( \frac{20122730162024161}{27891601562500} a + \frac{104798752060117927}{27891601562500} \)	\( \bigl[i\) , \( -i - 1\) , \( 1\) , \( -4111 i - 5763\) , \( 148881 i + 93187\bigr] \)	${y}^2+i{x}{y}+{y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(-4111i-5763\right){x}+148881i+93187$
42250.9-i4	42250.9-i	$8$	$12$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	42250.9	\( 2 \cdot 5^{3} \cdot 13^{2} \)	\( 2^{3} \cdot 5^{20} \cdot 13^{10} \)	$2.56227$	$(a+1), (-a-2), (2a+1), (2a+3)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B	$1$	\( 2^{5} \cdot 3 \)	$1.482688366$	$0.089703448$	6.384108451	\( \frac{20122730162024161}{27891601562500} a + \frac{104798752060117927}{27891601562500} \)	\( \bigl[i\) , \( -i\) , \( i\) , \( 6684 i - 2333\) , \( 168611 i + 37554\bigr] \)	${y}^2+i{x}{y}+i{y}={x}^{3}-i{x}^{2}+\left(6684i-2333\right){x}+168611i+37554$
52650.4-a4	52650.4-a	$8$	$12$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	52650.4	\( 2 \cdot 3^{4} \cdot 5^{2} \cdot 13 \)	\( 2^{3} \cdot 3^{12} \cdot 5^{14} \cdot 13^{4} \)	$2.70719$	$(a+1), (-a-2), (2a+1), (2a+3), (3)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B.1.2	$1$	\( 2^{5} \)	$0.836000358$	$0.241070774$	3.224564057	\( \frac{20122730162024161}{27891601562500} a + \frac{104798752060117927}{27891601562500} \)	\( \bigl[1\) , \( -1\) , \( i + 1\) , \( -977 i + 85\) , \( -4604 i + 7398\bigr] \)	${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}-{x}^{2}+\left(-977i+85\right){x}-4604i+7398$
67600.6-a4	67600.6-a	$8$	$12$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	67600.6	\( 2^{4} \cdot 5^{2} \cdot 13^{2} \)	\( 2^{15} \cdot 5^{14} \cdot 13^{10} \)	$2.88174$	$(a+1), (-a-2), (2a+1), (2a+3)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B	$1$	\( 2^{6} \)	$1.059422156$	$0.100291504$	3.400033334	\( \frac{20122730162024161}{27891601562500} a + \frac{104798752060117927}{27891601562500} \)	\( \bigl[i + 1\) , \( i - 1\) , \( 0\) , \( 1714 i - 5398\) , \( 43016 i - 113108\bigr] \)	${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(i-1\right){x}^{2}+\left(1714i-5398\right){x}+43016i-113108$
83200.4-n4	83200.4-n	$8$	$12$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	83200.4	\( 2^{8} \cdot 5^{2} \cdot 13 \)	\( 2^{27} \cdot 5^{14} \cdot 13^{4} \)	$3.03528$	$(a+1), (-a-2), (2a+1), (2a+3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B	$1$	\( 2^{5} \)	$1$	$0.180803080$	1.446424644	\( \frac{20122730162024161}{27891601562500} a + \frac{104798752060117927}{27891601562500} \)	\( \bigl[0\) , \( -i\) , \( 0\) , \( 1736 i - 152\) , \( -17536 i - 10912\bigr] \)	${y}^2={x}^{3}-i{x}^{2}+\left(1736i-152\right){x}-17536i-10912$

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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.