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-a8	650.4-a	$8$	$12$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	650.4	\( 2 \cdot 5^{2} \cdot 13 \)	\( 2^{3} \cdot 5^{11} \cdot 13 \)	$0.90240$	$(a+1), (-a-2), (2a+1), (2a+3)$	0	$\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B.1.1	$4$	\( 2 \cdot 3^{2} \)	$1$	$0.723212322$	1.446424644	\( -\frac{4023422266102893}{20312500} a + \frac{5856979210600901}{20312500} \)	\( \bigl[1\) , \( 0\) , \( i + 1\) , \( -609 i - 11\) , \( -4242 i + 3978\bigr] \)	${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+\left(-609i-11\right){x}-4242i+3978$
16250.6-a8	16250.6-a	$8$	$12$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	16250.6	\( 2 \cdot 5^{4} \cdot 13 \)	\( 2^{3} \cdot 5^{23} \cdot 13 \)	$2.01782$	$(a+1), (-a-2), (2a+1), (2a+3)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B	$1$	\( 2^{4} \)	$1.965455703$	$0.144642464$	2.274306853	\( -\frac{4023422266102893}{20312500} a + \frac{5856979210600901}{20312500} \)	\( \bigl[1\) , \( 1\) , \( i + 1\) , \( -15213 i - 263\) , \( -530188 i + 497250\bigr] \)	${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+{x}^{2}+\left(-15213i-263\right){x}-530188i+497250$
26000.4-f8	26000.4-f	$8$	$12$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	26000.4	\( 2^{4} \cdot 5^{3} \cdot 13 \)	\( 2^{15} \cdot 5^{17} \cdot 13 \)	$2.26940$	$(a+1), (-a-2), (2a+1), (2a+3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B	$4$	\( 2^{3} \)	$1$	$0.161715191$	1.293721531	\( -\frac{4023422266102893}{20312500} a + \frac{5856979210600901}{20312500} \)	\( \bigl[i + 1\) , \( -i - 1\) , \( 0\) , \( -7470 i + 9610\) , \( -282200 i - 436900\bigr] \)	${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(-7470i+9610\right){x}-282200i-436900$
26000.6-f8	26000.6-f	$8$	$12$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	26000.6	\( 2^{4} \cdot 5^{3} \cdot 13 \)	\( 2^{15} \cdot 5^{17} \cdot 13 \)	$2.26940$	$(a+1), (-a-2), (2a+1), (2a+3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B	$1$	\( 2^{6} \)	$1$	$0.161715191$	2.587443063	\( -\frac{4023422266102893}{20312500} a + \frac{5856979210600901}{20312500} \)	\( \bigl[i + 1\) , \( -i + 1\) , \( 0\) , \( -7134 i - 9862\) , \( -417928 i - 309604\bigr] \)	${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(-7134i-9862\right){x}-417928i-309604$
42250.6-e8	42250.6-e	$8$	$12$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	42250.6	\( 2 \cdot 5^{3} \cdot 13^{2} \)	\( 2^{3} \cdot 5^{17} \cdot 13^{7} \)	$2.56227$	$(a+1), (-a-2), (2a+1), (2a+3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B	$4$	\( 2^{3} \cdot 3 \)	$1$	$0.089703448$	2.152882762	\( -\frac{4023422266102893}{20312500} a + \frac{5856979210600901}{20312500} \)	\( \bigl[1\) , \( i + 1\) , \( i\) , \( -19491 i - 34423\) , \( 2094671 i + 2160277\bigr] \)	${y}^2+{x}{y}+i{y}={x}^{3}+\left(i+1\right){x}^{2}+\left(-19491i-34423\right){x}+2094671i+2160277$
42250.9-i8	42250.9-i	$8$	$12$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	42250.9	\( 2 \cdot 5^{3} \cdot 13^{2} \)	\( 2^{3} \cdot 5^{17} \cdot 13^{7} \)	$2.56227$	$(a+1), (-a-2), (2a+1), (2a+3)$	$1$	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B	$1$	\( 2^{7} \cdot 3 \)	$1.482688366$	$0.089703448$	6.384108451	\( -\frac{4023422266102893}{20312500} a + \frac{5856979210600901}{20312500} \)	\( \bigl[1\) , \( i\) , \( 1\) , \( 38504 i - 9074\) , \( 2742317 i + 1271550\bigr] \)	${y}^2+{x}{y}+{y}={x}^{3}+i{x}^{2}+\left(38504i-9074\right){x}+2742317i+1271550$
52650.4-a8	52650.4-a	$8$	$12$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	52650.4	\( 2 \cdot 3^{4} \cdot 5^{2} \cdot 13 \)	\( 2^{3} \cdot 3^{12} \cdot 5^{11} \cdot 13 \)	$2.70719$	$(a+1), (-a-2), (2a+1), (2a+3), (3)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B.1.2	$1$	\( 2^{5} \)	$0.836000358$	$0.241070774$	3.224564057	\( -\frac{4023422266102893}{20312500} a + \frac{5856979210600901}{20312500} \)	\( \bigl[i\) , \( 1\) , \( i + 1\) , \( -5477 i - 94\) , \( -114521 i + 107406\bigr] \)	${y}^2+i{x}{y}+\left(i+1\right){y}={x}^{3}+{x}^{2}+\left(-5477i-94\right){x}-114521i+107406$
67600.6-a8	67600.6-a	$8$	$12$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	67600.6	\( 2^{4} \cdot 5^{2} \cdot 13^{2} \)	\( 2^{15} \cdot 5^{11} \cdot 13^{7} \)	$2.88174$	$(a+1), (-a-2), (2a+1), (2a+3)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B	$1$	\( 2^{4} \)	$4.237688625$	$0.100291504$	3.400033334	\( -\frac{4023422266102893}{20312500} a + \frac{5856979210600901}{20312500} \)	\( \bigl[i + 1\) , \( i + 1\) , \( i + 1\) , \( 12675 i - 28998\) , \( 1245458 i - 1781967\bigr] \)	${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(i+1\right){x}^{2}+\left(12675i-28998\right){x}+1245458i-1781967$
83200.4-n8	83200.4-n	$8$	$12$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	83200.4	\( 2^{8} \cdot 5^{2} \cdot 13 \)	\( 2^{27} \cdot 5^{11} \cdot 13 \)	$3.03528$	$(a+1), (-a-2), (2a+1), (2a+3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B	$1$	\( 2^{5} \)	$1$	$0.180803080$	1.446424644	\( -\frac{4023422266102893}{20312500} a + \frac{5856979210600901}{20312500} \)	\( \bigl[0\) , \( i\) , \( 0\) , \( 9736 i + 168\) , \( -254592 i - 271456\bigr] \)	${y}^2={x}^{3}+i{x}^{2}+\left(9736i+168\right){x}-254592i-271456$

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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.