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
650.3-a5	650.3-a	$8$	$12$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	650.3	\( 2 \cdot 5^{2} \cdot 13 \)	\( 2^{2} \cdot 5^{14} \cdot 13^{6} \)	$0.90240$	$(a+1), (-a-2), (2a+1), (-3a-2)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2Cs, 3B.1.2	$1$	\( 2^{4} \cdot 3 \)	$1$	$0.482141548$	1.446424644	\( -\frac{12415547946147007137}{2356840332031250} a + \frac{5474429230691529908}{1178420166015625} \)	\( \bigl[1\) , \( 0\) , \( i + 1\) , \( -172 i - 221\) , \( 1271 i + 1038\bigr] \)	${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+\left(-172i-221\right){x}+1271i+1038$
16250.5-a5	16250.5-a	$8$	$12$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	16250.5	\( 2 \cdot 5^{4} \cdot 13 \)	\( 2^{2} \cdot 5^{26} \cdot 13^{6} \)	$2.01782$	$(a+1), (-a-2), (2a+1), (-3a-2)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2Cs, 3B	$1$	\( 2^{6} \)	$2.948183555$	$0.096428309$	2.274306853	\( -\frac{12415547946147007137}{2356840332031250} a + \frac{5474429230691529908}{1178420166015625} \)	\( \bigl[i\) , \( -1\) , \( i + 1\) , \( -4288 i - 5512\) , \( -158938 i - 129750\bigr] \)	${y}^2+i{x}{y}+\left(i+1\right){y}={x}^{3}-{x}^{2}+\left(-4288i-5512\right){x}-158938i-129750$
26000.3-f5	26000.3-f	$8$	$12$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	26000.3	\( 2^{4} \cdot 5^{3} \cdot 13 \)	\( 2^{14} \cdot 5^{20} \cdot 13^{6} \)	$2.26940$	$(a+1), (-a-2), (2a+1), (-3a-2)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2Cs, 3B	$1$	\( 2^{7} \cdot 3 \)	$1$	$0.107810127$	2.587443063	\( -\frac{12415547946147007137}{2356840332031250} a + \frac{5474429230691529908}{1178420166015625} \)	\( \bigl[i + 1\) , \( 1\) , \( 0\) , \( -5586 i + 98\) , \( 111688 i - 95284\bigr] \)	${y}^2+\left(i+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-5586i+98\right){x}+111688i-95284$
26000.5-f5	26000.5-f	$8$	$12$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	26000.5	\( 2^{4} \cdot 5^{3} \cdot 13 \)	\( 2^{14} \cdot 5^{20} \cdot 13^{6} \)	$2.26940$	$(a+1), (-a-2), (2a+1), (-3a-2)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2Cs, 3B	$1$	\( 2^{6} \cdot 3 \)	$1$	$0.107810127$	1.293721531	\( -\frac{12415547946147007137}{2356840332031250} a + \frac{5474429230691529908}{1178420166015625} \)	\( \bigl[i + 1\) , \( -i + 1\) , \( 0\) , \( 1470 i - 5390\) , \( -71000 i + 128500\bigr] \)	${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(1470i-5390\right){x}-71000i+128500$
42250.4-i5	42250.4-i	$8$	$12$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	42250.4	\( 2 \cdot 5^{3} \cdot 13^{2} \)	\( 2^{2} \cdot 5^{20} \cdot 13^{12} \)	$2.56227$	$(a+1), (-a-2), (2a+1), (-3a-2)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2Cs, 3B	$1$	\( 2^{7} \cdot 3 \)	$2.224032549$	$0.059802298$	6.384108451	\( -\frac{12415547946147007137}{2356840332031250} a + \frac{5474429230691529908}{1178420166015625} \)	\( \bigl[i\) , \( i\) , \( i\) , \( 7276 i + 16637\) , \( 766037 i - 429510\bigr] \)	${y}^2+i{x}{y}+i{y}={x}^{3}+i{x}^{2}+\left(7276i+16637\right){x}+766037i-429510$
42250.7-e5	42250.7-e	$8$	$12$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	42250.7	\( 2 \cdot 5^{3} \cdot 13^{2} \)	\( 2^{2} \cdot 5^{20} \cdot 13^{12} \)	$2.56227$	$(a+1), (-a-2), (2a+1), (-3a-2)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2Cs, 3B	$9$	\( 2^{6} \)	$1$	$0.059802298$	2.152882762	\( -\frac{12415547946147007137}{2356840332031250} a + \frac{5474429230691529908}{1178420166015625} \)	\( \bigl[i\) , \( i - 1\) , \( 1\) , \( -18010 i + 2327\) , \( 570821 i - 661327\bigr] \)	${y}^2+i{x}{y}+{y}={x}^{3}+\left(i-1\right){x}^{2}+\left(-18010i+2327\right){x}+570821i-661327$
52650.3-a5	52650.3-a	$8$	$12$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	52650.3	\( 2 \cdot 3^{4} \cdot 5^{2} \cdot 13 \)	\( 2^{2} \cdot 3^{12} \cdot 5^{14} \cdot 13^{6} \)	$2.70719$	$(a+1), (-a-2), (2a+1), (-3a-2), (3)$	$1$	$\Z/2\Z\oplus\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2Cs, 3B.1.1	$1$	\( 2^{7} \cdot 3^{2} \)	$1.254000538$	$0.160713849$	3.224564057	\( -\frac{12415547946147007137}{2356840332031250} a + \frac{5474429230691529908}{1178420166015625} \)	\( \bigl[i\) , \( 1\) , \( i + 1\) , \( -1544 i - 1984\) , \( 34330 i + 28026\bigr] \)	${y}^2+i{x}{y}+\left(i+1\right){y}={x}^{3}+{x}^{2}+\left(-1544i-1984\right){x}+34330i+28026$
67600.4-a5	67600.4-a	$8$	$12$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	67600.4	\( 2^{4} \cdot 5^{2} \cdot 13^{2} \)	\( 2^{14} \cdot 5^{14} \cdot 13^{12} \)	$2.88174$	$(a+1), (-a-2), (2a+1), (-3a-2)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2Cs, 3B	$1$	\( 2^{6} \)	$6.356532938$	$0.066861002$	3.400033334	\( -\frac{12415547946147007137}{2356840332031250} a + \frac{5474429230691529908}{1178420166015625} \)	\( \bigl[i + 1\) , \( i + 1\) , \( 0\) , \( -7154 i + 12642\) , \( -393176 i - 473532\bigr] \)	${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(i+1\right){x}^{2}+\left(-7154i+12642\right){x}-393176i-473532$
83200.3-e5	83200.3-e	$8$	$12$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	83200.3	\( 2^{8} \cdot 5^{2} \cdot 13 \)	\( 2^{26} \cdot 5^{14} \cdot 13^{6} \)	$3.03528$	$(a+1), (-a-2), (2a+1), (-3a-2)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2Cs, 3B	$1$	\( 2^{6} \cdot 3 \)	$1$	$0.120535387$	1.446424644	\( -\frac{12415547946147007137}{2356840332031250} a + \frac{5474429230691529908}{1178420166015625} \)	\( \bigl[0\) , \( i\) , \( 0\) , \( 2744 i + 3528\) , \( -66432 i + 81376\bigr] \)	${y}^2={x}^{3}+i{x}^{2}+\left(2744i+3528\right){x}-66432i+81376$

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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.