Elliptic curves over Q(−1)\Q(\sqrt{-1}) of conductor 32400.1

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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
32400.1-CMc1	32400.1-CMc	$1$	$1$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	32400.1	$2^{4} \cdot 3^{4} \cdot 5^{2}$	$2^{12} \cdot 3^{18} \cdot 5^{3}$	$2.39775$	$(a+1), (-a-2), (3)$	0	$\Z/2\Z$	$\textsf{yes}$	$-4$	$\mathrm{U}(1)$	✓			✓			$1$	$2^{2}$	$1$	$0.884830445$	0.884830445	$1728$	$\bigl[0$ , $0$ , $0$ , $-54 i + 27$ , $0\bigr]$	${y}^2={x}^{3}+\left(-54i+27\right){x}$
32400.1-CMb1	32400.1-CMb	$1$	$1$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	32400.1	$2^{4} \cdot 3^{4} \cdot 5^{2}$	$2^{12} \cdot 3^{12} \cdot 5^{9}$	$2.39775$	$(a+1), (-a-2), (3)$	0	$\Z/2\Z$	$\textsf{yes}$	$-4$	$\mathrm{U}(1)$	✓			✓	$5$	5Cs.4.1	$1$	$2^{2}$	$1$	$0.685386715$	0.685386715	$1728$	$\bigl[0$ , $0$ , $0$ , $-18 i + 99$ , $0\bigr]$	${y}^2={x}^{3}+\left(-18i+99\right){x}$
32400.1-CMa1	32400.1-CMa	$1$	$1$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	32400.1	$2^{4} \cdot 3^{4} \cdot 5^{2}$	$2^{12} \cdot 3^{6} \cdot 5^{3}$	$2.39775$	$(a+1), (-a-2), (3)$	0	$\Z/2\Z$	$\textsf{yes}$	$-4$	$\mathrm{U}(1)$	✓			✓			$1$	$2^{2}$	$1$	$2.654491335$	2.654491335	$1728$	$\bigl[0$ , $0$ , $0$ , $-6 i + 3$ , $0\bigr]$	${y}^2={x}^{3}+\left(-6i+3\right){x}$
32400.1-a1	32400.1-a	$4$	$15$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	32400.1	$2^{4} \cdot 3^{4} \cdot 5^{2}$	$2^{13} \cdot 3^{6} \cdot 5^{2}$	$2.39775$	$(a+1), (-a-2), (3)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$					$3, 5$	3B, 5B	$1$	$2^{2}$	$0.166712696$	$2.205171285$	2.941040409	$\frac{198261}{2} a - \frac{62613}{2}$	$\bigl[i + 1$ , $i$ , $i + 1$ , $-22 i - 9$ , $-45 i + 20\bigr]$	${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+i{x}^{2}+\left(-22i-9\right){x}-45i+20$
32400.1-a2	32400.1-a	$4$	$15$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	32400.1	$2^{4} \cdot 3^{4} \cdot 5^{2}$	$2^{15} \cdot 3^{18} \cdot 5^{2}$	$2.39775$	$(a+1), (-a-2), (3)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$					$3, 5$	3B, 5B	$1$	$2^{2}$	$0.500138089$	$0.735057095$	2.941040409	$-\frac{86643}{4} a - \frac{1971}{4}$	$\bigl[i + 1$ , $i$ , $i + 1$ , $-82 i - 129$ , $455 i + 540\bigr]$	${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+i{x}^{2}+\left(-82i-129\right){x}+455i+540$
32400.1-a3	32400.1-a	$4$	$15$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	32400.1	$2^{4} \cdot 3^{4} \cdot 5^{2}$	$2^{27} \cdot 3^{18} \cdot 5^{10}$	$2.39775$	$(a+1), (-a-2), (3)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$					$3, 5$	3B, 5B	$1$	$2^{2}$	$2.500690447$	$0.147011419$	2.941040409	$\frac{15363}{256} a - \frac{47709}{256}$	$\bigl[i + 1$ , $i$ , $0$ , $999 i + 411$ , $14428 i + 39825\bigr]$	${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(999i+411\right){x}+14428i+39825$
32400.1-a4	32400.1-a	$4$	$15$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	32400.1	$2^{4} \cdot 3^{4} \cdot 5^{2}$	$2^{17} \cdot 3^{6} \cdot 5^{10}$	$2.39775$	$(a+1), (-a-2), (3)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$					$3, 5$	3B, 5B	$1$	$2^{2}$	$0.833563482$	$0.441034257$	2.941040409	$-\frac{13670181}{8} a + \frac{19928133}{8}$	$\bigl[i + 1$ , $i$ , $0$ , $-441 i + 831$ , $8688 i + 7645\bigr]$	${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(-441i+831\right){x}+8688i+7645$
32400.1-b1	32400.1-b	$6$	$8$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	32400.1	$2^{4} \cdot 3^{4} \cdot 5^{2}$	$2^{10} \cdot 3^{28} \cdot 5^{6}$	$2.39775$	$(a+1), (-a-2), (3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	$2^{4}$	$1$	$0.270962768$	1.083851073	$\frac{207646}{6561}$	$\bigl[i + 1$ , $i$ , $0$ , $141 i + 105$ , $6540 i + 1109\bigr]$	${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(141i+105\right){x}+6540i+1109$
32400.1-b2	32400.1-b	$6$	$8$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	32400.1	$2^{4} \cdot 3^{4} \cdot 5^{2}$	$2^{8} \cdot 3^{14} \cdot 5^{6}$	$2.39775$	$(a+1), (-a-2), (3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	$2^{2}$	$1$	$1.083851073$	1.083851073	$\frac{2048}{3}$	$\bigl[0$ , $0$ , $0$ , $-24 i - 18$ , $-14 i + 77\bigr]$	${y}^2={x}^{3}+\left(-24i-18\right){x}-14i+77$
32400.1-b3	32400.1-b	$6$	$8$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	32400.1	$2^{4} \cdot 3^{4} \cdot 5^{2}$	$2^{4} \cdot 3^{16} \cdot 5^{6}$	$2.39775$	$(a+1), (-a-2), (3)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2Cs	$1$	$2^{4}$	$1$	$1.083851073$	1.083851073	$\frac{35152}{9}$	$\bigl[i + 1$ , $i$ , $0$ , $-39 i - 30$ , $-111 i + 2\bigr]$	${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(-39i-30\right){x}-111i+2$
32400.1-b4	32400.1-b	$6$	$8$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	32400.1	$2^{4} \cdot 3^{4} \cdot 5^{2}$	$2^{8} \cdot 3^{20} \cdot 5^{6}$	$2.39775$	$(a+1), (-a-2), (3)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2Cs	$1$	$2^{5}$	$1$	$0.541925536$	1.083851073	$\frac{1556068}{81}$	$\bigl[i + 1$ , $i$ , $0$ , $-219 i - 165$ , $1554 i + 407\bigr]$	${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(-219i-165\right){x}+1554i+407$
32400.1-b5	32400.1-b	$6$	$8$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	32400.1	$2^{4} \cdot 3^{4} \cdot 5^{2}$	$2^{8} \cdot 3^{14} \cdot 5^{6}$	$2.39775$	$(a+1), (-a-2), (3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	$2^{3}$	$1$	$0.541925536$	1.083851073	$\frac{28756228}{3}$	$\bigl[i + 1$ , $i$ , $i + 1$ , $-580 i - 435$ , $7155 i + 1630\bigr]$	${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+i{x}^{2}+\left(-580i-435\right){x}+7155i+1630$
32400.1-b6	32400.1-b	$6$	$8$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	32400.1	$2^{4} \cdot 3^{4} \cdot 5^{2}$	$2^{10} \cdot 3^{16} \cdot 5^{6}$	$2.39775$	$(a+1), (-a-2), (3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	$2^{4}$	$1$	$0.270962768$	1.083851073	$\frac{3065617154}{9}$	$\bigl[i + 1$ , $i$ , $0$ , $-3459 i - 2595$ , $106368 i + 21305\bigr]$	${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(-3459i-2595\right){x}+106368i+21305$
32400.1-c1	32400.1-c	$4$	$6$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	32400.1	$2^{4} \cdot 3^{4} \cdot 5^{2}$	$2^{8} \cdot 3^{6} \cdot 5^{6}$	$2.39775$	$(a+1), (-a-2), (3)$	$1$	$\Z/2\Z$	$\textsf{potential}$	$-3$	$N(\mathrm{U}(1))$	✓			✓	$2$	2B	$1$	$2^{3}$	$0.417946696$	$2.284418796$	3.819061154	$0$	$\bigl[0$ , $0$ , $0$ , $0$ , $2 i - 11\bigr]$	${y}^2={x}^{3}+2i-11$
32400.1-c2	32400.1-c	$4$	$6$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	32400.1	$2^{4} \cdot 3^{4} \cdot 5^{2}$	$2^{8} \cdot 3^{18} \cdot 5^{6}$	$2.39775$	$(a+1), (-a-2), (3)$	$1$	$\Z/2\Z$	$\textsf{potential}$	$-3$	$N(\mathrm{U}(1))$	✓			✓	$2$	2B	$1$	$2^{3}$	$1.253840088$	$0.761472932$	3.819061154	$0$	$\bigl[0$ , $0$ , $0$ , $0$ , $-54 i + 297\bigr]$	${y}^2={x}^{3}-54i+297$
32400.1-c3	32400.1-c	$4$	$6$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	32400.1	$2^{4} \cdot 3^{4} \cdot 5^{2}$	$2^{4} \cdot 3^{18} \cdot 5^{6}$	$2.39775$	$(a+1), (-a-2), (3)$	$1$	$\Z/2\Z$	$\textsf{potential}$	$-12$	$N(\mathrm{U}(1))$	✓			✓			$1$	$2^{2}$	$2.507680176$	$0.761472932$	3.819061154	$54000$	$\bigl[i + 1$ , $i$ , $0$ , $-135 i - 102$ , $766 i + 216\bigr]$	${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(-135i-102\right){x}+766i+216$
32400.1-c4	32400.1-c	$4$	$6$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	32400.1	$2^{4} \cdot 3^{4} \cdot 5^{2}$	$2^{4} \cdot 3^{6} \cdot 5^{6}$	$2.39775$	$(a+1), (-a-2), (3)$	$1$	$\Z/2\Z$	$\textsf{potential}$	$-12$	$N(\mathrm{U}(1))$	✓			✓			$1$	$2^{2}$	$0.835893392$	$2.284418796$	3.819061154	$54000$	$\bigl[i + 1$ , $i$ , $0$ , $-15 i - 12$ , $-36 i + 2\bigr]$	${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(-15i-12\right){x}-36i+2$
32400.1-d1	32400.1-d	$2$	$5$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	32400.1	$2^{4} \cdot 3^{4} \cdot 5^{2}$	$2^{17} \cdot 3^{14} \cdot 5^{8}$	$2.39775$	$(a+1), (-a-2), (3)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$					$5$	5B.4.1	$1$	$2^{2}$	$1$	$0.493355371$	1.973421484	$\frac{1039}{24} a + \frac{13913}{24}$	$\bigl[i + 1$ , $i$ , $i + 1$ , $-64 i - 123$ , $629 i - 502\bigr]$	${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+i{x}^{2}+\left(-64i-123\right){x}+629i-502$
32400.1-d2	32400.1-d	$2$	$5$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	32400.1	$2^{4} \cdot 3^{4} \cdot 5^{2}$	$2^{13} \cdot 3^{22} \cdot 5^{4}$	$2.39775$	$(a+1), (-a-2), (3)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$					$5$	5B.4.2	$1$	$2^{2}$	$1$	$0.493355371$	1.973421484	$\frac{957521}{486} a + \frac{776647}{486}$	$\bigl[i + 1$ , $i$ , $i + 1$ , $26 i + 207$ , $-765 i + 540\bigr]$	${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+i{x}^{2}+\left(26i+207\right){x}-765i+540$
32400.1-e1	32400.1-e	$1$	$1$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	32400.1	$2^{4} \cdot 3^{4} \cdot 5^{2}$	$2^{11} \cdot 3^{14} \cdot 5^{4}$	$2.39775$	$(a+1), (-a-2), (3)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$							$1$	$2^{3}$	$0.232411670$	$1.180177506$	4.388592414	$-\frac{2401}{3} a + \frac{343}{3}$	$\bigl[i + 1$ , $i$ , $0$ , $21 i + 15$ , $-48 i + 43\bigr]$	${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(21i+15\right){x}-48i+43$
32400.1-f1	32400.1-f	$4$	$15$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	32400.1	$2^{4} \cdot 3^{4} \cdot 5^{2}$	$2^{13} \cdot 3^{18} \cdot 5^{2}$	$2.39775$	$(a+1), (-a-2), (3)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$					$3, 5$	3B, 5B	$1$	$2^{3}$	$0.386917174$	$0.735057095$	4.550499426	$\frac{198261}{2} a - \frac{62613}{2}$	$\bigl[i + 1$ , $i$ , $0$ , $-189 i - 75$ , $-1124 i + 351\bigr]$	${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(-189i-75\right){x}-1124i+351$
32400.1-f2	32400.1-f	$4$	$15$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	32400.1	$2^{4} \cdot 3^{4} \cdot 5^{2}$	$2^{15} \cdot 3^{6} \cdot 5^{2}$	$2.39775$	$(a+1), (-a-2), (3)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$					$3, 5$	3B, 5B	$1$	$2^{3}$	$0.128972391$	$2.205171285$	4.550499426	$-\frac{86643}{4} a - \frac{1971}{4}$	$\bigl[i + 1$ , $i$ , $0$ , $-9 i - 15$ , $12 i + 23\bigr]$	${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(-9i-15\right){x}+12i+23$
32400.1-f3	32400.1-f	$4$	$15$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	32400.1	$2^{4} \cdot 3^{4} \cdot 5^{2}$	$2^{27} \cdot 3^{6} \cdot 5^{10}$	$2.39775$	$(a+1), (-a-2), (3)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$					$3, 5$	3B, 5B	$1$	$2^{3}$	$0.644861957$	$0.441034257$	4.550499426	$\frac{15363}{256} a - \frac{47709}{256}$	$\bigl[i + 1$ , $i$ , $i + 1$ , $110 i + 45$ , $549 i + 1438\bigr]$	${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+i{x}^{2}+\left(110i+45\right){x}+549i+1438$
32400.1-f4	32400.1-f	$4$	$15$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	32400.1	$2^{4} \cdot 3^{4} \cdot 5^{2}$	$2^{17} \cdot 3^{18} \cdot 5^{10}$	$2.39775$	$(a+1), (-a-2), (3)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$					$3, 5$	3B, 5B	$1$	$2^{3}$	$1.934585871$	$0.147011419$	4.550499426	$-\frac{13670181}{8} a + \frac{19928133}{8}$	$\bigl[i + 1$ , $i$ , $i + 1$ , $-3970 i + 7485$ , $227093 i + 202446\bigr]$	${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+i{x}^{2}+\left(-3970i+7485\right){x}+227093i+202446$

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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.