Elliptic curves over Q(−1)\Q(\sqrt{-1}) of conductor 68450.5

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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
68450.5-a1	68450.5-a	$4$	$4$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	68450.5	$2 \cdot 5^{2} \cdot 37^{2}$	$2^{2} \cdot 5^{2} \cdot 37^{8}$	$2.89076$	$(a+1), (-a-2), (2a+1), (a+6), (a-6)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2B	$1$	$2^{3}$	$0.604991208$	$0.858111294$	2.076599157	$\frac{1689410871}{18741610}$	$\bigl[i$ , $1$ , $0$ , $25$ , $209\bigr]$	${y}^2+i{x}{y}={x}^{3}+{x}^{2}+25{x}+209$
68450.5-a2	68450.5-a	$4$	$4$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	68450.5	$2 \cdot 5^{2} \cdot 37^{2}$	$2^{8} \cdot 5^{2} \cdot 37^{2}$	$2.89076$	$(a+1), (-a-2), (2a+1), (a+6), (a-6)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2B	$1$	$2$	$0.604991208$	$3.432445179$	2.076599157	$\frac{15438249}{2960}$	$\bigl[i$ , $1$ , $0$ , $-5$ , $-5\bigr]$	${y}^2+i{x}{y}={x}^{3}+{x}^{2}-5{x}-5$
68450.5-a3	68450.5-a	$4$	$4$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	68450.5	$2 \cdot 5^{2} \cdot 37^{2}$	$2^{4} \cdot 5^{4} \cdot 37^{4}$	$2.89076$	$(a+1), (-a-2), (2a+1), (a+6), (a-6)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2Cs	$1$	$2^{5}$	$0.302495604$	$1.716222589$	2.076599157	$\frac{1767172329}{136900}$	$\bigl[i$ , $1$ , $0$ , $-25$ , $39\bigr]$	${y}^2+i{x}{y}={x}^{3}+{x}^{2}-25{x}+39$
68450.5-a4	68450.5-a	$4$	$4$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	68450.5	$2 \cdot 5^{2} \cdot 37^{2}$	$2^{2} \cdot 5^{8} \cdot 37^{2}$	$2.89076$	$(a+1), (-a-2), (2a+1), (a+6), (a-6)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2B	$1$	$2^{3}$	$0.604991208$	$0.858111294$	2.076599157	$\frac{6825481747209}{46250}$	$\bigl[i$ , $1$ , $0$ , $-395$ , $2925\bigr]$	${y}^2+i{x}{y}={x}^{3}+{x}^{2}-395{x}+2925$
68450.5-b1	68450.5-b	$3$	$9$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	68450.5	$2 \cdot 5^{2} \cdot 37^{2}$	$2^{2} \cdot 5^{2} \cdot 37^{2}$	$2.89076$	$(a+1), (-a-2), (2a+1), (a+6), (a-6)$	$1$	$\Z/3\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$3$	3B.1.1	$1$	$2$	$2.402409187$	$2.186771298$	2.334897536	$-\frac{16954786009}{370}$	$\bigl[i$ , $0$ , $i$ , $-53$ , $-146\bigr]$	${y}^2+i{x}{y}+i{y}={x}^{3}-53{x}-146$
68450.5-b2	68450.5-b	$3$	$9$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	68450.5	$2 \cdot 5^{2} \cdot 37^{2}$	$2^{6} \cdot 5^{6} \cdot 37^{6}$	$2.89076$	$(a+1), (-a-2), (2a+1), (a+6), (a-6)$	$1$	$\Z/3\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$3$	3Cs.1.1	$1$	$2 \cdot 3^{2}$	$0.800803062$	$0.728923766$	2.334897536	$-\frac{702595369}{50653000}$	$\bigl[i$ , $0$ , $i$ , $-18$ , $-342\bigr]$	${y}^2+i{x}{y}+i{y}={x}^{3}-18{x}-342$
68450.5-b3	68450.5-b	$3$	$9$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	68450.5	$2 \cdot 5^{2} \cdot 37^{2}$	$2^{18} \cdot 5^{18} \cdot 37^{2}$	$2.89076$	$(a+1), (-a-2), (2a+1), (a+6), (a-6)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$3$	3B.1.2	$1$	$2$	$2.402409187$	$0.242974588$	2.334897536	$\frac{510273943271}{37000000000}$	$\bigl[i$ , $0$ , $i$ , $167$ , $9204\bigr]$	${y}^2+i{x}{y}+i{y}={x}^{3}+167{x}+9204$
68450.5-c1	68450.5-c	$2$	$2$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	68450.5	$2 \cdot 5^{2} \cdot 37^{2}$	$2^{3} \cdot 5^{15} \cdot 37^{3}$	$2.89076$	$(a+1), (-a-2), (2a+1), (a+6), (a-6)$	$2$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2$	2B	$1$	$2^{2} \cdot 7$	$0.292829669$	$0.563848334$	4.623122610	$\frac{381018345107444271}{33422851562500} a - \frac{27278761668403303}{33422851562500}$	$\bigl[1$ , $-i - 1$ , $1$ , $-183 i - 132$ , $-1226 i - 124\bigr]$	${y}^2+{x}{y}+{y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(-183i-132\right){x}-1226i-124$
68450.5-c2	68450.5-c	$2$	$2$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	68450.5	$2 \cdot 5^{2} \cdot 37^{2}$	$2^{6} \cdot 5^{9} \cdot 37^{3}$	$2.89076$	$(a+1), (-a-2), (2a+1), (a+6), (a-6)$	$2$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2$	2B	$1$	$2^{3} \cdot 7$	$0.073207417$	$1.127696669$	4.623122610	$-\frac{2967941642509}{855625000} a + \frac{110070123389}{106953125}$	$\bigl[i$ , $i + 1$ , $i$ , $-13 i - 41$ , $-42 i - 112\bigr]$	${y}^2+i{x}{y}+i{y}={x}^{3}+\left(i+1\right){x}^{2}+\left(-13i-41\right){x}-42i-112$
68450.5-d1	68450.5-d	$2$	$2$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	68450.5	$2 \cdot 5^{2} \cdot 37^{2}$	$2^{3} \cdot 5^{15} \cdot 37^{3}$	$2.89076$	$(a+1), (-a-2), (2a+1), (a+6), (a-6)$	$2$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2$	2B	$1$	$2^{2} \cdot 7$	$0.292829669$	$0.563848334$	4.623122610	$-\frac{381018345107444271}{33422851562500} a - \frac{27278761668403303}{33422851562500}$	$\bigl[i$ , $-i + 1$ , $i$ , $183 i - 131$ , $-1226 i + 124\bigr]$	${y}^2+i{x}{y}+i{y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(183i-131\right){x}-1226i+124$
68450.5-d2	68450.5-d	$2$	$2$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	68450.5	$2 \cdot 5^{2} \cdot 37^{2}$	$2^{6} \cdot 5^{9} \cdot 37^{3}$	$2.89076$	$(a+1), (-a-2), (2a+1), (a+6), (a-6)$	$2$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2$	2B	$1$	$2^{3} \cdot 7$	$0.073207417$	$1.127696669$	4.623122610	$\frac{2967941642509}{855625000} a + \frac{110070123389}{106953125}$	$\bigl[1$ , $i - 1$ , $1$ , $13 i - 42$ , $-42 i + 112\bigr]$	${y}^2+{x}{y}+{y}={x}^{3}+\left(i-1\right){x}^{2}+\left(13i-42\right){x}-42i+112$
68450.5-e1	68450.5-e	$1$	$1$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	68450.5	$2 \cdot 5^{2} \cdot 37^{2}$	$2^{22} \cdot 5^{2} \cdot 37^{2}$	$2.89076$	$(a+1), (-a-2), (2a+1), (a+6), (a-6)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓				$1$	$2$	$0.585252191$	$1.631436169$	3.819206376	$\frac{214921799}{378880}$	$\bigl[i$ , $-1$ , $0$ , $13$ , $19\bigr]$	${y}^2+i{x}{y}={x}^{3}-{x}^{2}+13{x}+19$
68450.5-f1	68450.5-f	$2$	$2$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	68450.5	$2 \cdot 5^{2} \cdot 37^{2}$	$2^{18} \cdot 5^{3} \cdot 37^{3}$	$2.89076$	$(a+1), (-a-2), (2a+1), (a+6), (a-6)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2$	2B	$1$	$2^{3} \cdot 3^{2}$	$0.134999260$	$1.317717944$	6.404074123	$\frac{1346487493}{17523200} a + \frac{7432037549}{4380800}$	$\bigl[i$ , $0$ , $i + 1$ , $11 i + 25$ , $-2 i - 14\bigr]$	${y}^2+i{x}{y}+\left(i+1\right){y}={x}^{3}+\left(11i+25\right){x}-2i-14$
68450.5-f2	68450.5-f	$2$	$2$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	68450.5	$2 \cdot 5^{2} \cdot 37^{2}$	$2^{9} \cdot 5^{3} \cdot 37^{6}$	$2.89076$	$(a+1), (-a-2), (2a+1), (a+6), (a-6)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2$	2B	$1$	$2^{3} \cdot 3^{2}$	$0.269998520$	$0.658858972$	6.404074123	$-\frac{155462940438507}{1499328800} a + \frac{237224048385169}{1499328800}$	$\bigl[i$ , $0$ , $i + 1$ , $91 i + 265$ , $-1586 i + 834\bigr]$	${y}^2+i{x}{y}+\left(i+1\right){y}={x}^{3}+\left(91i+265\right){x}-1586i+834$
68450.5-g1	68450.5-g	$2$	$2$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	68450.5	$2 \cdot 5^{2} \cdot 37^{2}$	$2^{18} \cdot 5^{3} \cdot 37^{3}$	$2.89076$	$(a+1), (-a-2), (2a+1), (a+6), (a-6)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2$	2B	$1$	$2^{3} \cdot 3^{2}$	$0.134999260$	$1.317717944$	6.404074123	$-\frac{1346487493}{17523200} a + \frac{7432037549}{4380800}$	$\bigl[1$ , $0$ , $i + 1$ , $-12 i + 24$ , $-2 i + 14\bigr]$	${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+\left(-12i+24\right){x}-2i+14$
68450.5-g2	68450.5-g	$2$	$2$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	68450.5	$2 \cdot 5^{2} \cdot 37^{2}$	$2^{9} \cdot 5^{3} \cdot 37^{6}$	$2.89076$	$(a+1), (-a-2), (2a+1), (a+6), (a-6)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2$	2B	$1$	$2^{3} \cdot 3^{2}$	$0.269998520$	$0.658858972$	6.404074123	$\frac{155462940438507}{1499328800} a + \frac{237224048385169}{1499328800}$	$\bigl[1$ , $0$ , $i + 1$ , $-92 i + 264$ , $-1586 i - 834\bigr]$	${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+\left(-92i+264\right){x}-1586i-834$
68450.5-h1	68450.5-h	$8$	$12$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	68450.5	$2 \cdot 5^{2} \cdot 37^{2}$	$2^{6} \cdot 5^{15} \cdot 37^{5}$	$2.89076$	$(a+1), (-a-2), (2a+1), (a+6), (a-6)$	0	$\Z/12\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓		$2, 3$	2B, 3B.1.1	$4$	$2^{5} \cdot 3^{3}$	$1$	$0.207070166$	4.969683988	$-\frac{818871339068490287063}{3660470703125000} a - \frac{45099024956931216152}{457558837890625}$	$\bigl[i$ , $0$ , $0$ , $-920 i + 2805$ , $54952 i + 28239\bigr]$	${y}^2+i{x}{y}={x}^{3}+\left(-920i+2805\right){x}+54952i+28239$
68450.5-h2	68450.5-h	$8$	$12$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	68450.5	$2 \cdot 5^{2} \cdot 37^{2}$	$2^{6} \cdot 5^{15} \cdot 37^{5}$	$2.89076$	$(a+1), (-a-2), (2a+1), (a+6), (a-6)$	0	$\Z/12\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓		$2, 3$	2B, 3B.1.1	$4$	$2^{5} \cdot 3^{3}$	$1$	$0.207070166$	4.969683988	$\frac{818871339068490287063}{3660470703125000} a - \frac{45099024956931216152}{457558837890625}$	$\bigl[i$ , $0$ , $0$ , $920 i + 2805$ , $-54952 i + 28239\bigr]$	${y}^2+i{x}{y}={x}^{3}+\left(920i+2805\right){x}-54952i+28239$
68450.5-h3	68450.5-h	$8$	$12$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	68450.5	$2 \cdot 5^{2} \cdot 37^{2}$	$2^{4} \cdot 5^{4} \cdot 37^{12}$	$2.89076$	$(a+1), (-a-2), (2a+1), (a+6), (a-6)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2Cs, 3B.1.2	$1$	$2^{6} \cdot 3^{2}$	$1$	$0.138046777$	4.969683988	$-\frac{16048965315233521}{256572640900}$	$\bigl[i$ , $0$ , $0$ , $-5255$ , $149075\bigr]$	${y}^2+i{x}{y}={x}^{3}-5255{x}+149075$
68450.5-h4	68450.5-h	$8$	$12$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	68450.5	$2 \cdot 5^{2} \cdot 37^{2}$	$2^{2} \cdot 5^{5} \cdot 37^{15}$	$2.89076$	$(a+1), (-a-2), (2a+1), (a+6), (a-6)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓		$2, 3$	2B, 3B.1.2	$4$	$2^{5} \cdot 3^{2}$	$1$	$0.069023388$	4.969683988	$-\frac{3925596463972580570890057}{8228690007300044101250} a + \frac{1684584749749505877267688}{4114345003650022050625}$	$\bigl[i$ , $0$ , $0$ , $5030 i - 5095$ , $293862 i + 186619\bigr]$	${y}^2+i{x}{y}={x}^{3}+\left(5030i-5095\right){x}+293862i+186619$
68450.5-h5	68450.5-h	$8$	$12$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	68450.5	$2 \cdot 5^{2} \cdot 37^{2}$	$2^{2} \cdot 5^{5} \cdot 37^{15}$	$2.89076$	$(a+1), (-a-2), (2a+1), (a+6), (a-6)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓		$2, 3$	2B, 3B.1.2	$4$	$2^{5} \cdot 3^{2}$	$1$	$0.069023388$	4.969683988	$\frac{3925596463972580570890057}{8228690007300044101250} a + \frac{1684584749749505877267688}{4114345003650022050625}$	$\bigl[i$ , $0$ , $0$ , $-5030 i - 5095$ , $-293862 i + 186619\bigr]$	${y}^2+i{x}{y}={x}^{3}+\left(-5030i-5095\right){x}-293862i+186619$
68450.5-h6	68450.5-h	$8$	$12$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	68450.5	$2 \cdot 5^{2} \cdot 37^{2}$	$2^{12} \cdot 5^{12} \cdot 37^{4}$	$2.89076$	$(a+1), (-a-2), (2a+1), (a+6), (a-6)$	0	$\Z/2\Z\oplus\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2Cs, 3B.1.1	$1$	$2^{6} \cdot 3^{3}$	$1$	$0.414140332$	4.969683988	$\frac{1625964918479}{1369000000}$	$\bigl[i$ , $0$ , $0$ , $245$ , $975\bigr]$	${y}^2+i{x}{y}={x}^{3}+245{x}+975$
68450.5-h7	68450.5-h	$8$	$12$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	68450.5	$2 \cdot 5^{2} \cdot 37^{2}$	$2^{24} \cdot 5^{6} \cdot 37^{2}$	$2.89076$	$(a+1), (-a-2), (2a+1), (a+6), (a-6)$	0	$\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3B.1.1	$1$	$2^{3} \cdot 3^{3}$	$1$	$0.828280664$	4.969683988	$\frac{46694890801}{18944000}$	$\bigl[i$ , $0$ , $0$ , $-75$ , $143\bigr]$	${y}^2+i{x}{y}={x}^{3}-75{x}+143$
68450.5-h8	68450.5-h	$8$	$12$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	68450.5	$2 \cdot 5^{2} \cdot 37^{2}$	$2^{8} \cdot 5^{2} \cdot 37^{6}$	$2.89076$	$(a+1), (-a-2), (2a+1), (a+6), (a-6)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3B.1.2	$1$	$2^{3} \cdot 3^{2}$	$1$	$0.276093554$	4.969683988	$\frac{16232905099479601}{4052240}$	$\bigl[i$ , $0$ , $0$ , $-5275$ , $147903\bigr]$	${y}^2+i{x}{y}={x}^{3}-5275{x}+147903$
68450.5-i1	68450.5-i	$4$	$4$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	68450.5	$2 \cdot 5^{2} \cdot 37^{2}$	$2^{4} \cdot 5^{5} \cdot 37^{3}$	$2.89076$	$(a+1), (-a-2), (2a+1), (a+6), (a-6)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2$	2B	$1$	$2^{5}$	$1$	$2.278397211$	4.556794423	$-\frac{34353674}{855625} a + \frac{2747628703}{3422500}$	$\bigl[i$ , $i$ , $i$ , $4 i + 6$ , $-5 i - 6\bigr]$	${y}^2+i{x}{y}+i{y}={x}^{3}+i{x}^{2}+\left(4i+6\right){x}-5i-6$
68450.5-i2	68450.5-i	$4$	$4$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	68450.5	$2 \cdot 5^{2} \cdot 37^{2}$	$2^{2} \cdot 5^{4} \cdot 37^{6}$	$2.89076$	$(a+1), (-a-2), (2a+1), (a+6), (a-6)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2$	2Cs	$1$	$2^{6}$	$1$	$1.139198605$	4.556794423	$\frac{517593117}{3748322} a + \frac{160844155574}{46854025}$	$\bigl[i$ , $i$ , $i$ , $-26 i - 34$ , $-73 i - 30\bigr]$	${y}^2+i{x}{y}+i{y}={x}^{3}+i{x}^{2}+\left(-26i-34\right){x}-73i-30$
68450.5-i3	68450.5-i	$4$	$4$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	68450.5	$2 \cdot 5^{2} \cdot 37^{2}$	$2 \cdot 5^{2} \cdot 37^{9}$	$2.89076$	$(a+1), (-a-2), (2a+1), (a+6), (a-6)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2$	2B	$4$	$2^{3}$	$1$	$0.569599302$	4.556794423	$-\frac{11118569221560365}{7024958907842} a + \frac{824691791614398091}{35124794539210}$	$\bigl[i$ , $i$ , $i$ , $-151 i - 209$ , $1177 i + 980\bigr]$	${y}^2+i{x}{y}+i{y}={x}^{3}+i{x}^{2}+\left(-151i-209\right){x}+1177i+980$
68450.5-i4	68450.5-i	$4$	$4$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	68450.5	$2 \cdot 5^{2} \cdot 37^{2}$	$2 \cdot 5^{5} \cdot 37^{6}$	$2.89076$	$(a+1), (-a-2), (2a+1), (a+6), (a-6)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2$	2B	$4$	$2^{5}$	$1$	$0.569599302$	4.556794423	$\frac{1743482895211437}{2342701250} a + \frac{15919076014245841}{2342701250}$	$\bigl[i$ , $i$ , $i$ , $-381 i - 499$ , $-5155 i - 3216\bigr]$	${y}^2+i{x}{y}+i{y}={x}^{3}+i{x}^{2}+\left(-381i-499\right){x}-5155i-3216$
68450.5-j1	68450.5-j	$4$	$4$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	68450.5	$2 \cdot 5^{2} \cdot 37^{2}$	$2^{4} \cdot 5^{5} \cdot 37^{3}$	$2.89076$	$(a+1), (-a-2), (2a+1), (a+6), (a-6)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2$	2B	$1$	$2^{5}$	$1$	$2.278397211$	4.556794423	$\frac{34353674}{855625} a + \frac{2747628703}{3422500}$	$\bigl[1$ , $i$ , $1$ , $-4 i + 5$ , $-5 i + 6\bigr]$	${y}^2+{x}{y}+{y}={x}^{3}+i{x}^{2}+\left(-4i+5\right){x}-5i+6$
68450.5-j2	68450.5-j	$4$	$4$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	68450.5	$2 \cdot 5^{2} \cdot 37^{2}$	$2^{2} \cdot 5^{4} \cdot 37^{6}$	$2.89076$	$(a+1), (-a-2), (2a+1), (a+6), (a-6)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2$	2Cs	$1$	$2^{6}$	$1$	$1.139198605$	4.556794423	$-\frac{517593117}{3748322} a + \frac{160844155574}{46854025}$	$\bigl[1$ , $i$ , $1$ , $26 i - 35$ , $-73 i + 30\bigr]$	${y}^2+{x}{y}+{y}={x}^{3}+i{x}^{2}+\left(26i-35\right){x}-73i+30$
68450.5-j3	68450.5-j	$4$	$4$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	68450.5	$2 \cdot 5^{2} \cdot 37^{2}$	$2 \cdot 5^{2} \cdot 37^{9}$	$2.89076$	$(a+1), (-a-2), (2a+1), (a+6), (a-6)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2$	2B	$4$	$2^{3}$	$1$	$0.569599302$	4.556794423	$\frac{11118569221560365}{7024958907842} a + \frac{824691791614398091}{35124794539210}$	$\bigl[1$ , $i$ , $1$ , $151 i - 210$ , $1177 i - 980\bigr]$	${y}^2+{x}{y}+{y}={x}^{3}+i{x}^{2}+\left(151i-210\right){x}+1177i-980$
68450.5-j4	68450.5-j	$4$	$4$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	68450.5	$2 \cdot 5^{2} \cdot 37^{2}$	$2 \cdot 5^{5} \cdot 37^{6}$	$2.89076$	$(a+1), (-a-2), (2a+1), (a+6), (a-6)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2$	2B	$4$	$2^{5}$	$1$	$0.569599302$	4.556794423	$-\frac{1743482895211437}{2342701250} a + \frac{15919076014245841}{2342701250}$	$\bigl[1$ , $i$ , $1$ , $381 i - 500$ , $-5155 i + 3216\bigr]$	${y}^2+{x}{y}+{y}={x}^{3}+i{x}^{2}+\left(381i-500\right){x}-5155i+3216$

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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.