Elliptic curves over Q(−1)\Q(\sqrt{-1}) of conductor 25600.2

Results (1-50 of 104 matches)

  Download displayed columns for results to

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
25600.2-a1	25600.2-a	$4$	$4$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	25600.2	$2^{10} \cdot 5^{2}$	$2^{16} \cdot 5^{4}$	$2.26063$	$(a+1), (-a-2), (2a+1)$	$2$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	$2^{4}$	$0.312721490$	$3.231914471$	4.042756438	$-\frac{3456}{25}$	$\bigl[0$ , $0$ , $0$ , $2$ , $-4 i\bigr]$	${y}^2={x}^{3}+2{x}-4i$
25600.2-a2	25600.2-a	$4$	$4$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	25600.2	$2^{10} \cdot 5^{2}$	$2^{23} \cdot 5^{5}$	$2.26063$	$(a+1), (-a-2), (2a+1)$	$2$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	$2^{3}$	$0.312721490$	$1.615957235$	4.042756438	$-\frac{12579624}{625} a + \frac{2240568}{625}$	$\bigl[0$ , $0$ , $0$ , $30 i - 8$ , $-60 i - 28\bigr]$	${y}^2={x}^{3}+\left(30i-8\right){x}-60i-28$
25600.2-a3	25600.2-a	$4$	$4$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	25600.2	$2^{10} \cdot 5^{2}$	$2^{23} \cdot 5^{5}$	$2.26063$	$(a+1), (-a-2), (2a+1)$	$2$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	$2^{3}$	$0.312721490$	$1.615957235$	4.042756438	$\frac{12579624}{625} a + \frac{2240568}{625}$	$\bigl[0$ , $0$ , $0$ , $-30 i - 8$ , $-60 i + 28\bigr]$	${y}^2={x}^{3}+\left(-30i-8\right){x}-60i+28$
25600.2-a4	25600.2-a	$4$	$4$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	25600.2	$2^{10} \cdot 5^{2}$	$2^{14} \cdot 5^{2}$	$2.26063$	$(a+1), (-a-2), (2a+1)$	$2$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	$1$	$1.250885960$	$3.231914471$	4.042756438	$\frac{1898208}{5}$	$\bigl[0$ , $0$ , $0$ , $-13$ , $18\bigr]$	${y}^2={x}^{3}-13{x}+18$
25600.2-b1	25600.2-b	$4$	$4$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	25600.2	$2^{10} \cdot 5^{2}$	$2^{23} \cdot 5^{10}$	$2.26063$	$(a+1), (-a-2), (2a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	$2^{3}$	$1$	$0.897871193$	1.795742386	$-\frac{324134216}{390625} a - \frac{1619282312}{390625}$	$\bigl[0$ , $-i$ , $0$ , $70 i + 5$ , $159 i + 238\bigr]$	${y}^2={x}^{3}-i{x}^{2}+\left(70i+5\right){x}+159i+238$
25600.2-b2	25600.2-b	$4$	$4$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	25600.2	$2^{10} \cdot 5^{2}$	$2^{23} \cdot 5^{10}$	$2.26063$	$(a+1), (-a-2), (2a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	$2^{3}$	$1$	$0.897871193$	1.795742386	$\frac{324134216}{390625} a - \frac{1619282312}{390625}$	$\bigl[0$ , $-i$ , $0$ , $-70 i + 5$ , $159 i - 238\bigr]$	${y}^2={x}^{3}-i{x}^{2}+\left(-70i+5\right){x}+159i-238$
25600.2-b3	25600.2-b	$4$	$4$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	25600.2	$2^{10} \cdot 5^{2}$	$2^{16} \cdot 5^{8}$	$2.26063$	$(a+1), (-a-2), (2a+1)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	$2^{4}$	$1$	$1.795742386$	1.795742386	$-\frac{1557376}{625}$	$\bigl[0$ , $-i$ , $0$ , $15$ , $25 i\bigr]$	${y}^2={x}^{3}-i{x}^{2}+15{x}+25i$
25600.2-b4	25600.2-b	$4$	$4$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	25600.2	$2^{10} \cdot 5^{2}$	$2^{14} \cdot 5^{4}$	$2.26063$	$(a+1), (-a-2), (2a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	$2^{2}$	$1$	$1.795742386$	1.795742386	$\frac{252179168}{25}$	$\bigl[0$ , $-1$ , $0$ , $-66$ , $230\bigr]$	${y}^2={x}^{3}-{x}^{2}-66{x}+230$
25600.2-c1	25600.2-c	$4$	$4$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	25600.2	$2^{10} \cdot 5^{2}$	$2^{20} \cdot 5^{6}$	$2.26063$	$(a+1), (-a-2), (2a+1)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2Cs	$1$	$2^{4}$	$1$	$1.934841452$	1.934841452	$\frac{119136}{625} a + \frac{1036352}{625}$	$\bigl[0$ , $i - 1$ , $0$ , $-4 i + 12$ , $0\bigr]$	${y}^2={x}^{3}+\left(i-1\right){x}^{2}+\left(-4i+12\right){x}$
25600.2-c2	25600.2-c	$4$	$4$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	25600.2	$2^{10} \cdot 5^{2}$	$2^{25} \cdot 5^{9}$	$2.26063$	$(a+1), (-a-2), (2a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{3}$	$1$	$0.967420726$	1.934841452	$-\frac{79113756}{390625} a + \frac{695553908}{390625}$	$\bigl[0$ , $i - 1$ , $0$ , $16 i - 48$ , $-64 i + 32\bigr]$	${y}^2={x}^{3}+\left(i-1\right){x}^{2}+\left(16i-48\right){x}-64i+32$
25600.2-c3	25600.2-c	$4$	$4$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	25600.2	$2^{10} \cdot 5^{2}$	$2^{10} \cdot 5^{3}$	$2.26063$	$(a+1), (-a-2), (2a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2$	$1$	$3.869682904$	1.934841452	$-\frac{2751872}{25} a + \frac{2323456}{25}$	$\bigl[0$ , $i - 1$ , $0$ , $-4 i + 7$ , $10 i + 4\bigr]$	${y}^2={x}^{3}+\left(i-1\right){x}^{2}+\left(-4i+7\right){x}+10i+4$
25600.2-c4	25600.2-c	$4$	$4$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	25600.2	$2^{10} \cdot 5^{2}$	$2^{25} \cdot 5^{6}$	$2.26063$	$(a+1), (-a-2), (2a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{3}$	$1$	$0.967420726$	1.934841452	$\frac{286742876}{625} a + \frac{195690268}{625}$	$\bigl[0$ , $i - 1$ , $0$ , $-24 i + 152$ , $-656 i - 208\bigr]$	${y}^2={x}^{3}+\left(i-1\right){x}^{2}+\left(-24i+152\right){x}-656i-208$
25600.2-d1	25600.2-d	$4$	$4$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	25600.2	$2^{10} \cdot 5^{2}$	$2^{20} \cdot 5^{6}$	$2.26063$	$(a+1), (-a-2), (2a+1)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2Cs	$1$	$2^{4}$	$1$	$1.934841452$	1.934841452	$-\frac{119136}{625} a + \frac{1036352}{625}$	$\bigl[0$ , $-i - 1$ , $0$ , $4 i + 12$ , $0\bigr]$	${y}^2={x}^{3}+\left(-i-1\right){x}^{2}+\left(4i+12\right){x}$
25600.2-d2	25600.2-d	$4$	$4$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	25600.2	$2^{10} \cdot 5^{2}$	$2^{25} \cdot 5^{9}$	$2.26063$	$(a+1), (-a-2), (2a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{3}$	$1$	$0.967420726$	1.934841452	$\frac{79113756}{390625} a + \frac{695553908}{390625}$	$\bigl[0$ , $-i - 1$ , $0$ , $-16 i - 48$ , $64 i + 32\bigr]$	${y}^2={x}^{3}+\left(-i-1\right){x}^{2}+\left(-16i-48\right){x}+64i+32$
25600.2-d3	25600.2-d	$4$	$4$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	25600.2	$2^{10} \cdot 5^{2}$	$2^{10} \cdot 5^{3}$	$2.26063$	$(a+1), (-a-2), (2a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2$	$1$	$3.869682904$	1.934841452	$\frac{2751872}{25} a + \frac{2323456}{25}$	$\bigl[0$ , $-i - 1$ , $0$ , $4 i + 7$ , $-10 i + 4\bigr]$	${y}^2={x}^{3}+\left(-i-1\right){x}^{2}+\left(4i+7\right){x}-10i+4$
25600.2-d4	25600.2-d	$4$	$4$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	25600.2	$2^{10} \cdot 5^{2}$	$2^{25} \cdot 5^{6}$	$2.26063$	$(a+1), (-a-2), (2a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{3}$	$1$	$0.967420726$	1.934841452	$-\frac{286742876}{625} a + \frac{195690268}{625}$	$\bigl[0$ , $-i - 1$ , $0$ , $24 i + 152$ , $656 i - 208\bigr]$	${y}^2={x}^{3}+\left(-i-1\right){x}^{2}+\left(24i+152\right){x}+656i-208$
25600.2-e1	25600.2-e	$4$	$4$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	25600.2	$2^{10} \cdot 5^{2}$	$2^{14} \cdot 5^{5}$	$2.26063$	$(a+1), (-a-2), (2a+1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2$	$1.084866568$	$3.127360497$	3.392768851	$\frac{421696}{625} a + \frac{663328}{625}$	$\bigl[0$ , $-1$ , $0$ , $4 i + 2$ , $-4 i - 2\bigr]$	${y}^2={x}^{3}-{x}^{2}+\left(4i+2\right){x}-4i-2$
25600.2-e2	25600.2-e	$4$	$4$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	25600.2	$2^{10} \cdot 5^{2}$	$2^{16} \cdot 5^{4}$	$2.26063$	$(a+1), (-a-2), (2a+1)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2Cs	$1$	$2^{4}$	$0.542433284$	$3.127360497$	3.392768851	$-\frac{29952}{25} a + \frac{10624}{5}$	$\bigl[0$ , $i$ , $0$ , $4 i + 3$ , $3 i - 4\bigr]$	${y}^2={x}^{3}+i{x}^{2}+\left(4i+3\right){x}+3i-4$
25600.2-e3	25600.2-e	$4$	$4$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	25600.2	$2^{10} \cdot 5^{2}$	$2^{23} \cdot 5^{5}$	$2.26063$	$(a+1), (-a-2), (2a+1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{4}$	$0.271216642$	$1.563680248$	3.392768851	$\frac{18091224}{625} a + \frac{10253768}{625}$	$\bigl[0$ , $i$ , $0$ , $34 i + 13$ , $25 i + 70\bigr]$	${y}^2={x}^{3}+i{x}^{2}+\left(34i+13\right){x}+25i+70$
25600.2-e4	25600.2-e	$4$	$4$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	25600.2	$2^{10} \cdot 5^{2}$	$2^{23} \cdot 5^{2}$	$2.26063$	$(a+1), (-a-2), (2a+1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{2}$	$1.084866568$	$1.563680248$	3.392768851	$-\frac{16691192}{5} a + \frac{311048}{5}$	$\bigl[0$ , $i$ , $0$ , $54 i + 53$ , $113 i - 254\bigr]$	${y}^2={x}^{3}+i{x}^{2}+\left(54i+53\right){x}+113i-254$
25600.2-f1	25600.2-f	$6$	$8$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	25600.2	$2^{10} \cdot 5^{2}$	$2^{24} \cdot 5^{3}$	$2.26063$	$(a+1), (-a-2), (2a+1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	$2^{2}$	$1.689027116$	$1.016598393$	3.434124507	$-\frac{649216016}{25} a - \frac{494572808}{25}$	$\bigl[0$ , $1$ , $0$ , $-106 i - 213$ , $-938 i - 1161\bigr]$	${y}^2={x}^{3}+{x}^{2}+\left(-106i-213\right){x}-938i-1161$
25600.2-f2	25600.2-f	$6$	$8$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	25600.2	$2^{10} \cdot 5^{2}$	$2^{24} \cdot 5^{3}$	$2.26063$	$(a+1), (-a-2), (2a+1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	$2^{3}$	$0.844513558$	$1.016598393$	3.434124507	$\frac{649216016}{25} a - \frac{494572808}{25}$	$\bigl[0$ , $-i$ , $0$ , $-106 i + 213$ , $-1161 i - 938\bigr]$	${y}^2={x}^{3}-i{x}^{2}+\left(-106i+213\right){x}-1161i-938$
25600.2-f3	25600.2-f	$6$	$8$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	25600.2	$2^{10} \cdot 5^{2}$	$2^{18} \cdot 5^{6}$	$2.26063$	$(a+1), (-a-2), (2a+1)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2Cs	$1$	$2^{5}$	$0.422256779$	$2.033196787$	3.434124507	$-\frac{3181056}{625} a - \frac{1129792}{625}$	$\bigl[0$ , $-i$ , $0$ , $-6 i + 13$ , $-21 i - 18\bigr]$	${y}^2={x}^{3}-i{x}^{2}+\left(-6i+13\right){x}-21i-18$
25600.2-f4	25600.2-f	$6$	$8$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	25600.2	$2^{10} \cdot 5^{2}$	$2^{18} \cdot 5^{6}$	$2.26063$	$(a+1), (-a-2), (2a+1)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2Cs	$1$	$2^{4}$	$0.844513558$	$2.033196787$	3.434124507	$\frac{3181056}{625} a - \frac{1129792}{625}$	$\bigl[0$ , $1$ , $0$ , $-6 i - 13$ , $-18 i - 21\bigr]$	${y}^2={x}^{3}+{x}^{2}+\left(-6i-13\right){x}-18i-21$
25600.2-f5	25600.2-f	$6$	$8$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	25600.2	$2^{10} \cdot 5^{2}$	$2^{24} \cdot 5^{9}$	$2.26063$	$(a+1), (-a-2), (2a+1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	$2^{2}$	$1.689027116$	$1.016598393$	3.434124507	$-\frac{256910704}{390625} a - \frac{293256872}{390625}$	$\bigl[0$ , $1$ , $0$ , $-26 i + 27$ , $-34 i - 129\bigr]$	${y}^2={x}^{3}+{x}^{2}+\left(-26i+27\right){x}-34i-129$
25600.2-f6	25600.2-f	$6$	$8$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	25600.2	$2^{10} \cdot 5^{2}$	$2^{24} \cdot 5^{9}$	$2.26063$	$(a+1), (-a-2), (2a+1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	$2^{5}$	$0.211128389$	$1.016598393$	3.434124507	$\frac{256910704}{390625} a - \frac{293256872}{390625}$	$\bigl[0$ , $i$ , $0$ , $-26 i - 27$ , $129 i + 34\bigr]$	${y}^2={x}^{3}+i{x}^{2}+\left(-26i-27\right){x}+129i+34$
25600.2-g1	25600.2-g	$4$	$4$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	25600.2	$2^{10} \cdot 5^{2}$	$2^{14} \cdot 5^{5}$	$2.26063$	$(a+1), (-a-2), (2a+1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{3}$	$0.287252687$	$3.127360497$	3.593370833	$-\frac{421696}{625} a + \frac{663328}{625}$	$\bigl[0$ , $i$ , $0$ , $4 i - 2$ , $-2 i - 4\bigr]$	${y}^2={x}^{3}+i{x}^{2}+\left(4i-2\right){x}-2i-4$
25600.2-g2	25600.2-g	$4$	$4$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	25600.2	$2^{10} \cdot 5^{2}$	$2^{16} \cdot 5^{4}$	$2.26063$	$(a+1), (-a-2), (2a+1)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2Cs	$1$	$2^{4}$	$0.574505375$	$3.127360497$	3.593370833	$\frac{29952}{25} a + \frac{10624}{5}$	$\bigl[0$ , $1$ , $0$ , $4 i - 3$ , $4 i - 3\bigr]$	${y}^2={x}^{3}+{x}^{2}+\left(4i-3\right){x}+4i-3$
25600.2-g3	25600.2-g	$4$	$4$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	25600.2	$2^{10} \cdot 5^{2}$	$2^{23} \cdot 5^{5}$	$2.26063$	$(a+1), (-a-2), (2a+1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{2}$	$1.149010751$	$1.563680248$	3.593370833	$-\frac{18091224}{625} a + \frac{10253768}{625}$	$\bigl[0$ , $1$ , $0$ , $34 i - 13$ , $-70 i - 25\bigr]$	${y}^2={x}^{3}+{x}^{2}+\left(34i-13\right){x}-70i-25$
25600.2-g4	25600.2-g	$4$	$4$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	25600.2	$2^{10} \cdot 5^{2}$	$2^{23} \cdot 5^{2}$	$2.26063$	$(a+1), (-a-2), (2a+1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{2}$	$1.149010751$	$1.563680248$	3.593370833	$\frac{16691192}{5} a + \frac{311048}{5}$	$\bigl[0$ , $1$ , $0$ , $54 i - 53$ , $254 i - 113\bigr]$	${y}^2={x}^{3}+{x}^{2}+\left(54i-53\right){x}+254i-113$
25600.2-h1	25600.2-h	$4$	$4$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	25600.2	$2^{10} \cdot 5^{2}$	$2^{18} \cdot 5^{4}$	$2.26063$	$(a+1), (-a-2), (2a+1)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2Cs	$1$	$2^{4}$	$0.643884228$	$2.902337071$	3.737538130	$-\frac{64}{25}$	$\bigl[0$ , $i - 1$ , $0$ , $0$ , $-4 i - 4\bigr]$	${y}^2={x}^{3}+\left(i-1\right){x}^{2}-4i-4$
25600.2-h2	25600.2-h	$4$	$4$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	25600.2	$2^{10} \cdot 5^{2}$	$2^{24} \cdot 5^{5}$	$2.26063$	$(a+1), (-a-2), (2a+1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	$2^{4}$	$0.321942114$	$1.451168535$	3.737538130	$-\frac{10307536}{625} a + \frac{24381448}{625}$	$\bigl[0$ , $i - 1$ , $0$ , $-20 i - 40$ , $-76 i - 68\bigr]$	${y}^2={x}^{3}+\left(i-1\right){x}^{2}+\left(-20i-40\right){x}-76i-68$
25600.2-h3	25600.2-h	$4$	$4$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	25600.2	$2^{10} \cdot 5^{2}$	$2^{24} \cdot 5^{5}$	$2.26063$	$(a+1), (-a-2), (2a+1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	$2^{2}$	$1.287768456$	$1.451168535$	3.737538130	$\frac{10307536}{625} a + \frac{24381448}{625}$	$\bigl[0$ , $i - 1$ , $0$ , $-20 i + 40$ , $-68 i - 76\bigr]$	${y}^2={x}^{3}+\left(i-1\right){x}^{2}+\left(-20i+40\right){x}-68i-76$
25600.2-h4	25600.2-h	$4$	$4$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	25600.2	$2^{10} \cdot 5^{2}$	$2^{18} \cdot 5^{2}$	$2.26063$	$(a+1), (-a-2), (2a+1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	$2$	$1.287768456$	$2.902337071$	3.737538130	$\frac{438976}{5}$	$\bigl[0$ , $i + 1$ , $0$ , $-12 i$ , $8 i - 8\bigr]$	${y}^2={x}^{3}+\left(i+1\right){x}^{2}-12i{x}+8i-8$
25600.2-i1	25600.2-i	$8$	$12$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	25600.2	$2^{10} \cdot 5^{2}$	$2^{26} \cdot 5^{5}$	$2.26063$	$(a+1), (-a-2), (2a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 3$	2B, 3B	$1$	$2^{3}$	$1$	$1.135453623$	2.270907247	$-\frac{59648644}{625} a - \frac{119744792}{625}$	$\bigl[0$ , $i + 1$ , $0$ , $88 i + 40$ , $-8 i - 376\bigr]$	${y}^2={x}^{3}+\left(i+1\right){x}^{2}+\left(88i+40\right){x}-8i-376$
25600.2-i2	25600.2-i	$8$	$12$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	25600.2	$2^{10} \cdot 5^{2}$	$2^{26} \cdot 5^{5}$	$2.26063$	$(a+1), (-a-2), (2a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 3$	2B, 3B	$1$	$2^{3}$	$1$	$1.135453623$	2.270907247	$\frac{59648644}{625} a - \frac{119744792}{625}$	$\bigl[0$ , $i + 1$ , $0$ , $88 i - 40$ , $376 i + 8\bigr]$	${y}^2={x}^{3}+\left(i+1\right){x}^{2}+\left(88i-40\right){x}+376i+8$
25600.2-i3	25600.2-i	$8$	$12$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	25600.2	$2^{10} \cdot 5^{2}$	$2^{26} \cdot 5^{15}$	$2.26063$	$(a+1), (-a-2), (2a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 3$	2B, 3B	$1$	$2^{3} \cdot 3$	$1$	$0.378484541$	2.270907247	$-\frac{893935595564}{244140625} a - \frac{1336401187352}{244140625}$	$\bigl[0$ , $i + 1$ , $0$ , $8 i + 440$ , $-3784 i + 8\bigr]$	${y}^2={x}^{3}+\left(i+1\right){x}^{2}+\left(8i+440\right){x}-3784i+8$
25600.2-i4	25600.2-i	$8$	$12$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	25600.2	$2^{10} \cdot 5^{2}$	$2^{26} \cdot 5^{15}$	$2.26063$	$(a+1), (-a-2), (2a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 3$	2B, 3B	$1$	$2^{3} \cdot 3$	$1$	$0.378484541$	2.270907247	$\frac{893935595564}{244140625} a - \frac{1336401187352}{244140625}$	$\bigl[0$ , $i + 1$ , $0$ , $8 i - 440$ , $-8 i + 3784\bigr]$	${y}^2={x}^{3}+\left(i+1\right){x}^{2}+\left(8i-440\right){x}-8i+3784$
25600.2-i5	25600.2-i	$8$	$12$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	25600.2	$2^{10} \cdot 5^{2}$	$2^{22} \cdot 5^{12}$	$2.26063$	$(a+1), (-a-2), (2a+1)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 3$	2Cs, 3B	$1$	$2^{4} \cdot 3$	$1$	$0.756969082$	2.270907247	$-\frac{20720464}{15625}$	$\bigl[0$ , $i + 1$ , $0$ , $-72 i$ , $-280 i + 280\bigr]$	${y}^2={x}^{3}+\left(i+1\right){x}^{2}-72i{x}-280i+280$
25600.2-i6	25600.2-i	$8$	$12$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	25600.2	$2^{10} \cdot 5^{2}$	$2^{22} \cdot 5^{4}$	$2.26063$	$(a+1), (-a-2), (2a+1)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 3$	2Cs, 3B	$1$	$2^{4}$	$1$	$2.270907247$	2.270907247	$\frac{21296}{25}$	$\bigl[0$ , $i + 1$ , $0$ , $8 i$ , $8 i - 8\bigr]$	${y}^2={x}^{3}+\left(i+1\right){x}^{2}+8i{x}+8i-8$
25600.2-i7	25600.2-i	$8$	$12$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	25600.2	$2^{10} \cdot 5^{2}$	$2^{14} \cdot 5^{2}$	$2.26063$	$(a+1), (-a-2), (2a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 3$	2B, 3B	$1$	$2$	$1$	$4.541814495$	2.270907247	$\frac{16384}{5}$	$\bigl[0$ , $i + 1$ , $0$ , $-2 i$ , $0\bigr]$	${y}^2={x}^{3}+\left(i+1\right){x}^{2}-2i{x}$
25600.2-i8	25600.2-i	$8$	$12$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	25600.2	$2^{10} \cdot 5^{2}$	$2^{14} \cdot 5^{6}$	$2.26063$	$(a+1), (-a-2), (2a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 3$	2B, 3B	$1$	$2 \cdot 3$	$1$	$1.513938165$	2.270907247	$\frac{488095744}{125}$	$\bigl[0$ , $i + 1$ , $0$ , $-82 i$ , $-232 i + 232\bigr]$	${y}^2={x}^{3}+\left(i+1\right){x}^{2}-82i{x}-232i+232$
25600.2-j1	25600.2-j	$10$	$16$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	25600.2	$2^{10} \cdot 5^{2}$	$2^{28} \cdot 5^{10}$	$2.26063$	$(a+1), (-a-2), (2a+1)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2Cs	$4$	$2^{4}$	$1$	$0.529780130$	2.119120521	$-\frac{35999730234}{390625} a - \frac{51700389912}{390625}$	$\bigl[0$ , $0$ , $0$ , $-346 i + 240$ , $404 i + 3316\bigr]$	${y}^2={x}^{3}+\left(-346i+240\right){x}+404i+3316$
25600.2-j2	25600.2-j	$10$	$16$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	25600.2	$2^{10} \cdot 5^{2}$	$2^{28} \cdot 5^{10}$	$2.26063$	$(a+1), (-a-2), (2a+1)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2Cs	$1$	$2^{6}$	$1$	$0.529780130$	2.119120521	$\frac{35999730234}{390625} a - \frac{51700389912}{390625}$	$\bigl[0$ , $0$ , $0$ , $-346 i - 240$ , $3316 i + 404\bigr]$	${y}^2={x}^{3}+\left(-346i-240\right){x}+3316i+404$
25600.2-j3	25600.2-j	$10$	$16$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	25600.2	$2^{10} \cdot 5^{2}$	$2^{26} \cdot 5^{8}$	$2.26063$	$(a+1), (-a-2), (2a+1)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2Cs	$1$	$2^{5}$	$1$	$1.059560260$	2.119120521	$\frac{237276}{625}$	$\bigl[0$ , $0$ , $0$ , $-26 i$ , $68 i + 68\bigr]$	${y}^2={x}^{3}-26i{x}+68i+68$
25600.2-j4	25600.2-j	$10$	$16$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	25600.2	$2^{10} \cdot 5^{2}$	$2^{29} \cdot 5^{17}$	$2.26063$	$(a+1), (-a-2), (2a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	$2^{5}$	$1$	$0.264890065$	2.119120521	$-\frac{22845545233191}{152587890625} a + \frac{135893651813613}{152587890625}$	$\bigl[0$ , $0$ , $0$ , $-266 i - 480$ , $2868 i - 3852\bigr]$	${y}^2={x}^{3}+\left(-266i-480\right){x}+2868i-3852$
25600.2-j5	25600.2-j	$10$	$16$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	25600.2	$2^{10} \cdot 5^{2}$	$2^{29} \cdot 5^{17}$	$2.26063$	$(a+1), (-a-2), (2a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$4$	$2^{3}$	$1$	$0.264890065$	2.119120521	$\frac{22845545233191}{152587890625} a + \frac{135893651813613}{152587890625}$	$\bigl[0$ , $0$ , $0$ , $-266 i + 480$ , $-3852 i + 2868\bigr]$	${y}^2={x}^{3}+\left(-266i+480\right){x}-3852i+2868$
25600.2-j6	25600.2-j	$10$	$16$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	25600.2	$2^{10} \cdot 5^{2}$	$2^{22} \cdot 5^{4}$	$2.26063$	$(a+1), (-a-2), (2a+1)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2Cs	$1$	$2^{4}$	$1$	$2.119120521$	2.119120521	$\frac{148176}{25}$	$\bigl[0$ , $0$ , $0$ , $14 i$ , $12 i + 12\bigr]$	${y}^2={x}^{3}+14i{x}+12i+12$
25600.2-j7	25600.2-j	$10$	$16$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	25600.2	$2^{10} \cdot 5^{2}$	$2^{14} \cdot 5^{2}$	$2.26063$	$(a+1), (-a-2), (2a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	$2$	$1$	$4.238241043$	2.119120521	$\frac{55296}{5}$	$\bigl[0$ , $0$ , $0$ , $4 i$ , $-2 i - 2\bigr]$	${y}^2={x}^{3}+4i{x}-2i-2$
25600.2-j8	25600.2-j	$10$	$16$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	25600.2	$2^{10} \cdot 5^{2}$	$2^{26} \cdot 5^{2}$	$2.26063$	$(a+1), (-a-2), (2a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$4$	$2$	$1$	$1.059560260$	2.119120521	$\frac{132304644}{5}$	$\bigl[0$ , $0$ , $0$ , $214 i$ , $852 i + 852\bigr]$	${y}^2={x}^{3}+214i{x}+852i+852$

  Download displayed columns for results to

  *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.