Elliptic curve search results

Results (1-50 of 249 matches)

 

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
25.1-CMa1	25.1-CMa	$1$	$1$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	25.1	\( 5^{2} \)	\( 5^{3} \)	$0.39963$	$(-a-2)$	0	$\Z/10\Z$	$\textsf{yes}$	$-4$	$\mathrm{U}(1)$	✓			✓	$5$	5Cs.1.1	$1$	\( 2 \)	$1$	$9.195427721$	0.183908554	\( 1728 \)	\( \bigl[i + 1\) , \( i\) , \( 1\) , \( -i - 1\) , \( 0\bigr] \)	${y}^2+\left(i+1\right){x}{y}+{y}={x}^{3}+i{x}^{2}+\left(-i-1\right){x}$
25.3-CMa1	25.3-CMa	$1$	$1$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	25.3	\( 5^{2} \)	\( 5^{3} \)	$0.39963$	$(2a+1)$	0	$\Z/10\Z$	$\textsf{yes}$	$-4$	$\mathrm{U}(1)$	✓			✓	$5$	5Cs.1.1	$1$	\( 2 \)	$1$	$9.195427721$	0.183908554	\( 1728 \)	\( \bigl[i + 1\) , \( i\) , \( i\) , \( 0\) , \( 0\bigr] \)	${y}^2+\left(i+1\right){x}{y}+i{y}={x}^{3}+i{x}^{2}$
64.1-CMa1	64.1-CMa	$2$	$2$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	64.1	\( 2^{6} \)	\( 2^{12} \)	$0.50549$	$(a+1)$	0	$\Z/2\Z\oplus\Z/4\Z$	$\textsf{yes}$	$-4$	$\mathrm{U}(1)$	✓	✓		✓	$2$	2Cs	$1$	\( 2^{2} \)	$1$	$6.875185818$	0.429699113	\( 1728 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( -1\) , \( 0\bigr] \)	${y}^2={x}^{3}-{x}$
169.1-CMa1	169.1-CMa	$1$	$1$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	169.1	\( 13^{2} \)	\( 13^{9} \)	$0.64438$	$(-3a-2)$	0	$\Z/2\Z$	$\textsf{yes}$	$-4$	$\mathrm{U}(1)$	✓			✓	$13$	13Cs.3.1	$1$	\( 2 \)	$1$	$2.008431027$	1.004215513	\( 1728 \)	\( \bigl[i + 1\) , \( i\) , \( 1\) , \( 11 i + 1\) , \( i - 6\bigr] \)	${y}^2+\left(i+1\right){x}{y}+{y}={x}^{3}+i{x}^{2}+\left(11i+1\right){x}+i-6$
169.3-CMa1	169.3-CMa	$1$	$1$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	169.3	\( 13^{2} \)	\( 13^{9} \)	$0.64438$	$(2a+3)$	0	$\Z/2\Z$	$\textsf{yes}$	$-4$	$\mathrm{U}(1)$	✓			✓	$13$	13Cs.3.1	$1$	\( 2 \)	$1$	$2.008431027$	1.004215513	\( 1728 \)	\( \bigl[i + 1\) , \( i\) , \( i\) , \( -12 i + 2\) , \( i + 6\bigr] \)	${y}^2+\left(i+1\right){x}{y}+i{y}={x}^{3}+i{x}^{2}+\left(-12i+2\right){x}+i+6$
256.1-CMa1	256.1-CMa	$2$	$2$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	256.1	\( 2^{8} \)	\( 2^{12} \)	$0.71487$	$(a+1)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{yes}$	$-4$	$\mathrm{U}(1)$	✓	✓		✓	$2$	2Cs	$1$	\( 2 \)	$1$	$6.875185818$	0.859398227	\( 1728 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( 1\) , \( 0\bigr] \)	${y}^2={x}^{3}+{x}$
400.1-CMa1	400.1-CMa	$1$	$1$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	400.1	\( 2^{4} \cdot 5^{2} \)	\( 2^{12} \cdot 5^{9} \)	$0.79925$	$(a+1), (-a-2)$	0	$\Z/2\Z$	$\textsf{yes}$	$-4$	$\mathrm{U}(1)$	✓			✓	$5$	5Cs.4.1	$1$	\( 2 \)	$1$	$2.056160146$	1.028080073	\( 1728 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( -2 i + 11\) , \( 0\bigr] \)	${y}^2={x}^{3}+\left(-2i+11\right){x}$
400.3-CMa1	400.3-CMa	$1$	$1$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	400.3	\( 2^{4} \cdot 5^{2} \)	\( 2^{12} \cdot 5^{9} \)	$0.79925$	$(a+1), (2a+1)$	0	$\Z/2\Z$	$\textsf{yes}$	$-4$	$\mathrm{U}(1)$	✓			✓	$5$	5Cs.4.1	$1$	\( 2 \)	$1$	$2.056160146$	1.028080073	\( 1728 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( 2 i + 11\) , \( 0\bigr] \)	${y}^2={x}^{3}+\left(2i+11\right){x}$
625.3-CMb1	625.3-CMb	$1$	$1$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	625.3	\( 5^{4} \)	\( 5^{15} \)	$0.89359$	$(-a-2), (2a+1)$	0	$\Z/2\Z$	$\textsf{yes}$	$-4$	$\mathrm{U}(1)$	✓			✓	$5$	5Cs.1.3	$1$	\( 2^{2} \)	$1$	$1.839085544$	1.839085544	\( 1728 \)	\( \bigl[i + 1\) , \( i\) , \( 1\) , \( -13 i + 5\) , \( 3 i + 6\bigr] \)	${y}^2+\left(i+1\right){x}{y}+{y}={x}^{3}+i{x}^{2}+\left(-13i+5\right){x}+3i+6$
625.3-CMa1	625.3-CMa	$1$	$1$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	625.3	\( 5^{4} \)	\( 5^{15} \)	$0.89359$	$(-a-2), (2a+1)$	0	$\Z/2\Z$	$\textsf{yes}$	$-4$	$\mathrm{U}(1)$	✓			✓	$5$	5Cs.1.3	$1$	\( 2^{2} \)	$1$	$1.839085544$	1.839085544	\( 1728 \)	\( \bigl[i + 1\) , \( i\) , \( i\) , \( 12 i + 6\) , \( 3 i - 6\bigr] \)	${y}^2+\left(i+1\right){x}{y}+i{y}={x}^{3}+i{x}^{2}+\left(12i+6\right){x}+3i-6$
841.1-CMa1	841.1-CMa	$1$	$1$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	841.1	\( 29^{2} \)	\( 29^{9} \)	$0.96243$	$(-2a+5)$	0	$\Z/2\Z$	$\textsf{yes}$	$-4$	$\mathrm{U}(1)$	✓			✓	$29$	29Cs.7.1	$1$	\( 2 \)	$1$	$1.100312223$	0.550156111	\( 1728 \)	\( \bigl[i + 1\) , \( i\) , \( i\) , \( -36 i + 16\) , \( 8 i + 18\bigr] \)	${y}^2+\left(i+1\right){x}{y}+i{y}={x}^{3}+i{x}^{2}+\left(-36i+16\right){x}+8i+18$
841.3-CMa1	841.3-CMa	$1$	$1$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	841.3	\( 29^{2} \)	\( 29^{9} \)	$0.96243$	$(2a+5)$	0	$\Z/2\Z$	$\textsf{yes}$	$-4$	$\mathrm{U}(1)$	✓			✓	$29$	29Cs.7.1	$1$	\( 2 \)	$1$	$1.100312223$	0.550156111	\( 1728 \)	\( \bigl[i + 1\) , \( i\) , \( 1\) , \( 35 i + 15\) , \( 8 i - 18\bigr] \)	${y}^2+\left(i+1\right){x}{y}+{y}={x}^{3}+i{x}^{2}+\left(35i+15\right){x}+8i-18$
1024.1-CMb1	1024.1-CMb	$2$	$2$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	1024.1	\( 2^{10} \)	\( 2^{18} \)	$1.01098$	$(a+1)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{yes}$	$-4$	$\mathrm{U}(1)$	✓			✓	$2$	2Cs	$1$	\( 2^{2} \)	$1$	$4.861490513$	1.215372628	\( 1728 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( 2 i\) , \( 0\bigr] \)	${y}^2={x}^{3}+2i{x}$
1024.1-CMa1	1024.1-CMa	$2$	$2$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	1024.1	\( 2^{10} \)	\( 2^{18} \)	$1.01098$	$(a+1)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{yes}$	$-4$	$\mathrm{U}(1)$	✓			✓	$2$	2Cs	$1$	\( 2^{2} \)	$1$	$4.861490513$	1.215372628	\( 1728 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( -2 i\) , \( 0\bigr] \)	${y}^2={x}^{3}-2i{x}$
1369.1-CMa1	1369.1-CMa	$1$	$1$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	1369.1	\( 37^{2} \)	\( 37^{3} \)	$1.08710$	$(a+6)$	0	$\Z/2\Z$	$\textsf{yes}$	$-4$	$\mathrm{U}(1)$	✓			✓	$37$	37Cs.7.1	$1$	\( 2 \)	$1$	$5.575245619$	2.787622809	\( 1728 \)	\( \bigl[i + 1\) , \( i\) , \( i\) , \( -2 i\) , \( 1\bigr] \)	${y}^2+\left(i+1\right){x}{y}+i{y}={x}^{3}+i{x}^{2}-2i{x}+1$
1369.3-CMa1	1369.3-CMa	$1$	$1$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	1369.3	\( 37^{2} \)	\( 37^{3} \)	$1.08710$	$(a-6)$	0	$\Z/2\Z$	$\textsf{yes}$	$-4$	$\mathrm{U}(1)$	✓			✓	$37$	37Cs.7.1	$1$	\( 2 \)	$1$	$5.575245619$	2.787622809	\( 1728 \)	\( \bigl[i + 1\) , \( i\) , \( 1\) , \( i - 1\) , \( -1\bigr] \)	${y}^2+\left(i+1\right){x}{y}+{y}={x}^{3}+i{x}^{2}+\left(i-1\right){x}-1$
1600.1-CMa1	1600.1-CMa	$2$	$2$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	1600.1	\( 2^{6} \cdot 5^{2} \)	\( 2^{12} \cdot 5^{6} \)	$1.13031$	$(a+1), (-a-2)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{yes}$	$-4$	$\mathrm{U}(1)$	✓			✓	$2$	2Cs	$1$	\( 2^{3} \)	$1$	$3.074676569$	1.537338284	\( 1728 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( 4 i + 3\) , \( 0\bigr] \)	${y}^2={x}^{3}+\left(4i+3\right){x}$
1600.3-CMa1	1600.3-CMa	$2$	$2$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	1600.3	\( 2^{6} \cdot 5^{2} \)	\( 2^{12} \cdot 5^{6} \)	$1.13031$	$(a+1), (2a+1)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{yes}$	$-4$	$\mathrm{U}(1)$	✓			✓	$2$	2Cs	$1$	\( 2^{3} \)	$1$	$3.074676569$	1.537338284	\( 1728 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( -4 i + 3\) , \( 0\bigr] \)	${y}^2={x}^{3}+\left(-4i+3\right){x}$
2025.1-CMc1	2025.1-CMc	$1$	$1$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	2025.1	\( 3^{4} \cdot 5^{2} \)	\( 3^{18} \cdot 5^{9} \)	$1.19888$	$(-a-2), (3)$	0	$\Z/2\Z$	$\textsf{yes}$	$-4$	$\mathrm{U}(1)$	✓			✓			$1$	\( 2^{2} \)	$1$	$0.791416409$	0.791416409	\( 1728 \)	\( \bigl[i + 1\) , \( i\) , \( i\) , \( -14 i + 74\) , \( 37 i + 7\bigr] \)	${y}^2+\left(i+1\right){x}{y}+i{y}={x}^{3}+i{x}^{2}+\left(-14i+74\right){x}+37i+7$
2025.1-CMb1	2025.1-CMb	$1$	$1$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	2025.1	\( 3^{4} \cdot 5^{2} \)	\( 3^{12} \cdot 5^{3} \)	$1.19888$	$(-a-2), (3)$	0	$\Z/2\Z$	$\textsf{yes}$	$-4$	$\mathrm{U}(1)$	✓			✓	$5$	5Cs.4.1	$1$	\( 2^{2} \)	$1$	$3.065142573$	3.065142573	\( 1728 \)	\( \bigl[i + 1\) , \( i\) , \( 1\) , \( -5 i + 1\) , \( i + 2\bigr] \)	${y}^2+\left(i+1\right){x}{y}+{y}={x}^{3}+i{x}^{2}+\left(-5i+1\right){x}+i+2$
2025.1-CMa1	2025.1-CMa	$1$	$1$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	2025.1	\( 3^{4} \cdot 5^{2} \)	\( 3^{6} \cdot 5^{9} \)	$1.19888$	$(-a-2), (3)$	0	$\Z/2\Z$	$\textsf{yes}$	$-4$	$\mathrm{U}(1)$	✓			✓			$1$	\( 2^{2} \)	$1$	$2.374249228$	2.374249228	\( 1728 \)	\( \bigl[i + 1\) , \( i\) , \( i\) , \( -2 i + 8\) , \( 4 i + 1\bigr] \)	${y}^2+\left(i+1\right){x}{y}+i{y}={x}^{3}+i{x}^{2}+\left(-2i+8\right){x}+4i+1$
2025.3-CMc1	2025.3-CMc	$1$	$1$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	2025.3	\( 3^{4} \cdot 5^{2} \)	\( 3^{18} \cdot 5^{9} \)	$1.19888$	$(2a+1), (3)$	0	$\Z/2\Z$	$\textsf{yes}$	$-4$	$\mathrm{U}(1)$	✓			✓			$1$	\( 2^{2} \)	$1$	$0.791416409$	0.791416409	\( 1728 \)	\( \bigl[i + 1\) , \( i\) , \( 1\) , \( 13 i + 73\) , \( 37 i - 7\bigr] \)	${y}^2+\left(i+1\right){x}{y}+{y}={x}^{3}+i{x}^{2}+\left(13i+73\right){x}+37i-7$
2025.3-CMb1	2025.3-CMb	$1$	$1$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	2025.3	\( 3^{4} \cdot 5^{2} \)	\( 3^{12} \cdot 5^{3} \)	$1.19888$	$(2a+1), (3)$	0	$\Z/2\Z$	$\textsf{yes}$	$-4$	$\mathrm{U}(1)$	✓			✓	$5$	5Cs.4.1	$1$	\( 2^{2} \)	$1$	$3.065142573$	3.065142573	\( 1728 \)	\( \bigl[i + 1\) , \( i\) , \( i\) , \( 4 i + 2\) , \( i - 2\bigr] \)	${y}^2+\left(i+1\right){x}{y}+i{y}={x}^{3}+i{x}^{2}+\left(4i+2\right){x}+i-2$
2025.3-CMa1	2025.3-CMa	$1$	$1$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	2025.3	\( 3^{4} \cdot 5^{2} \)	\( 3^{6} \cdot 5^{9} \)	$1.19888$	$(2a+1), (3)$	0	$\Z/2\Z$	$\textsf{yes}$	$-4$	$\mathrm{U}(1)$	✓			✓			$1$	\( 2^{2} \)	$1$	$2.374249228$	2.374249228	\( 1728 \)	\( \bigl[i + 1\) , \( i\) , \( 1\) , \( i + 7\) , \( 4 i - 1\bigr] \)	${y}^2+\left(i+1\right){x}{y}+{y}={x}^{3}+i{x}^{2}+\left(i+7\right){x}+4i-1$
2704.1-CMa1	2704.1-CMa	$1$	$1$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	2704.1	\( 2^{4} \cdot 13^{2} \)	\( 2^{12} \cdot 13^{3} \)	$1.28875$	$(a+1), (-3a-2)$	0	$\Z/2\Z$	$\textsf{yes}$	$-4$	$\mathrm{U}(1)$	✓			✓	$13$	13Cs.4.1	$1$	\( 2 \)	$1$	$3.620750525$	1.810375262	\( 1728 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( -2 i + 3\) , \( 0\bigr] \)	${y}^2={x}^{3}+\left(-2i+3\right){x}$
2704.3-CMa1	2704.3-CMa	$1$	$1$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	2704.3	\( 2^{4} \cdot 13^{2} \)	\( 2^{12} \cdot 13^{3} \)	$1.28875$	$(a+1), (2a+3)$	0	$\Z/2\Z$	$\textsf{yes}$	$-4$	$\mathrm{U}(1)$	✓			✓	$13$	13Cs.4.1	$1$	\( 2 \)	$1$	$3.620750525$	1.810375262	\( 1728 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( 2 i + 3\) , \( 0\bigr] \)	${y}^2={x}^{3}+\left(2i+3\right){x}$
2809.1-CMa1	2809.1-CMa	$1$	$1$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	2809.1	\( 53^{2} \)	\( 53^{3} \)	$1.30109$	$(-2a+7)$	0	$\Z/2\Z$	$\textsf{yes}$	$-4$	$\mathrm{U}(1)$	✓			✓	$53$	53Cs.10.1	$1$	\( 2 \)	$1$	$5.096188327$	2.548094163	\( 1728 \)	\( \bigl[i + 1\) , \( i\) , \( i\) , \( -2\) , \( -i\bigr] \)	${y}^2+\left(i+1\right){x}{y}+i{y}={x}^{3}+i{x}^{2}-2{x}-i$
2809.3-CMa1	2809.3-CMa	$1$	$1$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	2809.3	\( 53^{2} \)	\( 53^{3} \)	$1.30109$	$(2a+7)$	0	$\Z/2\Z$	$\textsf{yes}$	$-4$	$\mathrm{U}(1)$	✓			✓	$53$	53Cs.10.1	$1$	\( 2 \)	$1$	$5.096188327$	2.548094163	\( 1728 \)	\( \bigl[i + 1\) , \( i\) , \( 1\) , \( -i - 3\) , \( -i\bigr] \)	${y}^2+\left(i+1\right){x}{y}+{y}={x}^{3}+i{x}^{2}+\left(-i-3\right){x}-i$
3721.1-CMa1	3721.1-CMa	$1$	$1$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	3721.1	\( 61^{2} \)	\( 61^{9} \)	$1.39583$	$(-6a-5)$	0	$\Z/2\Z$	$\textsf{yes}$	$-4$	$\mathrm{U}(1)$	✓			✓	$61$	61Cs.12.1	$9$	\( 2 \)	$1$	$0.629965926$	2.834846668	\( 1728 \)	\( \bigl[i + 1\) , \( i\) , \( i\) , \( 58 i - 104\) , \( -52 i - 29\bigr] \)	${y}^2+\left(i+1\right){x}{y}+i{y}={x}^{3}+i{x}^{2}+\left(58i-104\right){x}-52i-29$
3721.3-CMa1	3721.3-CMa	$1$	$1$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	3721.3	\( 61^{2} \)	\( 61^{9} \)	$1.39583$	$(5a+6)$	0	$\Z/2\Z$	$\textsf{yes}$	$-4$	$\mathrm{U}(1)$	✓			✓	$61$	61Cs.12.1	$9$	\( 2 \)	$1$	$0.629965926$	2.834846668	\( 1728 \)	\( \bigl[i + 1\) , \( i\) , \( 1\) , \( -59 i - 105\) , \( -52 i + 29\bigr] \)	${y}^2+\left(i+1\right){x}{y}+{y}={x}^{3}+i{x}^{2}+\left(-59i-105\right){x}-52i+29$
4096.1-CMd1	4096.1-CMd	$1$	$1$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	4096.1	\( 2^{12} \)	\( 2^{18} \)	$1.42974$	$(a+1)$	$2$	$\Z/2\Z$	$\textsf{yes}$	$-4$	$\mathrm{U}(1)$	✓	✓		✓			$1$	\( 2^{2} \)	$0.092631671$	$4.861490513$	1.801311967	\( 1728 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( -2\) , \( 0\bigr] \)	${y}^2={x}^{3}-2{x}$
4096.1-CMc1	4096.1-CMc	$1$	$1$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	4096.1	\( 2^{12} \)	\( 2^{18} \)	$1.42974$	$(a+1)$	0	$\Z/2\Z$	$\textsf{yes}$	$-4$	$\mathrm{U}(1)$	✓	✓		✓			$1$	\( 2 \)	$1$	$4.861490513$	2.430745256	\( 1728 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( 2\) , \( 0\bigr] \)	${y}^2={x}^{3}+2{x}$
4096.1-CMb1	4096.1-CMb	$1$	$1$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	4096.1	\( 2^{12} \)	\( 2^{12} \)	$1.42974$	$(a+1)$	0	$\Z/2\Z$	$\textsf{yes}$	$-4$	$\mathrm{U}(1)$	✓			✓			$1$	\( 1 \)	$1$	$6.875185818$	1.718796454	\( 1728 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( i\) , \( 0\bigr] \)	${y}^2={x}^{3}+i{x}$
4096.1-CMa1	4096.1-CMa	$1$	$1$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	4096.1	\( 2^{12} \)	\( 2^{12} \)	$1.42974$	$(a+1)$	0	$\Z/2\Z$	$\textsf{yes}$	$-4$	$\mathrm{U}(1)$	✓			✓			$1$	\( 1 \)	$1$	$6.875185818$	1.718796454	\( 1728 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( -i\) , \( 0\bigr] \)	${y}^2={x}^{3}-i{x}$
4225.1-CMb1	4225.1-CMb	$1$	$1$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	4225.1	\( 5^{2} \cdot 13^{2} \)	\( 5^{9} \cdot 13^{6} \)	$1.44087$	$(-a-2), (-3a-2)$	0	$\Z/2\Z$	$\textsf{yes}$	$-4$	$\mathrm{U}(1)$	✓			✓	$5$	5Cs.4.1	$1$	\( 2^{2} \)	$1$	$1.140552436$	1.140552436	\( 1728 \)	\( \bigl[i + 1\) , \( i\) , \( 1\) , \( 35 i - 9\) , \( -4 i - 18\bigr] \)	${y}^2+\left(i+1\right){x}{y}+{y}={x}^{3}+i{x}^{2}+\left(35i-9\right){x}-4i-18$
4225.1-CMa1	4225.1-CMa	$1$	$1$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	4225.1	\( 5^{2} \cdot 13^{2} \)	\( 5^{6} \cdot 13^{3} \)	$1.44087$	$(-a-2), (-3a-2)$	0	$\Z/2\Z$	$\textsf{yes}$	$-4$	$\mathrm{U}(1)$	✓			✓	$13$	13Cs.4.1	$1$	\( 2^{2} \)	$1$	$3.238497722$	3.238497722	\( 1728 \)	\( \bigl[i + 1\) , \( i\) , \( 1\) , \( i + 3\) , \( 2 i - 1\bigr] \)	${y}^2+\left(i+1\right){x}{y}+{y}={x}^{3}+i{x}^{2}+\left(i+3\right){x}+2i-1$
4225.3-CMb1	4225.3-CMb	$1$	$1$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	4225.3	\( 5^{2} \cdot 13^{2} \)	\( 5^{9} \cdot 13^{6} \)	$1.44087$	$(-a-2), (2a+3)$	0	$\Z/2\Z$	$\textsf{yes}$	$-4$	$\mathrm{U}(1)$	✓			✓	$5$	5Cs.4.1	$1$	\( 2^{3} \)	$1$	$1.140552436$	2.281104873	\( 1728 \)	\( \bigl[i + 1\) , \( i\) , \( 1\) , \( -31 i - 21\) , \( -10 i + 15\bigr] \)	${y}^2+\left(i+1\right){x}{y}+{y}={x}^{3}+i{x}^{2}+\left(-31i-21\right){x}-10i+15$
4225.3-CMa1	4225.3-CMa	$1$	$1$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	4225.3	\( 5^{2} \cdot 13^{2} \)	\( 5^{6} \cdot 13^{3} \)	$1.44087$	$(-a-2), (2a+3)$	$2$	$\Z/2\Z$	$\textsf{yes}$	$-4$	$\mathrm{U}(1)$	✓			✓	$13$	13Cs.4.1	$1$	\( 2^{3} \)	$0.046240206$	$3.238497722$	1.197990421	\( 1728 \)	\( \bigl[i + 1\) , \( i\) , \( i\) , \( 4 i\) , \( -2\bigr] \)	${y}^2+\left(i+1\right){x}{y}+i{y}={x}^{3}+i{x}^{2}+4i{x}-2$
4225.7-CMb1	4225.7-CMb	$1$	$1$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	4225.7	\( 5^{2} \cdot 13^{2} \)	\( 5^{9} \cdot 13^{6} \)	$1.44087$	$(2a+1), (-3a-2)$	0	$\Z/2\Z$	$\textsf{yes}$	$-4$	$\mathrm{U}(1)$	✓			✓	$5$	5Cs.4.1	$1$	\( 2^{3} \)	$1$	$1.140552436$	2.281104873	\( 1728 \)	\( \bigl[i + 1\) , \( i\) , \( i\) , \( 30 i - 20\) , \( -10 i - 15\bigr] \)	${y}^2+\left(i+1\right){x}{y}+i{y}={x}^{3}+i{x}^{2}+\left(30i-20\right){x}-10i-15$
4225.7-CMa1	4225.7-CMa	$1$	$1$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	4225.7	\( 5^{2} \cdot 13^{2} \)	\( 5^{6} \cdot 13^{3} \)	$1.44087$	$(2a+1), (-3a-2)$	$2$	$\Z/2\Z$	$\textsf{yes}$	$-4$	$\mathrm{U}(1)$	✓			✓	$13$	13Cs.4.1	$1$	\( 2^{3} \)	$0.046240206$	$3.238497722$	1.197990421	\( 1728 \)	\( \bigl[i + 1\) , \( i\) , \( 1\) , \( -5 i - 1\) , \( 2\bigr] \)	${y}^2+\left(i+1\right){x}{y}+{y}={x}^{3}+i{x}^{2}+\left(-5i-1\right){x}+2$
4225.9-CMb1	4225.9-CMb	$1$	$1$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	4225.9	\( 5^{2} \cdot 13^{2} \)	\( 5^{9} \cdot 13^{6} \)	$1.44087$	$(2a+1), (2a+3)$	0	$\Z/2\Z$	$\textsf{yes}$	$-4$	$\mathrm{U}(1)$	✓			✓	$5$	5Cs.4.1	$1$	\( 2^{2} \)	$1$	$1.140552436$	1.140552436	\( 1728 \)	\( \bigl[i + 1\) , \( i\) , \( i\) , \( -36 i - 8\) , \( -4 i + 18\bigr] \)	${y}^2+\left(i+1\right){x}{y}+i{y}={x}^{3}+i{x}^{2}+\left(-36i-8\right){x}-4i+18$
4225.9-CMa1	4225.9-CMa	$1$	$1$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	4225.9	\( 5^{2} \cdot 13^{2} \)	\( 5^{6} \cdot 13^{3} \)	$1.44087$	$(2a+1), (2a+3)$	0	$\Z/2\Z$	$\textsf{yes}$	$-4$	$\mathrm{U}(1)$	✓			✓	$13$	13Cs.4.1	$1$	\( 2^{2} \)	$1$	$3.238497722$	3.238497722	\( 1728 \)	\( \bigl[i + 1\) , \( i\) , \( i\) , \( -2 i + 4\) , \( 2 i + 1\bigr] \)	${y}^2+\left(i+1\right){x}{y}+i{y}={x}^{3}+i{x}^{2}+\left(-2i+4\right){x}+2i+1$
5184.1-CMc1	5184.1-CMc	$1$	$1$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	5184.1	\( 2^{6} \cdot 3^{4} \)	\( 2^{12} \cdot 3^{18} \)	$1.51647$	$(a+1), (3)$	0	$\Z/2\Z$	$\textsf{yes}$	$-4$	$\mathrm{U}(1)$	✓	✓		✓			$1$	\( 2^{3} \)	$1$	$1.323130127$	2.646260255	\( 1728 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( 27\) , \( 0\bigr] \)	${y}^2={x}^{3}+27{x}$
5184.1-CMb1	5184.1-CMb	$2$	$2$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	5184.1	\( 2^{6} \cdot 3^{4} \)	\( 2^{12} \cdot 3^{12} \)	$1.51647$	$(a+1), (3)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{yes}$	$-4$	$\mathrm{U}(1)$	✓	✓		✓	$2$	2Cs	$1$	\( 2^{4} \)	$1$	$2.291728606$	2.291728606	\( 1728 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( -9\) , \( 0\bigr] \)	${y}^2={x}^{3}-9{x}$
5184.1-CMa1	5184.1-CMa	$1$	$1$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	5184.1	\( 2^{6} \cdot 3^{4} \)	\( 2^{12} \cdot 3^{6} \)	$1.51647$	$(a+1), (3)$	$2$	$\Z/2\Z$	$\textsf{yes}$	$-4$	$\mathrm{U}(1)$	✓	✓		✓			$1$	\( 2^{3} \)	$0.062795947$	$3.969390382$	1.994093041	\( 1728 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( 3\) , \( 0\bigr] \)	${y}^2={x}^{3}+3{x}$
6400.1-CMc1	6400.1-CMc	$1$	$1$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	6400.1	\( 2^{8} \cdot 5^{2} \)	\( 2^{12} \cdot 5^{9} \)	$1.59850$	$(a+1), (-a-2)$	0	$\Z/2\Z$	$\textsf{yes}$	$-4$	$\mathrm{U}(1)$	✓			✓	$5$	5Cs.4.1	$1$	\( 2 \)	$1$	$2.056160146$	1.028080073	\( 1728 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( 2 i - 11\) , \( 0\bigr] \)	${y}^2={x}^{3}+\left(2i-11\right){x}$
6400.1-CMb1	6400.1-CMb	$2$	$2$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	6400.1	\( 2^{8} \cdot 5^{2} \)	\( 2^{12} \cdot 5^{6} \)	$1.59850$	$(a+1), (-a-2)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{yes}$	$-4$	$\mathrm{U}(1)$	✓			✓	$2$	2Cs	$1$	\( 2^{3} \)	$1$	$3.074676569$	1.537338284	\( 1728 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( -4 i - 3\) , \( 0\bigr] \)	${y}^2={x}^{3}+\left(-4i-3\right){x}$
6400.1-CMa1	6400.1-CMa	$1$	$1$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	6400.1	\( 2^{8} \cdot 5^{2} \)	\( 2^{12} \cdot 5^{3} \)	$1.59850$	$(a+1), (-a-2)$	0	$\Z/2\Z$	$\textsf{yes}$	$-4$	$\mathrm{U}(1)$	✓			✓	$5$	5Cs.4.1	$1$	\( 2 \)	$1$	$4.597713860$	2.298856930	\( 1728 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( -2 i + 1\) , \( 0\bigr] \)	${y}^2={x}^{3}+\left(-2i+1\right){x}$
6400.3-CMc1	6400.3-CMc	$1$	$1$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	6400.3	\( 2^{8} \cdot 5^{2} \)	\( 2^{12} \cdot 5^{9} \)	$1.59850$	$(a+1), (2a+1)$	0	$\Z/2\Z$	$\textsf{yes}$	$-4$	$\mathrm{U}(1)$	✓			✓	$5$	5Cs.4.1	$1$	\( 2 \)	$1$	$2.056160146$	1.028080073	\( 1728 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( -2 i - 11\) , \( 0\bigr] \)	${y}^2={x}^{3}+\left(-2i-11\right){x}$
6400.3-CMb1	6400.3-CMb	$2$	$2$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	6400.3	\( 2^{8} \cdot 5^{2} \)	\( 2^{12} \cdot 5^{6} \)	$1.59850$	$(a+1), (2a+1)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{yes}$	$-4$	$\mathrm{U}(1)$	✓			✓	$2$	2Cs	$1$	\( 2^{3} \)	$1$	$3.074676569$	1.537338284	\( 1728 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( 4 i - 3\) , \( 0\bigr] \)	${y}^2={x}^{3}+\left(4i-3\right){x}$

 

  *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.