Elliptic curves over \(\Q(\sqrt{-7}) \) of conductor 16384.7

Results (20 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
16384.7-a1	16384.7-a	$2$	$2$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	16384.7	\( 2^{14} \)	\( 2^{23} \)	$2.67481$	$(a), (-a+1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$				✓	$2$	2B	$1$	\( 2^{3} \)	$0.293544577$	$3.149279240$	2.795285676	\( 15344 a - 224 \)	\( \bigl[0\) , \( a\) , \( 0\) , \( -3 a + 8\) , \( -3 a - 2\bigr] \)	${y}^2={x}^{3}+a{x}^{2}+\left(-3a+8\right){x}-3a-2$
16384.7-a2	16384.7-a	$2$	$2$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	16384.7	\( 2^{14} \)	\( 2^{25} \)	$2.67481$	$(a), (-a+1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$				✓	$2$	2B	$1$	\( 2^{2} \)	$0.587089154$	$3.149279240$	2.795285676	\( -1472 a + 2880 \)	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -3 a - 3\) , \( 3 a - 1\bigr] \)	${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-3a-3\right){x}+3a-1$
16384.7-b1	16384.7-b	$2$	$2$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	16384.7	\( 2^{14} \)	\( 2^{29} \)	$2.67481$	$(a), (-a+1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$				✓	$2$	2B	$1$	\( 2^{2} \)	$1.093826575$	$2.226876707$	3.682609039	\( 15344 a - 224 \)	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 13 a - 11\) , \( 23 a - 13\bigr] \)	${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(13a-11\right){x}+23a-13$
16384.7-b2	16384.7-b	$2$	$2$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	16384.7	\( 2^{14} \)	\( 2^{19} \)	$2.67481$	$(a), (-a+1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$				✓	$2$	2B	$1$	\( 2^{2} \)	$0.546913287$	$4.453753414$	3.682609039	\( -1472 a + 2880 \)	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 3 a - 1\) , \( a - 3\bigr] \)	${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(3a-1\right){x}+a-3$
16384.7-c1	16384.7-c	$2$	$2$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	16384.7	\( 2^{14} \)	\( 2^{29} \)	$2.67481$	$(a), (-a+1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$				✓	$2$	2B	$1$	\( 2^{2} \)	$0.958064720$	$2.304563215$	3.338062354	\( 9232 a - 6432 \)	\( \bigl[0\) , \( a\) , \( 0\) , \( -9 a + 10\) , \( a - 14\bigr] \)	${y}^2={x}^{3}+a{x}^{2}+\left(-9a+10\right){x}+a-14$
16384.7-c2	16384.7-c	$2$	$2$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	16384.7	\( 2^{14} \)	\( 2^{19} \)	$2.67481$	$(a), (-a+1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$				✓	$2$	2B	$1$	\( 2^{2} \)	$0.479032360$	$4.609126430$	3.338062354	\( -64 a - 320 \)	\( \bigl[0\) , \( a\) , \( 0\) , \( a\) , \( a - 2\bigr] \)	${y}^2={x}^{3}+a{x}^{2}+a{x}+a-2$
16384.7-d1	16384.7-d	$2$	$2$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	16384.7	\( 2^{14} \)	\( 2^{23} \)	$2.67481$	$(a), (-a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$				✓	$2$	2B	$1$	\( 2^{2} \)	$1$	$3.259144554$	2.463681707	\( 9232 a - 6432 \)	\( \bigl[0\) , \( 1\) , \( 0\) , \( 2 a - 7\) , \( -2 a + 5\bigr] \)	${y}^2={x}^{3}+{x}^{2}+\left(2a-7\right){x}-2a+5$
16384.7-d2	16384.7-d	$2$	$2$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	16384.7	\( 2^{14} \)	\( 2^{25} \)	$2.67481$	$(a), (-a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$				✓	$2$	2B	$1$	\( 2^{2} \)	$1$	$3.259144554$	2.463681707	\( -64 a - 320 \)	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a - 3\) , \( -a + 3\bigr] \)	${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a-3\right){x}-a+3$
16384.7-e1	16384.7-e	$2$	$2$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	16384.7	\( 2^{14} \)	\( 2^{21} \)	$2.67481$	$(a), (-a+1)$	$1$	$\Z/2\Z$	$\textsf{potential}$	$-4$	$N(\mathrm{U}(1))$	✓			✓			$1$	\( 2 \)	$1.344808282$	$4.088009945$	4.155787136	\( 1728 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( a + 2\) , \( 0\bigr] \)	${y}^2={x}^{3}+\left(a+2\right){x}$
16384.7-e2	16384.7-e	$2$	$2$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	16384.7	\( 2^{14} \)	\( 2^{21} \)	$2.67481$	$(a), (-a+1)$	$1$	$\Z/2\Z$	$\textsf{potential}$	$-4$	$N(\mathrm{U}(1))$	✓			✓			$1$	\( 2^{2} \)	$0.672404141$	$4.088009945$	4.155787136	\( 1728 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( -2 a + 2\) , \( 0\bigr] \)	${y}^2={x}^{3}+\left(-2a+2\right){x}$
16384.7-f1	16384.7-f	$2$	$2$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	16384.7	\( 2^{14} \)	\( 2^{15} \)	$2.67481$	$(a), (-a+1)$	0	$\Z/2\Z$	$\textsf{potential}$	$-4$	$N(\mathrm{U}(1))$	✓			✓			$1$	\( 2 \)	$1$	$5.781319108$	2.185133230	\( 1728 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( -a\) , \( 0\bigr] \)	${y}^2={x}^{3}-a{x}$
16384.7-f2	16384.7-f	$2$	$2$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	16384.7	\( 2^{14} \)	\( 2^{27} \)	$2.67481$	$(a), (-a+1)$	0	$\Z/2\Z$	$\textsf{potential}$	$-4$	$N(\mathrm{U}(1))$	✓			✓			$1$	\( 2^{2} \)	$1$	$2.890659554$	2.185133230	\( 1728 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( 4 a\) , \( 0\bigr] \)	${y}^2={x}^{3}+4a{x}$
16384.7-g1	16384.7-g	$2$	$2$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	16384.7	\( 2^{14} \)	\( 2^{29} \)	$2.67481$	$(a), (-a+1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$				✓	$2$	2B	$1$	\( 2^{2} \)	$1.203094330$	$2.304563215$	4.191787681	\( 9232 a - 6432 \)	\( \bigl[0\) , \( -a\) , \( 0\) , \( -9 a + 10\) , \( -a + 14\bigr] \)	${y}^2={x}^{3}-a{x}^{2}+\left(-9a+10\right){x}-a+14$
16384.7-g2	16384.7-g	$2$	$2$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	16384.7	\( 2^{14} \)	\( 2^{19} \)	$2.67481$	$(a), (-a+1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$				✓	$2$	2B	$1$	\( 2^{2} \)	$0.601547165$	$4.609126430$	4.191787681	\( -64 a - 320 \)	\( \bigl[0\) , \( -a\) , \( 0\) , \( a\) , \( -a + 2\bigr] \)	${y}^2={x}^{3}-a{x}^{2}+a{x}-a+2$
16384.7-h1	16384.7-h	$2$	$2$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	16384.7	\( 2^{14} \)	\( 2^{23} \)	$2.67481$	$(a), (-a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$				✓	$2$	2B	$1$	\( 2^{2} \)	$1$	$3.259144554$	2.463681707	\( 9232 a - 6432 \)	\( \bigl[0\) , \( -1\) , \( 0\) , \( 2 a - 7\) , \( 2 a - 5\bigr] \)	${y}^2={x}^{3}-{x}^{2}+\left(2a-7\right){x}+2a-5$
16384.7-h2	16384.7-h	$2$	$2$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	16384.7	\( 2^{14} \)	\( 2^{25} \)	$2.67481$	$(a), (-a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$				✓	$2$	2B	$1$	\( 2^{2} \)	$1$	$3.259144554$	2.463681707	\( -64 a - 320 \)	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a - 3\) , \( a - 3\bigr] \)	${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(a-3\right){x}+a-3$
16384.7-i1	16384.7-i	$2$	$2$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	16384.7	\( 2^{14} \)	\( 2^{23} \)	$2.67481$	$(a), (-a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$				✓	$2$	2B	$1$	\( 2^{2} \)	$1$	$3.149279240$	2.380631337	\( 15344 a - 224 \)	\( \bigl[0\) , \( -a\) , \( 0\) , \( -3 a + 8\) , \( 3 a + 2\bigr] \)	${y}^2={x}^{3}-a{x}^{2}+\left(-3a+8\right){x}+3a+2$
16384.7-i2	16384.7-i	$2$	$2$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	16384.7	\( 2^{14} \)	\( 2^{25} \)	$2.67481$	$(a), (-a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$				✓	$2$	2B	$1$	\( 2^{2} \)	$1$	$3.149279240$	2.380631337	\( -1472 a + 2880 \)	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -3 a - 3\) , \( -3 a + 1\bigr] \)	${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-3a-3\right){x}-3a+1$
16384.7-j1	16384.7-j	$2$	$2$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	16384.7	\( 2^{14} \)	\( 2^{29} \)	$2.67481$	$(a), (-a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$				✓	$2$	2B	$1$	\( 2^{3} \)	$1$	$2.226876707$	3.366721124	\( 15344 a - 224 \)	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 13 a - 11\) , \( -23 a + 13\bigr] \)	${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(13a-11\right){x}-23a+13$
16384.7-j2	16384.7-j	$2$	$2$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	16384.7	\( 2^{14} \)	\( 2^{19} \)	$2.67481$	$(a), (-a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$				✓	$2$	2B	$1$	\( 2^{2} \)	$1$	$4.453753414$	3.366721124	\( -1472 a + 2880 \)	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 3 a - 1\) , \( -a + 3\bigr] \)	${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(3a-1\right){x}-a+3$

 

  *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.