Elliptic curve search results

Results (9 matches)

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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
650.4-a1	650.4-a	$8$	$12$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	650.4	\( 2 \cdot 5^{2} \cdot 13 \)	\( 2^{4} \cdot 5^{7} \cdot 13^{3} \)	$0.90240$	$(a+1), (-a-2), (2a+1), (2a+3)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B.1.2	$1$	\( 2^{3} \cdot 3 \)	$1$	$0.964283096$	1.446424644	\( \frac{1411302663595036}{34328125} a - \frac{1774751413484333}{137312500} \)	\( \bigl[1\) , \( 0\) , \( i + 1\) , \( 161 i - 221\) , \( -1400 i + 996\bigr] \)	${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+\left(161i-221\right){x}-1400i+996$
16250.6-a1	16250.6-a	$8$	$12$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	16250.6	\( 2 \cdot 5^{4} \cdot 13 \)	\( 2^{4} \cdot 5^{19} \cdot 13^{3} \)	$2.01782$	$(a+1), (-a-2), (2a+1), (2a+3)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B	$1$	\( 2^{4} \)	$1.474091777$	$0.192856619$	2.274306853	\( \frac{1411302663595036}{34328125} a - \frac{1774751413484333}{137312500} \)	\( \bigl[1\) , \( 1\) , \( i + 1\) , \( 4037 i - 5513\) , \( -174938 i + 124500\bigr] \)	${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+{x}^{2}+\left(4037i-5513\right){x}-174938i+124500$
26000.4-f1	26000.4-f	$8$	$12$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	26000.4	\( 2^{4} \cdot 5^{3} \cdot 13 \)	\( 2^{16} \cdot 5^{13} \cdot 13^{3} \)	$2.26940$	$(a+1), (-a-2), (2a+1), (2a+3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B	$1$	\( 2^{3} \cdot 3 \)	$1$	$0.215620255$	1.293721531	\( \frac{1411302663595036}{34328125} a - \frac{1774751413484333}{137312500} \)	\( \bigl[i + 1\) , \( -i - 1\) , \( 0\) , \( -1590 i - 5230\) , \( -65256 i - 139092\bigr] \)	${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(-1590i-5230\right){x}-65256i-139092$
26000.6-f1	26000.6-f	$8$	$12$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	26000.6	\( 2^{4} \cdot 5^{3} \cdot 13 \)	\( 2^{16} \cdot 5^{13} \cdot 13^{3} \)	$2.26940$	$(a+1), (-a-2), (2a+1), (2a+3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B	$1$	\( 2^{4} \cdot 3 \)	$1$	$0.215620255$	2.587443063	\( \frac{1411302663595036}{34328125} a - \frac{1774751413484333}{137312500} \)	\( \bigl[i + 1\) , \( -i + 1\) , \( 0\) , \( 5466 i - 62\) , \( -110040 i - 107220\bigr] \)	${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(5466i-62\right){x}-110040i-107220$
42250.6-e1	42250.6-e	$8$	$12$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	42250.6	\( 2 \cdot 5^{3} \cdot 13^{2} \)	\( 2^{4} \cdot 5^{13} \cdot 13^{9} \)	$2.56227$	$(a+1), (-a-2), (2a+1), (2a+3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B	$9$	\( 2^{3} \)	$1$	$0.119604597$	2.152882762	\( \frac{1411302663595036}{34328125} a - \frac{1774751413484333}{137312500} \)	\( \bigl[1\) , \( i + 1\) , \( i\) , \( 17679 i + 1767\) , \( 549379 i + 728133\bigr] \)	${y}^2+{x}{y}+i{y}={x}^{3}+\left(i+1\right){x}^{2}+\left(17679i+1767\right){x}+549379i+728133$
42250.9-i1	42250.9-i	$8$	$12$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	42250.9	\( 2 \cdot 5^{3} \cdot 13^{2} \)	\( 2^{4} \cdot 5^{13} \cdot 13^{9} \)	$2.56227$	$(a+1), (-a-2), (2a+1), (2a+3)$	$1$	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B	$1$	\( 2^{7} \cdot 3 \)	$1.112016274$	$0.119604597$	6.384108451	\( \frac{1411302663595036}{34328125} a - \frac{1774751413484333}{137312500} \)	\( \bigl[1\) , \( i\) , \( 1\) , \( -6646 i + 16476\) , \( 769829 i + 499366\bigr] \)	${y}^2+{x}{y}+{y}={x}^{3}+i{x}^{2}+\left(-6646i+16476\right){x}+769829i+499366$
52650.4-a1	52650.4-a	$8$	$12$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	52650.4	\( 2 \cdot 3^{4} \cdot 5^{2} \cdot 13 \)	\( 2^{4} \cdot 3^{12} \cdot 5^{7} \cdot 13^{3} \)	$2.70719$	$(a+1), (-a-2), (2a+1), (2a+3), (3)$	$1$	$\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B.1.1	$1$	\( 2^{3} \cdot 3^{2} \)	$2.508001076$	$0.321427698$	3.224564057	\( \frac{1411302663595036}{34328125} a - \frac{1774751413484333}{137312500} \)	\( \bigl[i\) , \( 1\) , \( i + 1\) , \( 1453 i - 1984\) , \( -37787 i + 26892\bigr] \)	${y}^2+i{x}{y}+\left(i+1\right){y}={x}^{3}+{x}^{2}+\left(1453i-1984\right){x}-37787i+26892$
67600.6-a1	67600.6-a	$8$	$12$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	67600.6	\( 2^{4} \cdot 5^{2} \cdot 13^{2} \)	\( 2^{16} \cdot 5^{7} \cdot 13^{9} \)	$2.88174$	$(a+1), (-a-2), (2a+1), (2a+3)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B	$1$	\( 2^{4} \)	$3.178266469$	$0.133722005$	3.400033334	\( \frac{1411302663595036}{34328125} a - \frac{1774751413484333}{137312500} \)	\( \bigl[i + 1\) , \( i + 1\) , \( i + 1\) , \( 7355 i + 12162\) , \( 455466 i - 474647\bigr] \)	${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(i+1\right){x}^{2}+\left(7355i+12162\right){x}+455466i-474647$
83200.4-n1	83200.4-n	$8$	$12$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	83200.4	\( 2^{8} \cdot 5^{2} \cdot 13 \)	\( 2^{28} \cdot 5^{7} \cdot 13^{3} \)	$3.03528$	$(a+1), (-a-2), (2a+1), (2a+3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B	$1$	\( 2^{3} \cdot 3 \)	$1$	$0.241070774$	1.446424644	\( \frac{1411302663595036}{34328125} a - \frac{1774751413484333}{137312500} \)	\( \bigl[0\) , \( i\) , \( 0\) , \( -2584 i + 3528\) , \( -63744 i - 89568\bigr] \)	${y}^2={x}^{3}+i{x}^{2}+\left(-2584i+3528\right){x}-63744i-89568$

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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.