Elliptic curve search results

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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
1.1-a2	1.1-a	$2$	$37$	6.6.300125.1	$6$	$[6, 0]$	1.1	\( 1 \)	\( 1 \)	$48.95416$	$\textsf{none}$	0	$\Z/37\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓	✓	$37$	37B.1.1	$1$	\( 1 \)	$1$	$391404.4679$	0.521880	\( -9317 \)	\( \bigl[-2 a^{5} + a^{4} + 14 a^{3} + 4 a^{2} - 9 a - 2\) , \( -3 a^{5} + 2 a^{4} + 20 a^{3} + 3 a^{2} - 12 a\) , \( -5 a^{5} + a^{4} + 37 a^{3} + 18 a^{2} - 26 a - 7\) , \( 7 a^{5} - a^{4} - 51 a^{3} - 28 a^{2} + 27 a + 11\) , \( -13 a^{5} + 4 a^{4} + 92 a^{3} + 40 a^{2} - 56 a - 16\bigr] \)	${y}^2+\left(-2a^{5}+a^{4}+14a^{3}+4a^{2}-9a-2\right){x}{y}+\left(-5a^{5}+a^{4}+37a^{3}+18a^{2}-26a-7\right){y}={x}^{3}+\left(-3a^{5}+2a^{4}+20a^{3}+3a^{2}-12a\right){x}^{2}+\left(7a^{5}-a^{4}-51a^{3}-28a^{2}+27a+11\right){x}-13a^{5}+4a^{4}+92a^{3}+40a^{2}-56a-16$
841.16-a2	841.16-a	$2$	$37$	6.6.300125.1	$6$	$[6, 0]$	841.16	\( 29^{2} \)	\( 29^{6} \)	$85.80698$	$(a^4-a^3-6a^2+2)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$37$	37B.36.1	$1$	\( 1 \)	$1$	$982.0658897$	1.79263	\( -9317 \)	\( \bigl[-a^{5} + 8 a^{3} + 4 a^{2} - 7 a - 1\) , \( -a^{5} + 7 a^{3} + 6 a^{2} - 2 a - 3\) , \( -8 a^{5} + 2 a^{4} + 58 a^{3} + 27 a^{2} - 39 a - 12\) , \( -3 a^{5} + 25 a^{3} + 9 a^{2} - 18 a - 4\) , \( -9 a^{5} + 6 a^{4} + 58 a^{3} + 18 a^{2} - 39 a - 11\bigr] \)	${y}^2+\left(-a^{5}+8a^{3}+4a^{2}-7a-1\right){x}{y}+\left(-8a^{5}+2a^{4}+58a^{3}+27a^{2}-39a-12\right){y}={x}^{3}+\left(-a^{5}+7a^{3}+6a^{2}-2a-3\right){x}^{2}+\left(-3a^{5}+25a^{3}+9a^{2}-18a-4\right){x}-9a^{5}+6a^{4}+58a^{3}+18a^{2}-39a-11$
841.17-a2	841.17-a	$2$	$37$	6.6.300125.1	$6$	$[6, 0]$	841.17	\( 29^{2} \)	\( 29^{6} \)	$85.80698$	$(-a^5+7a^3+5a^2-2a-2)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$37$	37B.36.1	$1$	\( 1 \)	$1$	$982.0658897$	1.79263	\( -9317 \)	\( \bigl[-6 a^{5} + 2 a^{4} + 43 a^{3} + 17 a^{2} - 28 a - 6\) , \( -a^{5} + 8 a^{3} + 5 a^{2} - 9 a - 4\) , \( -2 a^{5} + 15 a^{3} + 10 a^{2} - 9 a - 5\) , \( -a^{5} - 2 a^{4} + 8 a^{3} + 19 a^{2} - 10\) , \( 7 a^{5} - 5 a^{4} - 49 a^{3} - a^{2} + 38 a - 6\bigr] \)	${y}^2+\left(-6a^{5}+2a^{4}+43a^{3}+17a^{2}-28a-6\right){x}{y}+\left(-2a^{5}+15a^{3}+10a^{2}-9a-5\right){y}={x}^{3}+\left(-a^{5}+8a^{3}+5a^{2}-9a-4\right){x}^{2}+\left(-a^{5}-2a^{4}+8a^{3}+19a^{2}-10\right){x}+7a^{5}-5a^{4}-49a^{3}-a^{2}+38a-6$
841.18-a2	841.18-a	$2$	$37$	6.6.300125.1	$6$	$[6, 0]$	841.18	\( 29^{2} \)	\( 29^{6} \)	$85.80698$	$(-a^5+a^4+7a^3-2a^2-6a+1)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$37$	37B.36.1	$1$	\( 1 \)	$1$	$982.0658897$	1.79263	\( -9317 \)	\( \bigl[-3 a^{5} + 23 a^{3} + 14 a^{2} - 16 a - 5\) , \( 9 a^{5} - 2 a^{4} - 65 a^{3} - 32 a^{2} + 40 a + 13\) , \( 3 a^{5} - a^{4} - 21 a^{3} - 9 a^{2} + 12 a + 5\) , \( 29 a^{5} - 7 a^{4} - 209 a^{3} - 98 a^{2} + 129 a + 35\) , \( 22 a^{5} - 5 a^{4} - 157 a^{3} - 80 a^{2} + 93 a + 30\bigr] \)	${y}^2+\left(-3a^{5}+23a^{3}+14a^{2}-16a-5\right){x}{y}+\left(3a^{5}-a^{4}-21a^{3}-9a^{2}+12a+5\right){y}={x}^{3}+\left(9a^{5}-2a^{4}-65a^{3}-32a^{2}+40a+13\right){x}^{2}+\left(29a^{5}-7a^{4}-209a^{3}-98a^{2}+129a+35\right){x}+22a^{5}-5a^{4}-157a^{3}-80a^{2}+93a+30$
841.19-a2	841.19-a	$2$	$37$	6.6.300125.1	$6$	$[6, 0]$	841.19	\( 29^{2} \)	\( 29^{6} \)	$85.80698$	$(9a^5-3a^4-64a^3-26a^2+40a+10)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$37$	37B.36.1	$1$	\( 1 \)	$1$	$982.0658897$	1.79263	\( -9317 \)	\( \bigl[3 a^{5} - a^{4} - 21 a^{3} - 9 a^{2} + 13 a + 5\) , \( 7 a^{5} - a^{4} - 51 a^{3} - 28 a^{2} + 31 a + 11\) , \( a + 1\) , \( -9 a^{5} + 3 a^{4} + 64 a^{3} + 27 a^{2} - 39 a - 11\) , \( 2 a^{5} - a^{4} - 14 a^{3} - 5 a^{2} + 7 a + 2\bigr] \)	${y}^2+\left(3a^{5}-a^{4}-21a^{3}-9a^{2}+13a+5\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(7a^{5}-a^{4}-51a^{3}-28a^{2}+31a+11\right){x}^{2}+\left(-9a^{5}+3a^{4}+64a^{3}+27a^{2}-39a-11\right){x}+2a^{5}-a^{4}-14a^{3}-5a^{2}+7a+2$
841.20-a2	841.20-a	$2$	$37$	6.6.300125.1	$6$	$[6, 0]$	841.20	\( 29^{2} \)	\( 29^{6} \)	$85.80698$	$(-5a^5+a^4+36a^3+19a^2-21a-9)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$37$	37B.36.1	$1$	\( 1 \)	$1$	$982.0658897$	1.79263	\( -9317 \)	\( \bigl[-a^{5} + 8 a^{3} + 5 a^{2} - 8 a - 3\) , \( -5 a^{5} + a^{4} + 36 a^{3} + 19 a^{2} - 21 a - 9\) , \( -8 a^{5} + 2 a^{4} + 58 a^{3} + 27 a^{2} - 38 a - 11\) , \( -18 a^{5} + 5 a^{4} + 130 a^{3} + 56 a^{2} - 83 a - 23\) , \( -9 a^{5} + 2 a^{4} + 66 a^{3} + 30 a^{2} - 43 a - 13\bigr] \)	${y}^2+\left(-a^{5}+8a^{3}+5a^{2}-8a-3\right){x}{y}+\left(-8a^{5}+2a^{4}+58a^{3}+27a^{2}-38a-11\right){y}={x}^{3}+\left(-5a^{5}+a^{4}+36a^{3}+19a^{2}-21a-9\right){x}^{2}+\left(-18a^{5}+5a^{4}+130a^{3}+56a^{2}-83a-23\right){x}-9a^{5}+2a^{4}+66a^{3}+30a^{2}-43a-13$
841.21-a2	841.21-a	$2$	$37$	6.6.300125.1	$6$	$[6, 0]$	841.21	\( 29^{2} \)	\( 29^{6} \)	$85.80698$	$(-2a^5+15a^3+10a^2-11a-5)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$37$	37B.36.1	$1$	\( 1 \)	$1$	$982.0658897$	1.79263	\( -9317 \)	\( \bigl[-2 a^{5} + a^{4} + 14 a^{3} + 4 a^{2} - 10 a - 1\) , \( -3 a^{5} + 23 a^{3} + 14 a^{2} - 18 a - 5\) , \( -6 a^{5} + 2 a^{4} + 43 a^{3} + 17 a^{2} - 28 a - 6\) , \( 20 a^{5} - 7 a^{4} - 141 a^{3} - 56 a^{2} + 82 a + 21\) , \( 20 a^{5} - 6 a^{4} - 142 a^{3} - 62 a^{2} + 83 a + 22\bigr] \)	${y}^2+\left(-2a^{5}+a^{4}+14a^{3}+4a^{2}-10a-1\right){x}{y}+\left(-6a^{5}+2a^{4}+43a^{3}+17a^{2}-28a-6\right){y}={x}^{3}+\left(-3a^{5}+23a^{3}+14a^{2}-18a-5\right){x}^{2}+\left(20a^{5}-7a^{4}-141a^{3}-56a^{2}+82a+21\right){x}+20a^{5}-6a^{4}-142a^{3}-62a^{2}+83a+22$

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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.