LMFDB - Elliptic curves over 6.6.300125.1 of conductor 1.1

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Base field	Conductor norm	Rank*	Torsion order	CM discriminant

Base field degree/signature	Bad $p$	$\Q$-curves	Torsion structure	CM

Analytic order of Ш*	Cyclic isogeny degree	Isogeny class size	Reduction	Galois image

j-invariant	Regulator*	Curves per isogeny class	Isogeny class degree	Nonmax$\ \ell$

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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-a1	1.1-a	$2$	$37$	6.6.300125.1	$6$	$[6, 0]$	1.1	$ 1 $	$ 1 $	$48.95416$	$\textsf{none}$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓	✓	$37$	37B.1.2	$1874161$	$ 1 $	$1$	$0.000152551$	0.521880	$ -162677523113838677 $	$ \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$ , $ 321037 a^{5} - 77286 a^{4} - 2300766 a^{3} - 1111743 a^{2} + 1379267 a + 398326$ , $ 54665451 a^{5} - 12782935 a^{4} - 392075036 a^{3} - 191607310 a^{2} + 234159226 a + 69935775\bigr] $	${y}^2+\left(-2a^{5}+a^{4}+14a^{3}+4a^{2}-9a-2\right){x}{y}+\left(-5a^{5}+a^{4}+37a^{3}+18a^{2}-26a-7\right){y}={x}^{3}+\left(-3a^{5}+2a^{4}+20a^{3}+3a^{2}-12a\right){x}^{2}+\left(321037a^{5}-77286a^{4}-2300766a^{3}-1111743a^{2}+1379267a+398326\right){x}+54665451a^{5}-12782935a^{4}-392075036a^{3}-191607310a^{2}+234159226a+69935775$
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] $	${y}^2+\left(-2a^{5}+a^{4}+14a^{3}+4a^{2}-9a-2\right){x}{y}+\left(-5a^{5}+a^{4}+37a^{3}+18a^{2}-26a-7\right){y}={x}^{3}+\left(-3a^{5}+2a^{4}+20a^{3}+3a^{2}-12a\right){x}^{2}+\left(7a^{5}-a^{4}-51a^{3}-28a^{2}+27a+11\right){x}-13a^{5}+4a^{4}+92a^{3}+40a^{2}-56a-16$

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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.

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