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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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Results (12 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	Sato-Tate	$\Q$-curve	Nonmax $\ell$	mod-$\ell$ images	$Ш_{\textrm{an}}$	Tamagawa	Regulator	Period	Leading coeff	j-invariant	Weierstrass coefficients	Weierstrass equation
1536.1-b3	1536.1-b	$4$	$4$	$\Q(\sqrt{3}) $	$2$	$[2, 0]$	1536.1	$ 2^{9} \cdot 3 $	$ 2^{17} \cdot 3 $	$1.93788$	$(a+1), (a)$	0	$\Z/4\Z$	$\textsf{no}$	$\mathrm{SU}(2)$	✓	$2$	2B	$1$	$ 2^{2} $	$1$	$24.28254506$	1.752441741	$ -\frac{17879000}{3} a + 10335000 $	$ \bigl[0$ , $ -a - 1$ , $ 0$ , $ -6 a - 17$ , $ 23 a + 45\bigr] $	${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-6a-17\right){x}+23a+45$
1536.1-k3	1536.1-k	$4$	$4$	$\Q(\sqrt{3}) $	$2$	$[2, 0]$	1536.1	$ 2^{9} \cdot 3 $	$ 2^{17} \cdot 3 $	$1.93788$	$(a+1), (a)$	0	$\Z/2\Z$	$\textsf{no}$	$\mathrm{SU}(2)$	✓	$2$	2B	$1$	$ 1 $	$1$	$24.28254506$	1.752441741	$ -\frac{17879000}{3} a + 10335000 $	$ \bigl[0$ , $ -a + 1$ , $ 0$ , $ 26 a - 47$ , $ -77 a + 135\bigr] $	${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(26a-47\right){x}-77a+135$
1536.1-n3	1536.1-n	$4$	$4$	$\Q(\sqrt{3}) $	$2$	$[2, 0]$	1536.1	$ 2^{9} \cdot 3 $	$ 2^{17} \cdot 3 $	$1.93788$	$(a+1), (a)$	0	$\Z/2\Z$	$\textsf{no}$	$\mathrm{SU}(2)$	✓	$2$	2B	$1$	$ 2^{2} $	$1$	$6.070636265$	1.752441741	$ -\frac{17879000}{3} a + 10335000 $	$ \bigl[0$ , $ a + 1$ , $ 0$ , $ -6 a - 17$ , $ -23 a - 45\bigr] $	${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-6a-17\right){x}-23a-45$
1536.1-w3	1536.1-w	$4$	$4$	$\Q(\sqrt{3}) $	$2$	$[2, 0]$	1536.1	$ 2^{9} \cdot 3 $	$ 2^{17} \cdot 3 $	$1.93788$	$(a+1), (a)$	0	$\Z/2\Z$	$\textsf{no}$	$\mathrm{SU}(2)$	✓	$2$	2B	$4$	$ 1 $	$1$	$6.070636265$	1.752441741	$ -\frac{17879000}{3} a + 10335000 $	$ \bigl[0$ , $ a - 1$ , $ 0$ , $ 26 a - 47$ , $ 77 a - 135\bigr] $	${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(26a-47\right){x}+77a-135$
3072.1-d3	3072.1-d	$4$	$4$	$\Q(\sqrt{3}) $	$2$	$[2, 0]$	3072.1	$ 2^{10} \cdot 3 $	$ 2^{23} \cdot 3 $	$2.30454$	$(a+1), (a)$	$1$	$\Z/2\Z$	$\textsf{no}$	$\mathrm{SU}(2)$	✓	$2$	2B	$1$	$ 2 $	$2.415050467$	$6.405092923$	4.465406728	$ -\frac{17879000}{3} a + 10335000 $	$ \bigl[0$ , $ 1$ , $ 0$ , $ 10 a - 33$ , $ 50 a - 69\bigr] $	${y}^2={x}^{3}+{x}^{2}+\left(10a-33\right){x}+50a-69$
3072.1-bb3	3072.1-bb	$4$	$4$	$\Q(\sqrt{3}) $	$2$	$[2, 0]$	3072.1	$ 2^{10} \cdot 3 $	$ 2^{23} \cdot 3 $	$2.30454$	$(a+1), (a)$	$1$	$\Z/2\Z$	$\textsf{no}$	$\mathrm{SU}(2)$	✓	$2$	2B	$1$	$ 2 $	$1.696743987$	$6.405092923$	3.137264466	$ -\frac{17879000}{3} a + 10335000 $	$ \bigl[0$ , $ -a - 1$ , $ 0$ , $ 204 a - 352$ , $ 2132 a - 3692\bigr] $	${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(204a-352\right){x}+2132a-3692$
3072.1-bn3	3072.1-bn	$4$	$4$	$\Q(\sqrt{3}) $	$2$	$[2, 0]$	3072.1	$ 2^{10} \cdot 3 $	$ 2^{23} \cdot 3 $	$2.30454$	$(a+1), (a)$	$2$	$\Z/2\Z$	$\textsf{no}$	$\mathrm{SU}(2)$	✓	$2$	2B	$1$	$ 2^{2} $	$0.298069290$	$11.50728806$	3.960587271	$ -\frac{17879000}{3} a + 10335000 $	$ \bigl[0$ , $ -1$ , $ 0$ , $ 10 a - 33$ , $ -50 a + 69\bigr] $	${y}^2={x}^{3}-{x}^{2}+\left(10a-33\right){x}-50a+69$
3072.1-bu3	3072.1-bu	$4$	$4$	$\Q(\sqrt{3}) $	$2$	$[2, 0]$	3072.1	$ 2^{10} \cdot 3 $	$ 2^{23} \cdot 3 $	$2.30454$	$(a+1), (a)$	0	$\Z/2\Z$	$\textsf{no}$	$\mathrm{SU}(2)$	✓	$2$	2B	$1$	$ 2^{2} $	$1$	$11.50728806$	3.321867930	$ -\frac{17879000}{3} a + 10335000 $	$ \bigl[0$ , $ a + 1$ , $ 0$ , $ 204 a - 352$ , $ -2132 a + 3692\bigr] $	${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(204a-352\right){x}-2132a+3692$
4608.1-g3	4608.1-g	$4$	$4$	$\Q(\sqrt{3}) $	$2$	$[2, 0]$	4608.1	$ 2^{9} \cdot 3^{2} $	$ 2^{17} \cdot 3^{7} $	$2.55039$	$(a+1), (a)$	$1$	$\Z/2\Z$	$\textsf{no}$	$\mathrm{SU}(2)$	✓	$2$	2B	$1$	$ 2^{3} $	$0.373870495$	$9.395661359$	4.056186517	$ -\frac{17879000}{3} a + 10335000 $	$ \bigl[0$ , $ -a$ , $ 0$ , $ 80 a - 144$ , $ -484 a + 836\bigr] $	${y}^2={x}^{3}-a{x}^{2}+\left(80a-144\right){x}-484a+836$
4608.1-j3	4608.1-j	$4$	$4$	$\Q(\sqrt{3}) $	$2$	$[2, 0]$	4608.1	$ 2^{9} \cdot 3^{2} $	$ 2^{17} \cdot 3^{7} $	$2.55039$	$(a+1), (a)$	$1$	$\Z/2\Z$	$\textsf{no}$	$\mathrm{SU}(2)$	✓	$2$	2B	$1$	$ 2 $	$1.495481981$	$9.395661359$	4.056186517	$ -\frac{17879000}{3} a + 10335000 $	$ \bigl[0$ , $ a$ , $ 0$ , $ -20 a - 54$ , $ -116 a - 154\bigr] $	${y}^2={x}^{3}+a{x}^{2}+\left(-20a-54\right){x}-116a-154$
4608.1-r3	4608.1-r	$4$	$4$	$\Q(\sqrt{3}) $	$2$	$[2, 0]$	4608.1	$ 2^{9} \cdot 3^{2} $	$ 2^{17} \cdot 3^{7} $	$2.55039$	$(a+1), (a)$	0	$\Z/2\Z$	$\textsf{no}$	$\mathrm{SU}(2)$	✓	$2$	2B	$1$	$ 2^{2} $	$1$	$5.229736472$	1.509694880	$ -\frac{17879000}{3} a + 10335000 $	$ \bigl[0$ , $ a$ , $ 0$ , $ 80 a - 144$ , $ 484 a - 836\bigr] $	${y}^2={x}^{3}+a{x}^{2}+\left(80a-144\right){x}+484a-836$
4608.1-bd3	4608.1-bd	$4$	$4$	$\Q(\sqrt{3}) $	$2$	$[2, 0]$	4608.1	$ 2^{9} \cdot 3^{2} $	$ 2^{17} \cdot 3^{7} $	$2.55039$	$(a+1), (a)$	0	$\Z/2\Z$	$\textsf{no}$	$\mathrm{SU}(2)$	✓	$2$	2B	$1$	$ 2^{2} $	$1$	$5.229736472$	1.509694880	$ -\frac{17879000}{3} a + 10335000 $	$ \bigl[0$ , $ -a$ , $ 0$ , $ -20 a - 54$ , $ 116 a + 154\bigr] $	${y}^2={x}^{3}-a{x}^{2}+\left(-20a-54\right){x}+116a+154$

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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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Results (12 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	Sato-Tate	$\Q$-curve	Nonmax $\ell$	mod-$\ell$ images	$Ш_{\textrm{an}}$	Tamagawa	Regulator	Period	Leading coeff	j-invariant	Weierstrass coefficients	Weierstrass equation
1536.1-b3	1536.1-b	$4$	$4$	\(\Q(\sqrt{3}) \)	$2$	$[2, 0]$	1536.1	\( 2^{9} \cdot 3 \)	\( 2^{17} \cdot 3 \)	$1.93788$	$(a+1), (a)$	0	$\Z/4\Z$	$\textsf{no}$	$\mathrm{SU}(2)$	✓	$2$	2B	$1$	\( 2^{2} \)	$1$	$24.28254506$	1.752441741	\( -\frac{17879000}{3} a + 10335000 \)	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -6 a - 17\) , \( 23 a + 45\bigr] \)	${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-6a-17\right){x}+23a+45$
1536.1-k3	1536.1-k	$4$	$4$	\(\Q(\sqrt{3}) \)	$2$	$[2, 0]$	1536.1	\( 2^{9} \cdot 3 \)	\( 2^{17} \cdot 3 \)	$1.93788$	$(a+1), (a)$	0	$\Z/2\Z$	$\textsf{no}$	$\mathrm{SU}(2)$	✓	$2$	2B	$1$	\( 1 \)	$1$	$24.28254506$	1.752441741	\( -\frac{17879000}{3} a + 10335000 \)	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 26 a - 47\) , \( -77 a + 135\bigr] \)	${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(26a-47\right){x}-77a+135$
1536.1-n3	1536.1-n	$4$	$4$	\(\Q(\sqrt{3}) \)	$2$	$[2, 0]$	1536.1	\( 2^{9} \cdot 3 \)	\( 2^{17} \cdot 3 \)	$1.93788$	$(a+1), (a)$	0	$\Z/2\Z$	$\textsf{no}$	$\mathrm{SU}(2)$	✓	$2$	2B	$1$	\( 2^{2} \)	$1$	$6.070636265$	1.752441741	\( -\frac{17879000}{3} a + 10335000 \)	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -6 a - 17\) , \( -23 a - 45\bigr] \)	${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-6a-17\right){x}-23a-45$
1536.1-w3	1536.1-w	$4$	$4$	\(\Q(\sqrt{3}) \)	$2$	$[2, 0]$	1536.1	\( 2^{9} \cdot 3 \)	\( 2^{17} \cdot 3 \)	$1.93788$	$(a+1), (a)$	0	$\Z/2\Z$	$\textsf{no}$	$\mathrm{SU}(2)$	✓	$2$	2B	$4$	\( 1 \)	$1$	$6.070636265$	1.752441741	\( -\frac{17879000}{3} a + 10335000 \)	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 26 a - 47\) , \( 77 a - 135\bigr] \)	${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(26a-47\right){x}+77a-135$
3072.1-d3	3072.1-d	$4$	$4$	\(\Q(\sqrt{3}) \)	$2$	$[2, 0]$	3072.1	\( 2^{10} \cdot 3 \)	\( 2^{23} \cdot 3 \)	$2.30454$	$(a+1), (a)$	$1$	$\Z/2\Z$	$\textsf{no}$	$\mathrm{SU}(2)$	✓	$2$	2B	$1$	\( 2 \)	$2.415050467$	$6.405092923$	4.465406728	\( -\frac{17879000}{3} a + 10335000 \)	\( \bigl[0\) , \( 1\) , \( 0\) , \( 10 a - 33\) , \( 50 a - 69\bigr] \)	${y}^2={x}^{3}+{x}^{2}+\left(10a-33\right){x}+50a-69$
3072.1-bb3	3072.1-bb	$4$	$4$	\(\Q(\sqrt{3}) \)	$2$	$[2, 0]$	3072.1	\( 2^{10} \cdot 3 \)	\( 2^{23} \cdot 3 \)	$2.30454$	$(a+1), (a)$	$1$	$\Z/2\Z$	$\textsf{no}$	$\mathrm{SU}(2)$	✓	$2$	2B	$1$	\( 2 \)	$1.696743987$	$6.405092923$	3.137264466	\( -\frac{17879000}{3} a + 10335000 \)	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 204 a - 352\) , \( 2132 a - 3692\bigr] \)	${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(204a-352\right){x}+2132a-3692$
3072.1-bn3	3072.1-bn	$4$	$4$	\(\Q(\sqrt{3}) \)	$2$	$[2, 0]$	3072.1	\( 2^{10} \cdot 3 \)	\( 2^{23} \cdot 3 \)	$2.30454$	$(a+1), (a)$	$2$	$\Z/2\Z$	$\textsf{no}$	$\mathrm{SU}(2)$	✓	$2$	2B	$1$	\( 2^{2} \)	$0.298069290$	$11.50728806$	3.960587271	\( -\frac{17879000}{3} a + 10335000 \)	\( \bigl[0\) , \( -1\) , \( 0\) , \( 10 a - 33\) , \( -50 a + 69\bigr] \)	${y}^2={x}^{3}-{x}^{2}+\left(10a-33\right){x}-50a+69$
3072.1-bu3	3072.1-bu	$4$	$4$	\(\Q(\sqrt{3}) \)	$2$	$[2, 0]$	3072.1	\( 2^{10} \cdot 3 \)	\( 2^{23} \cdot 3 \)	$2.30454$	$(a+1), (a)$	0	$\Z/2\Z$	$\textsf{no}$	$\mathrm{SU}(2)$	✓	$2$	2B	$1$	\( 2^{2} \)	$1$	$11.50728806$	3.321867930	\( -\frac{17879000}{3} a + 10335000 \)	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 204 a - 352\) , \( -2132 a + 3692\bigr] \)	${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(204a-352\right){x}-2132a+3692$
4608.1-g3	4608.1-g	$4$	$4$	\(\Q(\sqrt{3}) \)	$2$	$[2, 0]$	4608.1	\( 2^{9} \cdot 3^{2} \)	\( 2^{17} \cdot 3^{7} \)	$2.55039$	$(a+1), (a)$	$1$	$\Z/2\Z$	$\textsf{no}$	$\mathrm{SU}(2)$	✓	$2$	2B	$1$	\( 2^{3} \)	$0.373870495$	$9.395661359$	4.056186517	\( -\frac{17879000}{3} a + 10335000 \)	\( \bigl[0\) , \( -a\) , \( 0\) , \( 80 a - 144\) , \( -484 a + 836\bigr] \)	${y}^2={x}^{3}-a{x}^{2}+\left(80a-144\right){x}-484a+836$
4608.1-j3	4608.1-j	$4$	$4$	\(\Q(\sqrt{3}) \)	$2$	$[2, 0]$	4608.1	\( 2^{9} \cdot 3^{2} \)	\( 2^{17} \cdot 3^{7} \)	$2.55039$	$(a+1), (a)$	$1$	$\Z/2\Z$	$\textsf{no}$	$\mathrm{SU}(2)$	✓	$2$	2B	$1$	\( 2 \)	$1.495481981$	$9.395661359$	4.056186517	\( -\frac{17879000}{3} a + 10335000 \)	\( \bigl[0\) , \( a\) , \( 0\) , \( -20 a - 54\) , \( -116 a - 154\bigr] \)	${y}^2={x}^{3}+a{x}^{2}+\left(-20a-54\right){x}-116a-154$
4608.1-r3	4608.1-r	$4$	$4$	\(\Q(\sqrt{3}) \)	$2$	$[2, 0]$	4608.1	\( 2^{9} \cdot 3^{2} \)	\( 2^{17} \cdot 3^{7} \)	$2.55039$	$(a+1), (a)$	0	$\Z/2\Z$	$\textsf{no}$	$\mathrm{SU}(2)$	✓	$2$	2B	$1$	\( 2^{2} \)	$1$	$5.229736472$	1.509694880	\( -\frac{17879000}{3} a + 10335000 \)	\( \bigl[0\) , \( a\) , \( 0\) , \( 80 a - 144\) , \( 484 a - 836\bigr] \)	${y}^2={x}^{3}+a{x}^{2}+\left(80a-144\right){x}+484a-836$
4608.1-bd3	4608.1-bd	$4$	$4$	\(\Q(\sqrt{3}) \)	$2$	$[2, 0]$	4608.1	\( 2^{9} \cdot 3^{2} \)	\( 2^{17} \cdot 3^{7} \)	$2.55039$	$(a+1), (a)$	0	$\Z/2\Z$	$\textsf{no}$	$\mathrm{SU}(2)$	✓	$2$	2B	$1$	\( 2^{2} \)	$1$	$5.229736472$	1.509694880	\( -\frac{17879000}{3} a + 10335000 \)	\( \bigl[0\) , \( -a\) , \( 0\) , \( -20 a - 54\) , \( 116 a + 154\bigr] \)	${y}^2={x}^{3}-a{x}^{2}+\left(-20a-54\right){x}+116a+154$