Elliptic curve search results

Results (8 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
128.1-a3	128.1-a	$4$	$4$	\(\Q(\sqrt{2}) \)	$2$	$[2, 0]$	128.1	\( 2^{7} \)	\( 2^{14} \)	$0.85013$	$(a)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$2$	2Cs	$1$	\( 2 \)	$1$	$22.17917604$	0.980190361	\( 10976 \)	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 4 a - 6\) , \( -10 a + 14\bigr] \)	${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(4a-6\right){x}-10a+14$
128.1-b3	128.1-b	$4$	$4$	\(\Q(\sqrt{2}) \)	$2$	$[2, 0]$	128.1	\( 2^{7} \)	\( 2^{14} \)	$0.85013$	$(a)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$2$	2Cs	$1$	\( 2 \)	$1$	$22.17917604$	0.980190361	\( 10976 \)	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 4 a - 6\) , \( 10 a - 14\bigr] \)	${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(4a-6\right){x}+10a-14$
256.1-b3	256.1-b	$4$	$4$	\(\Q(\sqrt{2}) \)	$2$	$[2, 0]$	256.1	\( 2^{8} \)	\( 2^{14} \)	$1.01098$	$(a)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓		✓	$2$	2Cs	$1$	\( 2^{2} \)	$1$	$15.09590514$	1.334302111	\( 10976 \)	\( \bigl[0\) , \( 1\) , \( 0\) , \( -2\) , \( -2\bigr] \)	${y}^2={x}^{3}+{x}^{2}-2{x}-2$
256.1-d3	256.1-d	$4$	$4$	\(\Q(\sqrt{2}) \)	$2$	$[2, 0]$	256.1	\( 2^{8} \)	\( 2^{14} \)	$1.01098$	$(a)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓		✓	$2$	2Cs	$1$	\( 2^{2} \)	$0.216165582$	$32.58604536$	1.245211766	\( 10976 \)	\( \bigl[0\) , \( -1\) , \( 0\) , \( -2\) , \( 2\bigr] \)	${y}^2={x}^{3}-{x}^{2}-2{x}+2$
1024.1-g3	1024.1-g	$4$	$4$	\(\Q(\sqrt{2}) \)	$2$	$[2, 0]$	1024.1	\( 2^{10} \)	\( 2^{20} \)	$1.42974$	$(a)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$2$	2Cs	$1$	\( 2^{2} \)	$1$	$15.68304578$	1.386198502	\( 10976 \)	\( \bigl[0\) , \( -a\) , \( 0\) , \( -4\) , \( 4 a\bigr] \)	${y}^2={x}^{3}-a{x}^{2}-4{x}+4a$
1024.1-h3	1024.1-h	$4$	$4$	\(\Q(\sqrt{2}) \)	$2$	$[2, 0]$	1024.1	\( 2^{10} \)	\( 2^{20} \)	$1.42974$	$(a)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$2$	2Cs	$1$	\( 2^{2} \)	$1$	$10.67441689$	0.943494071	\( 10976 \)	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -10 a - 13\) , \( -19 a - 27\bigr] \)	${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-10a-13\right){x}-19a-27$
1024.1-i3	1024.1-i	$4$	$4$	\(\Q(\sqrt{2}) \)	$2$	$[2, 0]$	1024.1	\( 2^{10} \)	\( 2^{20} \)	$1.42974$	$(a)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$2$	2Cs	$1$	\( 2^{2} \)	$1$	$15.68304578$	1.386198502	\( 10976 \)	\( \bigl[0\) , \( a\) , \( 0\) , \( -4\) , \( -4 a\bigr] \)	${y}^2={x}^{3}+a{x}^{2}-4{x}-4a$
1024.1-j3	1024.1-j	$4$	$4$	\(\Q(\sqrt{2}) \)	$2$	$[2, 0]$	1024.1	\( 2^{10} \)	\( 2^{20} \)	$1.42974$	$(a)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$2$	2Cs	$1$	\( 2^{2} \)	$1$	$23.04181365$	2.036627835	\( 10976 \)	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -10 a - 13\) , \( 19 a + 27\bigr] \)	${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-10a-13\right){x}+19a+27$

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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.