Elliptic curve search results

Results (4 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
19.1-a3	19.1-a	$3$	$9$	\(\Q(\sqrt{57}) \)	$2$	$[2, 0]$	19.1	\( 19 \)	\( 19^{2} \)	$1.40852$	$(10a-43)$	$1$	$\Z/3\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$3$	3B.1.1	$1$	\( 2 \)	$1.022490498$	$16.64051879$	1.001627401	\( \frac{32768}{19} \)	\( \bigl[0\) , \( 1\) , \( 1\) , \( 1\) , \( 0\bigr] \)	${y}^2+{y}={x}^{3}+{x}^{2}+{x}$
19.1-b3	19.1-b	$3$	$9$	\(\Q(\sqrt{57}) \)	$2$	$[2, 0]$	19.1	\( 19 \)	\( 19^{2} \)	$1.40852$	$(10a-43)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$3$	3B.1.2	$1$	\( 2 \)	$0.225966868$	$17.03289160$	2.039180708	\( \frac{32768}{19} \)	\( \bigl[0\) , \( -a + 1\) , \( 1\) , \( 8053 a + 26379\) , \( 24987 a + 81833\bigr] \)	${y}^2+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(8053a+26379\right){x}+24987a+81833$
171.1-c3	171.1-c	$3$	$9$	\(\Q(\sqrt{57}) \)	$2$	$[2, 0]$	171.1	\( 3^{2} \cdot 19 \)	\( 3^{6} \cdot 19^{2} \)	$2.43964$	$(4a+13), (10a-43)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$3$	3B	$1$	\( 2^{2} \)	$0.262784271$	$9.720016340$	2.706567867	\( \frac{32768}{19} \)	\( \bigl[0\) , \( a + 1\) , \( 1\) , \( 81 a + 267\) , \( 108 a + 353\bigr] \)	${y}^2+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(81a+267\right){x}+108a+353$
171.1-j3	171.1-j	$3$	$9$	\(\Q(\sqrt{57}) \)	$2$	$[2, 0]$	171.1	\( 3^{2} \cdot 19 \)	\( 3^{6} \cdot 19^{2} \)	$2.43964$	$(4a+13), (10a-43)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$3$	3B	$1$	\( 2^{2} \)	$0.262784271$	$9.720016340$	2.706567867	\( \frac{32768}{19} \)	\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( -79 a + 347\) , \( -28 a + 114\bigr] \)	${y}^2+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-79a+347\right){x}-28a+114$

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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.