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
196.1-a2	196.1-a	$2$	$3$	\(\Q(\sqrt{21}) \)	$2$	$[2, 0]$	196.1	\( 2^{2} \cdot 7^{2} \)	\( 2^{18} \cdot 7^{4} \)	$1.53219$	$(a+3), (2)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$3$	3B	$1$	\( 1 \)	$1$	$5.190836609$	1.132733413	\( \frac{189}{512} \)	\( \bigl[a\) , \( a\) , \( 0\) , \( 2 a + 4\) , \( -16 a - 28\bigr] \)	${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(2a+4\right){x}-16a-28$
196.1-b2	196.1-b	$2$	$3$	\(\Q(\sqrt{21}) \)	$2$	$[2, 0]$	196.1	\( 2^{2} \cdot 7^{2} \)	\( 2^{18} \cdot 7^{4} \)	$1.53219$	$(a+3), (2)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$3$	3B	$1$	\( 1 \)	$1$	$5.190836609$	1.132733413	\( \frac{189}{512} \)	\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( 3 a + 8\) , \( 21 a - 43\bigr] \)	${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(3a+8\right){x}+21a-43$
1764.1-b2	1764.1-b	$2$	$3$	\(\Q(\sqrt{21}) \)	$2$	$[2, 0]$	1764.1	\( 2^{2} \cdot 3^{2} \cdot 7^{2} \)	\( 2^{18} \cdot 3^{6} \cdot 7^{4} \)	$2.65383$	$(-a+2), (a+3), (2)$	0	$\Z/3\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$3$	3B.1.1	$1$	\( 2^{2} \cdot 3^{3} \)	$1$	$1.770823918$	4.637105514	\( \frac{189}{512} \)	\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -8 a + 21\) , \( 942 a - 2630\bigr] \)	${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-8a+21\right){x}+942a-2630$
1764.1-o2	1764.1-o	$2$	$3$	\(\Q(\sqrt{21}) \)	$2$	$[2, 0]$	1764.1	\( 2^{2} \cdot 3^{2} \cdot 7^{2} \)	\( 2^{18} \cdot 3^{6} \cdot 7^{4} \)	$2.65383$	$(-a+2), (a+3), (2)$	$2$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$3$	3B.1.2	$1$	\( 2^{2} \cdot 3^{3} \)	$0.009772816$	$5.071986438$	4.672743225	\( \frac{189}{512} \)	\( \bigl[1\) , \( -1\) , \( 1\) , \( 1\) , \( 39\bigr] \)	${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+{x}+39$

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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.