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
9604.3-a2	9604.3-a	$2$	$3$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	9604.3	\( 2^{2} \cdot 7^{4} \)	\( 2^{18} \cdot 7^{10} \)	$1.53219$	$(-3a+1), (3a-2), (2)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$3$	3B[2]	$1$	\( 1 \)	$1$	$0.980975911$	1.132733413	\( \frac{189}{512} \)	\( \bigl[a\) , \( -1\) , \( 0\) , \( 2 a - 3\) , \( 87 a + 76\bigr] \)	${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(2a-3\right){x}+87a+76$
9604.3-b2	9604.3-b	$2$	$3$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	9604.3	\( 2^{2} \cdot 7^{4} \)	\( 2^{18} \cdot 7^{10} \)	$1.53219$	$(-3a+1), (3a-2), (2)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$3$	3B[2]	$1$	\( 1 \)	$1$	$0.980975911$	1.132733413	\( \frac{189}{512} \)	\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( 3 a - 2\) , \( -87 a + 163\bigr] \)	${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(3a-2\right){x}-87a+163$
86436.3-h2	86436.3-h	$2$	$3$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	86436.3	\( 2^{2} \cdot 3^{2} \cdot 7^{4} \)	\( 2^{18} \cdot 3^{6} \cdot 7^{4} \)	$2.65383$	$(-2a+1), (-3a+1), (3a-2), (2)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$3$	3B[2]	$1$	\( 2 \cdot 3^{2} \)	$0.071245209$	$1.498465456$	4.437866884	\( \frac{189}{512} \)	\( \bigl[1\) , \( -1\) , \( 1\) , \( 1\) , \( 39\bigr] \)	${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+{x}+39$
86436.3-j2	86436.3-j	$2$	$3$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	86436.3	\( 2^{2} \cdot 3^{2} \cdot 7^{4} \)	\( 2^{18} \cdot 3^{6} \cdot 7^{16} \)	$2.65383$	$(-2a+1), (-3a+1), (3a-2), (2)$	$1$	$\Z/3\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$3$	3B.1.1[2]	$1$	\( 2 \cdot 3^{4} \)	$0.548686226$	$0.214066493$	4.882526660	\( \frac{189}{512} \)	\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 64 a - 65\) , \( -13597\bigr] \)	${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(64a-65\right){x}-13597$

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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.