Elliptic curve search results

Results (6 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
288.1-a4	288.1-a	$4$	$4$	\(\Q(\sqrt{2}) \)	$2$	$[2, 0]$	288.1	\( 2^{5} \cdot 3^{2} \)	\( 2^{6} \cdot 3^{2} \)	$1.04119$	$(a), (3)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	\( 2 \)	$1$	$26.82794265$	1.185638761	\( \frac{98115010000}{3} a + 46251861000 \)	\( \bigl[a\) , \( -1\) , \( a\) , \( 50 a - 73\) , \( -4 a + 6\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(50a-73\right){x}-4a+6$
288.1-d4	288.1-d	$4$	$4$	\(\Q(\sqrt{2}) \)	$2$	$[2, 0]$	288.1	\( 2^{5} \cdot 3^{2} \)	\( 2^{6} \cdot 3^{2} \)	$1.04119$	$(a), (3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	\( 2 \)	$1$	$6.706985663$	1.185638761	\( \frac{98115010000}{3} a + 46251861000 \)	\( \bigl[a\) , \( 0\) , \( a\) , \( 50 a - 73\) , \( 4 a - 7\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^{3}+\left(50a-73\right){x}+4a-7$
2304.1-j4	2304.1-j	$4$	$4$	\(\Q(\sqrt{2}) \)	$2$	$[2, 0]$	2304.1	\( 2^{8} \cdot 3^{2} \)	\( 2^{18} \cdot 3^{2} \)	$1.75107$	$(a), (3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	\( 2 \)	$1$	$3.337851468$	0.590054352	\( \frac{98115010000}{3} a + 46251861000 \)	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 24 a - 64\) , \( -36 a - 44\bigr] \)	${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(24a-64\right){x}-36a-44$
2304.1-l4	2304.1-l	$4$	$4$	\(\Q(\sqrt{2}) \)	$2$	$[2, 0]$	2304.1	\( 2^{8} \cdot 3^{2} \)	\( 2^{18} \cdot 3^{2} \)	$1.75107$	$(a), (3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	\( 2 \)	$1$	$13.47682996$	2.382389464	\( \frac{98115010000}{3} a + 46251861000 \)	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 24 a - 64\) , \( 36 a + 44\bigr] \)	${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(24a-64\right){x}+36a+44$
2592.1-b4	2592.1-b	$4$	$4$	\(\Q(\sqrt{2}) \)	$2$	$[2, 0]$	2592.1	\( 2^{5} \cdot 3^{4} \)	\( 2^{6} \cdot 3^{14} \)	$1.80340$	$(a), (3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	\( 2^{3} \)	$1$	$2.235661887$	1.580851681	\( \frac{98115010000}{3} a + 46251861000 \)	\( \bigl[a\) , \( 1\) , \( a\) , \( 450 a - 649\) , \( 108 a - 176\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(450a-649\right){x}+108a-176$
2592.1-g4	2592.1-g	$4$	$4$	\(\Q(\sqrt{2}) \)	$2$	$[2, 0]$	2592.1	\( 2^{5} \cdot 3^{4} \)	\( 2^{6} \cdot 3^{14} \)	$1.80340$	$(a), (3)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	\( 2^{3} \)	$1$	$8.942647551$	1.580851681	\( \frac{98115010000}{3} a + 46251861000 \)	\( \bigl[a\) , \( 1\) , \( 0\) , \( 450 a - 648\) , \( 342 a - 473\bigr] \)	${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(450a-648\right){x}+342a-473$

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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.