Elliptic curve search results

Results (10 matches)

 

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
147.2-a1	147.2-a	$8$	$16$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	147.2	\( 3 \cdot 7^{2} \)	\( 3 \cdot 7^{20} \)	$0.53893$	$(-2a+1), (-3a+1), (3a-2)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓		$2$	2B	$1$	\( 2^{2} \)	$1$	$0.431038464$	0.497720347	\( -\frac{1866593950165482334}{99698791708803} a + \frac{793626053533786727}{99698791708803} \)	\( \bigl[1\) , \( 0\) , \( 0\) , \( -470 a + 321\) , \( 1866 a - 3772\bigr] \)	${y}^2+{x}{y}={x}^{3}+\left(-470a+321\right){x}+1866a-3772$
3087.2-a1	3087.2-a	$8$	$16$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	3087.2	\( 3^{2} \cdot 7^{3} \)	\( 3^{7} \cdot 7^{26} \)	$1.15367$	$(-2a+1), (-3a+1), (3a-2)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	\( 2^{6} \)	$1$	$0.094060304$	1.737783746	\( -\frac{1866593950165482334}{99698791708803} a + \frac{793626053533786727}{99698791708803} \)	\( \bigl[1\) , \( a\) , \( 0\) , \( 3474 a + 6465\) , \( -321486 a + 306732\bigr] \)	${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(3474a+6465\right){x}-321486a+306732$
3087.3-a1	3087.3-a	$8$	$16$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	3087.3	\( 3^{2} \cdot 7^{3} \)	\( 3^{7} \cdot 7^{26} \)	$1.15367$	$(-2a+1), (-3a+1), (3a-2)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	\( 2^{6} \)	$1$	$0.094060304$	1.737783746	\( -\frac{1866593950165482334}{99698791708803} a + \frac{793626053533786727}{99698791708803} \)	\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -654 a - 8391\) , \( 19194 a + 304332\bigr] \)	${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-654a-8391\right){x}+19194a+304332$
7203.3-a1	7203.3-a	$8$	$16$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	7203.3	\( 3 \cdot 7^{4} \)	\( 3 \cdot 7^{32} \)	$1.42586$	$(-2a+1), (-3a+1), (3a-2)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	\( 2^{3} \)	$5.277017646$	$0.061576923$	1.500845174	\( -\frac{1866593950165482334}{99698791708803} a + \frac{793626053533786727}{99698791708803} \)	\( \bigl[1\) , \( 1\) , \( 1\) , \( -23030 a + 15728\) , \( -663068 a + 1309524\bigr] \)	${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-23030a+15728\right){x}-663068a+1309524$
24843.4-b5	24843.4-b	$8$	$16$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	24843.4	\( 3 \cdot 7^{2} \cdot 13^{2} \)	\( 3 \cdot 7^{20} \cdot 13^{6} \)	$1.94312$	$(-2a+1), (-3a+1), (3a-2), (-4a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	\( 2^{6} \)	$1$	$0.119548560$	2.208684594	\( -\frac{1866593950165482334}{99698791708803} a + \frac{793626053533786727}{99698791708803} \)	\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -1055 a - 4803\) , \( -36894 a - 131300\bigr] \)	${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(-1055a-4803\right){x}-36894a-131300$
24843.6-b5	24843.6-b	$8$	$16$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	24843.6	\( 3 \cdot 7^{2} \cdot 13^{2} \)	\( 3 \cdot 7^{20} \cdot 13^{6} \)	$1.94312$	$(-2a+1), (-3a+1), (3a-2), (4a-3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$4$	\( 2^{4} \)	$1$	$0.119548560$	2.208684594	\( -\frac{1866593950165482334}{99698791708803} a + \frac{793626053533786727}{99698791708803} \)	\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -6007 a + 1525\) , \( 167514 a - 132740\bigr] \)	${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-6007a+1525\right){x}+167514a-132740$
37632.2-f5	37632.2-f	$8$	$16$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	37632.2	\( 2^{8} \cdot 3 \cdot 7^{2} \)	\( 2^{24} \cdot 3 \cdot 7^{20} \)	$2.15570$	$(-2a+1), (-3a+1), (3a-2), (2)$	$1$	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	\( 2^{7} \)	$1.492598417$	$0.107759616$	2.971586411	\( -\frac{1866593950165482334}{99698791708803} a + \frac{793626053533786727}{99698791708803} \)	\( \bigl[0\) , \( -1\) , \( 0\) , \( -7520 a + 5136\) , \( -119424 a + 241408\bigr] \)	${y}^2={x}^{3}-{x}^{2}+\left(-7520a+5136\right){x}-119424a+241408$
91875.2-c5	91875.2-c	$8$	$16$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	91875.2	\( 3 \cdot 5^{4} \cdot 7^{2} \)	\( 3 \cdot 5^{12} \cdot 7^{20} \)	$2.69463$	$(-2a+1), (-3a+1), (3a-2), (5)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	\( 2^{7} \)	$0.472574897$	$0.086207692$	3.010689818	\( -\frac{1866593950165482334}{99698791708803} a + \frac{793626053533786727}{99698791708803} \)	\( \bigl[a + 1\) , \( a\) , \( 1\) , \( 8025 a + 3724\) , \( 245000 a - 479525\bigr] \)	${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(8025a+3724\right){x}+245000a-479525$
112896.2-q5	112896.2-q	$8$	$16$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	112896.2	\( 2^{8} \cdot 3^{2} \cdot 7^{2} \)	\( 2^{24} \cdot 3^{7} \cdot 7^{20} \)	$2.83706$	$(-2a+1), (-3a+1), (3a-2), (2)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	\( 2^{9} \)	$1$	$0.062215043$	2.298871812	\( -\frac{1866593950165482334}{99698791708803} a + \frac{793626053533786727}{99698791708803} \)	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 22561 a - 15407\) , \( 1083023 a + 14880\bigr] \)	${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(22561a-15407\right){x}+1083023a+14880$
112896.2-y5	112896.2-y	$8$	$16$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	112896.2	\( 2^{8} \cdot 3^{2} \cdot 7^{2} \)	\( 2^{24} \cdot 3^{7} \cdot 7^{20} \)	$2.83706$	$(-2a+1), (-3a+1), (3a-2), (2)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$4$	\( 2^{5} \)	$1$	$0.062215043$	2.298871812	\( -\frac{1866593950165482334}{99698791708803} a + \frac{793626053533786727}{99698791708803} \)	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 22561 a - 15407\) , \( -1083023 a - 14880\bigr] \)	${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(22561a-15407\right){x}-1083023a-14880$

 

  *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.