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-a2	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	\( \frac{1866593950165482334}{99698791708803} a - \frac{1072967896631695607}{99698791708803} \)	\( \bigl[1\) , \( 0\) , \( 0\) , \( 470 a - 149\) , \( -1866 a - 1906\bigr] \)	${y}^2+{x}{y}={x}^{3}+\left(470a-149\right){x}-1866a-1906$
3087.2-a2	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	\( \frac{1866593950165482334}{99698791708803} a - \frac{1072967896631695607}{99698791708803} \)	\( \bigl[1\) , \( a\) , \( 0\) , \( 654 a - 9045\) , \( -19194 a + 323526\bigr] \)	${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(654a-9045\right){x}-19194a+323526$
3087.3-a2	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	\( \frac{1866593950165482334}{99698791708803} a - \frac{1072967896631695607}{99698791708803} \)	\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -3474 a + 9939\) , \( 321486 a - 14754\bigr] \)	${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-3474a+9939\right){x}+321486a-14754$
7203.3-a2	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	\( \frac{1866593950165482334}{99698791708803} a - \frac{1072967896631695607}{99698791708803} \)	\( \bigl[1\) , \( 1\) , \( 1\) , \( 23030 a - 7302\) , \( 663068 a + 646456\bigr] \)	${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(23030a-7302\right){x}+663068a+646456$
24843.4-b1	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	$4$	\( 2^{4} \)	$1$	$0.119548560$	2.208684594	\( \frac{1866593950165482334}{99698791708803} a - \frac{1072967896631695607}{99698791708803} \)	\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -1525 a + 6007\) , \( -167514 a + 34774\bigr] \)	${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(-1525a+6007\right){x}-167514a+34774$
24843.6-b1	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	$1$	\( 2^{6} \)	$1$	$0.119548560$	2.208684594	\( \frac{1866593950165482334}{99698791708803} a - \frac{1072967896631695607}{99698791708803} \)	\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 4803 a + 1055\) , \( 36894 a - 168194\bigr] \)	${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(4803a+1055\right){x}+36894a-168194$
37632.2-f1	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	\( \frac{1866593950165482334}{99698791708803} a - \frac{1072967896631695607}{99698791708803} \)	\( \bigl[0\) , \( -1\) , \( 0\) , \( 7520 a - 2384\) , \( 119424 a + 121984\bigr] \)	${y}^2={x}^{3}-{x}^{2}+\left(7520a-2384\right){x}+119424a+121984$
91875.2-c1	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	\( \frac{1866593950165482334}{99698791708803} a - \frac{1072967896631695607}{99698791708803} \)	\( \bigl[a + 1\) , \( a\) , \( 1\) , \( -3725 a - 8026\) , \( -245000 a - 234525\bigr] \)	${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-3725a-8026\right){x}-245000a-234525$
112896.2-q1	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	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$4$	\( 2^{5} \)	$1$	$0.062215043$	2.298871812	\( \frac{1866593950165482334}{99698791708803} a - \frac{1072967896631695607}{99698791708803} \)	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -22559 a + 7153\) , \( 1105583 a - 1105056\bigr] \)	${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-22559a+7153\right){x}+1105583a-1105056$
112896.2-y1	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	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	\( 2^{9} \)	$1$	$0.062215043$	2.298871812	\( \frac{1866593950165482334}{99698791708803} a - \frac{1072967896631695607}{99698791708803} \)	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -22559 a + 7153\) , \( -1105583 a + 1105056\bigr] \)	${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-22559a+7153\right){x}-1105583a+1105056$

 

  *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.