Elliptic curve search results

Results (9 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
650.4-a6	650.4-a	$8$	$12$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	650.4	\( 2 \cdot 5^{2} \cdot 13 \)	\( 2 \cdot 5^{10} \cdot 13^{12} \)	$0.90240$	$(a+1), (-a-2), (2a+1), (2a+3)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B.1.2	$1$	\( 2^{5} \cdot 3 \)	$1$	$0.241070774$	1.446424644	\( -\frac{4240925829815707588031}{728065160077531250} a + \frac{3613304062782124177817}{728065160077531250} \)	\( \bigl[1\) , \( 0\) , \( i + 1\) , \( 976 i - 586\) , \( 13841 i + 979\bigr] \)	${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+\left(976i-586\right){x}+13841i+979$
16250.6-a6	16250.6-a	$8$	$12$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	16250.6	\( 2 \cdot 5^{4} \cdot 13 \)	\( 2 \cdot 5^{22} \cdot 13^{12} \)	$2.01782$	$(a+1), (-a-2), (2a+1), (2a+3)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B	$1$	\( 2^{4} \)	$5.896367111$	$0.048214154$	2.274306853	\( -\frac{4240925829815707588031}{728065160077531250} a + \frac{3613304062782124177817}{728065160077531250} \)	\( \bigl[i\) , \( -1\) , \( i + 1\) , \( 24412 i - 14637\) , \( -1730188 i - 122375\bigr] \)	${y}^2+i{x}{y}+\left(i+1\right){y}={x}^{3}-{x}^{2}+\left(24412i-14637\right){x}-1730188i-122375$
26000.4-f6	26000.4-f	$8$	$12$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	26000.4	\( 2^{4} \cdot 5^{3} \cdot 13 \)	\( 2^{13} \cdot 5^{16} \cdot 13^{12} \)	$2.26940$	$(a+1), (-a-2), (2a+1), (2a+3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B	$1$	\( 2^{5} \cdot 3 \)	$1$	$0.053905063$	1.293721531	\( -\frac{4240925829815707588031}{728065160077531250} a + \frac{3613304062782124177817}{728065160077531250} \)	\( \bigl[i + 1\) , \( 1\) , \( 0\) , \( 2350 i - 22650\) , \( 307616 i - 1202388\bigr] \)	${y}^2+\left(i+1\right){x}{y}={x}^{3}+{x}^{2}+\left(2350i-22650\right){x}+307616i-1202388$
26000.6-f6	26000.6-f	$8$	$12$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	26000.6	\( 2^{4} \cdot 5^{3} \cdot 13 \)	\( 2^{13} \cdot 5^{16} \cdot 13^{12} \)	$2.26940$	$(a+1), (-a-2), (2a+1), (2a+3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B	$1$	\( 2^{6} \cdot 3 \)	$1$	$0.053905063$	2.587443063	\( -\frac{4240925829815707588031}{728065160077531250} a + \frac{3613304062782124177817}{728065160077531250} \)	\( \bigl[i + 1\) , \( -1\) , \( 0\) , \( 21086 i + 8598\) , \( -135312 i - 1233716\bigr] \)	${y}^2+\left(i+1\right){x}{y}={x}^{3}-{x}^{2}+\left(21086i+8598\right){x}-135312i-1233716$
42250.6-e6	42250.6-e	$8$	$12$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	42250.6	\( 2 \cdot 5^{3} \cdot 13^{2} \)	\( 2 \cdot 5^{16} \cdot 13^{18} \)	$2.56227$	$(a+1), (-a-2), (2a+1), (2a+3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B	$9$	\( 2^{5} \)	$1$	$0.029901149$	2.152882762	\( -\frac{4240925829815707588031}{728065160077531250} a + \frac{3613304062782124177817}{728065160077531250} \)	\( \bigl[i\) , \( -i - 1\) , \( 1\) , \( 65014 i + 35362\) , \( -481119 i + 7224437\bigr] \)	${y}^2+i{x}{y}+{y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(65014i+35362\right){x}-481119i+7224437$
42250.9-i6	42250.9-i	$8$	$12$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	42250.9	\( 2 \cdot 5^{3} \cdot 13^{2} \)	\( 2 \cdot 5^{16} \cdot 13^{18} \)	$2.56227$	$(a+1), (-a-2), (2a+1), (2a+3)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B	$1$	\( 2^{5} \cdot 3 \)	$4.448065099$	$0.029901149$	6.384108451	\( -\frac{4240925829815707588031}{728065160077531250} a + \frac{3613304062782124177817}{728065160077531250} \)	\( \bigl[i\) , \( -i\) , \( i\) , \( -52151 i + 52512\) , \( 2113463 i + 6889490\bigr] \)	${y}^2+i{x}{y}+i{y}={x}^{3}-i{x}^{2}+\left(-52151i+52512\right){x}+2113463i+6889490$
52650.4-a6	52650.4-a	$8$	$12$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	52650.4	\( 2 \cdot 3^{4} \cdot 5^{2} \cdot 13 \)	\( 2 \cdot 3^{12} \cdot 5^{10} \cdot 13^{12} \)	$2.70719$	$(a+1), (-a-2), (2a+1), (2a+3), (3)$	$1$	$\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B.1.1	$1$	\( 2^{5} \cdot 3^{2} \)	$2.508001076$	$0.080356924$	3.224564057	\( -\frac{4240925829815707588031}{728065160077531250} a + \frac{3613304062782124177817}{728065160077531250} \)	\( \bigl[1\) , \( -1\) , \( i + 1\) , \( 8788 i - 5270\) , \( -373721 i - 26433\bigr] \)	${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}-{x}^{2}+\left(8788i-5270\right){x}-373721i-26433$
67600.6-a6	67600.6-a	$8$	$12$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	67600.6	\( 2^{4} \cdot 5^{2} \cdot 13^{2} \)	\( 2^{13} \cdot 5^{10} \cdot 13^{18} \)	$2.88174$	$(a+1), (-a-2), (2a+1), (2a+3)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B	$1$	\( 2^{6} \)	$3.178266469$	$0.033430501$	3.400033334	\( -\frac{4240925829815707588031}{728065160077531250} a + \frac{3613304062782124177817}{728065160077531250} \)	\( \bigl[i + 1\) , \( i - 1\) , \( 0\) , \( 8574 i + 58582\) , \( 5164160 i - 636316\bigr] \)	${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(i-1\right){x}^{2}+\left(8574i+58582\right){x}+5164160i-636316$
83200.4-n6	83200.4-n	$8$	$12$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	83200.4	\( 2^{8} \cdot 5^{2} \cdot 13 \)	\( 2^{25} \cdot 5^{10} \cdot 13^{12} \)	$3.03528$	$(a+1), (-a-2), (2a+1), (2a+3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B	$1$	\( 2^{5} \cdot 3 \)	$1$	$0.060267693$	1.446424644	\( -\frac{4240925829815707588031}{728065160077531250} a + \frac{3613304062782124177817}{728065160077531250} \)	\( \bigl[0\) , \( -i\) , \( 0\) , \( -15624 i + 9368\) , \( 62656 i - 885856\bigr] \)	${y}^2={x}^{3}-i{x}^{2}+\left(-15624i+9368\right){x}+62656i-885856$

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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.