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
650.3-a6	650.3-a	$8$	$12$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	650.3	\( 2 \cdot 5^{2} \cdot 13 \)	\( 2 \cdot 5^{10} \cdot 13^{12} \)	$0.90240$	$(a+1), (-a-2), (2a+1), (-3a-2)$	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	\( \frac{4240925829815707588031}{728065160077531250} a + \frac{3613304062782124177817}{728065160077531250} \)	\( \bigl[1\) , \( 0\) , \( i + 1\) , \( -977 i - 586\) , \( -13842 i + 979\bigr] \)	${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+\left(-977i-586\right){x}-13842i+979$
16250.5-a6	16250.5-a	$8$	$12$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	16250.5	\( 2 \cdot 5^{4} \cdot 13 \)	\( 2 \cdot 5^{22} \cdot 13^{12} \)	$2.01782$	$(a+1), (-a-2), (2a+1), (-3a-2)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B	$1$	\( 2^{4} \)	$5.896367111$	$0.048214154$	2.274306853	\( \frac{4240925829815707588031}{728065160077531250} a + \frac{3613304062782124177817}{728065160077531250} \)	\( \bigl[i\) , \( -1\) , \( i + 1\) , \( -24413 i - 14637\) , \( 1730187 i - 122375\bigr] \)	${y}^2+i{x}{y}+\left(i+1\right){y}={x}^{3}-{x}^{2}+\left(-24413i-14637\right){x}+1730187i-122375$
26000.3-f6	26000.3-f	$8$	$12$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	26000.3	\( 2^{4} \cdot 5^{3} \cdot 13 \)	\( 2^{13} \cdot 5^{16} \cdot 13^{12} \)	$2.26940$	$(a+1), (-a-2), (2a+1), (-3a-2)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B	$1$	\( 2^{6} \cdot 3 \)	$1$	$0.053905063$	2.587443063	\( \frac{4240925829815707588031}{728065160077531250} a + \frac{3613304062782124177817}{728065160077531250} \)	\( \bigl[i + 1\) , \( 1\) , \( 0\) , \( -21086 i + 8598\) , \( -135312 i + 1233716\bigr] \)	${y}^2+\left(i+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-21086i+8598\right){x}-135312i+1233716$
26000.5-f6	26000.5-f	$8$	$12$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	26000.5	\( 2^{4} \cdot 5^{3} \cdot 13 \)	\( 2^{13} \cdot 5^{16} \cdot 13^{12} \)	$2.26940$	$(a+1), (-a-2), (2a+1), (-3a-2)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B	$1$	\( 2^{5} \cdot 3 \)	$1$	$0.053905063$	1.293721531	\( \frac{4240925829815707588031}{728065160077531250} a + \frac{3613304062782124177817}{728065160077531250} \)	\( \bigl[i + 1\) , \( -i + 1\) , \( 0\) , \( -2350 i - 22650\) , \( -307616 i - 1202388\bigr] \)	${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(-2350i-22650\right){x}-307616i-1202388$
42250.4-i6	42250.4-i	$8$	$12$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	42250.4	\( 2 \cdot 5^{3} \cdot 13^{2} \)	\( 2 \cdot 5^{16} \cdot 13^{18} \)	$2.56227$	$(a+1), (-a-2), (2a+1), (-3a-2)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B	$1$	\( 2^{5} \cdot 3 \)	$4.448065099$	$0.029901149$	6.384108451	\( \frac{4240925829815707588031}{728065160077531250} a + \frac{3613304062782124177817}{728065160077531250} \)	\( \bigl[i\) , \( i\) , \( i\) , \( 52151 i + 52512\) , \( -2113463 i + 6889490\bigr] \)	${y}^2+i{x}{y}+i{y}={x}^{3}+i{x}^{2}+\left(52151i+52512\right){x}-2113463i+6889490$
42250.7-e6	42250.7-e	$8$	$12$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	42250.7	\( 2 \cdot 5^{3} \cdot 13^{2} \)	\( 2 \cdot 5^{16} \cdot 13^{18} \)	$2.56227$	$(a+1), (-a-2), (2a+1), (-3a-2)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B	$9$	\( 2^{5} \)	$1$	$0.029901149$	2.152882762	\( \frac{4240925829815707588031}{728065160077531250} a + \frac{3613304062782124177817}{728065160077531250} \)	\( \bigl[i\) , \( i - 1\) , \( 1\) , \( -65015 i + 35362\) , \( 481119 i + 7224437\bigr] \)	${y}^2+i{x}{y}+{y}={x}^{3}+\left(i-1\right){x}^{2}+\left(-65015i+35362\right){x}+481119i+7224437$
52650.3-a6	52650.3-a	$8$	$12$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	52650.3	\( 2 \cdot 3^{4} \cdot 5^{2} \cdot 13 \)	\( 2 \cdot 3^{12} \cdot 5^{10} \cdot 13^{12} \)	$2.70719$	$(a+1), (-a-2), (2a+1), (-3a-2), (3)$	$1$	$\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B.1.1	$1$	\( 2^{5} \cdot 3^{2} \)	$2.508001076$	$0.080356924$	3.224564057	\( \frac{4240925829815707588031}{728065160077531250} a + \frac{3613304062782124177817}{728065160077531250} \)	\( \bigl[i\) , \( 1\) , \( i + 1\) , \( -8789 i - 5269\) , \( -373721 i + 26433\bigr] \)	${y}^2+i{x}{y}+\left(i+1\right){y}={x}^{3}+{x}^{2}+\left(-8789i-5269\right){x}-373721i+26433$
67600.4-a6	67600.4-a	$8$	$12$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	67600.4	\( 2^{4} \cdot 5^{2} \cdot 13^{2} \)	\( 2^{13} \cdot 5^{10} \cdot 13^{18} \)	$2.88174$	$(a+1), (-a-2), (2a+1), (-3a-2)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B	$1$	\( 2^{6} \)	$3.178266469$	$0.033430501$	3.400033334	\( \frac{4240925829815707588031}{728065160077531250} a + \frac{3613304062782124177817}{728065160077531250} \)	\( \bigl[i + 1\) , \( i + 1\) , \( 0\) , \( -8574 i + 58582\) , \( 5164160 i + 636316\bigr] \)	${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(i+1\right){x}^{2}+\left(-8574i+58582\right){x}+5164160i+636316$
83200.3-e6	83200.3-e	$8$	$12$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	83200.3	\( 2^{8} \cdot 5^{2} \cdot 13 \)	\( 2^{25} \cdot 5^{10} \cdot 13^{12} \)	$3.03528$	$(a+1), (-a-2), (2a+1), (-3a-2)$	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.