Elliptic curve search results

Results (4 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
19.1-b4	19.1-b	$4$	$10$	3.3.148.1	$3$	$[3, 0]$	19.1	\( 19 \)	\( - 19^{5} \)	$1.77580$	$(-a^2-a-1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 5$	2B, 5B.1.2	$1$	\( 1 \)	$2.529681702$	$2.907033256$	0.453363221	\( \frac{21475865428001583104}{2476099} a^{2} - \frac{53285799291084800000}{2476099} a + \frac{14499029076062806016}{2476099} \)	\( \bigl[0\) , \( -a^{2} + 2 a + 3\) , \( 1\) , \( -14413186731445 a^{2} - 16864675023680 a + 6641756824108\) , \( -63968762883395881049 a^{2} - 74848985016046516967 a + 29477517729190614798\bigr] \)	${y}^2+{y}={x}^{3}+\left(-a^{2}+2a+3\right){x}^{2}+\left(-14413186731445a^{2}-16864675023680a+6641756824108\right){x}-63968762883395881049a^{2}-74848985016046516967a+29477517729190614798$
304.1-g4	304.1-g	$4$	$10$	3.3.148.1	$3$	$[3, 0]$	304.1	\( 2^{4} \cdot 19 \)	\( - 2^{12} \cdot 19^{5} \)	$2.81891$	$(a^2-a-2), (-a^2-a-1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 5$	2B, 5B.4.2	$1$	\( 5 \)	$1$	$20.09383536$	2.064628865	\( \frac{21475865428001583104}{2476099} a^{2} - \frac{53285799291084800000}{2476099} a + \frac{14499029076062806016}{2476099} \)	\( \bigl[0\) , \( -a^{2} + 2 a + 3\) , \( 0\) , \( -165965341312 a^{2} - 194193803116 a + 76478676008\) , \( 79041132025753191 a^{2} + 92484960470958028 a - 36423033143090658\bigr] \)	${y}^2={x}^{3}+\left(-a^{2}+2a+3\right){x}^{2}+\left(-165965341312a^{2}-194193803116a+76478676008\right){x}+79041132025753191a^{2}+92484960470958028a-36423033143090658$
361.2-a3	361.2-a	$4$	$10$	3.3.148.1	$3$	$[3, 0]$	361.2	\( 19^{2} \)	\( - 19^{11} \)	$2.90082$	$(-a^2-a-1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 5$	2B, 5B.4.2	$25$	\( 2^{2} \)	$1$	$1.829152679$	3.758885601	\( \frac{21475865428001583104}{2476099} a^{2} - \frac{53285799291084800000}{2476099} a + \frac{14499029076062806016}{2476099} \)	\( \bigl[0\) , \( a^{2} - 2\) , \( a^{2} - 2\) , \( -25887000022915 a^{2} - 30290028906100 a + 11929017660105\) , \( 153975054462382521802 a^{2} + 180164130503941360671 a - 70953418405815227560\bigr] \)	${y}^2+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(-25887000022915a^{2}-30290028906100a+11929017660105\right){x}+153975054462382521802a^{2}+180164130503941360671a-70953418405815227560$
475.2-a4	475.2-a	$4$	$10$	3.3.148.1	$3$	$[3, 0]$	475.2	\( 5^{2} \cdot 19 \)	\( - 5^{6} \cdot 19^{5} \)	$3.03658$	$(a^2-a-1), (-a^2-a-1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 5$	2B, 5B.4.2	$1$	\( 2 \cdot 5 \)	$1$	$15.63274437$	3.212509180	\( \frac{21475865428001583104}{2476099} a^{2} - \frac{53285799291084800000}{2476099} a + \frac{14499029076062806016}{2476099} \)	\( \bigl[0\) , \( a - 1\) , \( a^{2} - 2\) , \( -160804400212360 a^{2} - 188155055678488 a + 74100456918827\) , \( -2383827087438207587333 a^{2} - 2789283861464543203831 a + 1098494047186335627733\bigr] \)	${y}^2+\left(a^{2}-2\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-160804400212360a^{2}-188155055678488a+74100456918827\right){x}-2383827087438207587333a^{2}-2789283861464543203831a+1098494047186335627733$

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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.