Elliptic curves over 3.3.148.1 of conductor 361.2

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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
361.2-a1	361.2-a	$4$	$10$	3.3.148.1	$3$	$[3, 0]$	361.2	\( 19^{2} \)	\( - 19^{8} \)	$2.90082$	$(-a^2-a-1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 5$	2B, 5B.4.1	$1$	\( 2^{2} \)	$1$	$45.72881698$	3.758885601	\( \frac{19422176}{361} a^{2} - \frac{29688224}{361} a + \frac{7279536}{361} \)	\( \bigl[a^{2} - a - 2\) , \( a\) , \( a^{2} - 2\) , \( -a^{2} + 12 a - 21\) , \( -3 a^{2} - 29 a + 75\bigr] \)	${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+a{x}^{2}+\left(-a^{2}+12a-21\right){x}-3a^{2}-29a+75$
361.2-a2	361.2-a	$4$	$10$	3.3.148.1	$3$	$[3, 0]$	361.2	\( 19^{2} \)	\( - 19^{16} \)	$2.90082$	$(-a^2-a-1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 5$	2B, 5B.4.2	$25$	\( 2^{2} \)	$1$	$1.829152679$	3.758885601	\( \frac{34600248516351310880}{6131066257801} a^{2} + \frac{14707001073639931296}{6131066257801} a - \frac{7931450838072839760}{6131066257801} \)	\( \bigl[a^{2} - a - 2\) , \( 1\) , \( 1\) , \( -135415 a^{2} - 158416 a + 62393\) , \( 49915104 a^{2} + 58405091 a - 23001468\bigr] \)	${y}^2+\left(a^{2}-a-2\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(-135415a^{2}-158416a+62393\right){x}+49915104a^{2}+58405091a-23001468$
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	\( \frac{21475865428001583104}{2476099} a^{2} - \frac{53285799291084800000}{2476099} a + \frac{14499029076062806016}{2476099} \)	\( \bigl[0\) , \( a^{2} - 2\) , \( a^{2} - 2\) , \( -25887000022915 a^{2} - 30290028906100 a + 11929017660105\) , \( 153975054462382521802 a^{2} + 180164130503941360671 a - 70953418405815227560\bigr] \)	${y}^2+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(-25887000022915a^{2}-30290028906100a+11929017660105\right){x}+153975054462382521802a^{2}+180164130503941360671a-70953418405815227560$
361.2-a4	361.2-a	$4$	$10$	3.3.148.1	$3$	$[3, 0]$	361.2	\( 19^{2} \)	\( - 19^{7} \)	$2.90082$	$(-a^2-a-1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 5$	2B, 5B.4.1	$1$	\( 2^{2} \)	$1$	$45.72881698$	3.758885601	\( -\frac{2985984}{19} a^{2} + \frac{2048000}{19} a + \frac{9617408}{19} \)	\( \bigl[0\) , \( -a^{2} + 3\) , \( a^{2} - 2\) , \( -4352941 a^{2} - 5093316 a + 2005886\) , \( -189816234978 a^{2} - 222101411490 a + 87469433199\bigr] \)	${y}^2+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(-4352941a^{2}-5093316a+2005886\right){x}-189816234978a^{2}-222101411490a+87469433199$
361.2-b1	361.2-b	$1$	$1$	3.3.148.1	$3$	$[3, 0]$	361.2	\( 19^{2} \)	\( 19^{10} \)	$2.90082$	$(-a^2-a-1)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$				✓			$1$	\( 1 \)	$1$	$10.45463190$	0.859365449	\( 729 a^{2} + 985 a - 377 \)	\( \bigl[a^{2} - a - 1\) , \( -a^{2} + a + 3\) , \( a\) , \( -13 a^{2} - 14 a + 10\) , \( 35 a^{2} + 30 a - 33\bigr] \)	${y}^2+\left(a^{2}-a-1\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-13a^{2}-14a+10\right){x}+35a^{2}+30a-33$
361.2-c1	361.2-c	$4$	$6$	3.3.148.1	$3$	$[3, 0]$	361.2	\( 19^{2} \)	\( - 19^{8} \)	$2.90082$	$(-a^2-a-1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B	$1$	\( 2^{2} \)	$1$	$13.70838959$	1.126822683	\( \frac{309847904}{361} a^{2} + \frac{362105728}{361} a - \frac{142642480}{361} \)	\( \bigl[a^{2} - a - 2\) , \( a - 1\) , \( a^{2} - a - 1\) , \( -18379 a^{2} - 21505 a + 8468\) , \( -2505848 a^{2} - 2932058 a + 1154722\bigr] \)	${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{2}-a-1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-18379a^{2}-21505a+8468\right){x}-2505848a^{2}-2932058a+1154722$
361.2-c2	361.2-c	$4$	$6$	3.3.148.1	$3$	$[3, 0]$	361.2	\( 19^{2} \)	\( - 19^{12} \)	$2.90082$	$(-a^2-a-1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B	$9$	\( 2^{2} \)	$1$	$1.523154399$	1.126822683	\( \frac{15636831814539296}{47045881} a^{2} - \frac{38648046941482112}{47045881} a + \frac{10231591814174352}{47045881} \)	\( \bigl[a^{2} - a - 2\) , \( a - 1\) , \( a^{2} - a - 1\) , \( -44144 a^{2} - 51650 a + 20338\) , \( 5820525 a^{2} + 6810519 a - 2682165\bigr] \)	${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{2}-a-1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-44144a^{2}-51650a+20338\right){x}+5820525a^{2}+6810519a-2682165$
361.2-c3	361.2-c	$4$	$6$	3.3.148.1	$3$	$[3, 0]$	361.2	\( 19^{2} \)	\( - 19^{9} \)	$2.90082$	$(-a^2-a-1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B	$9$	\( 2 \)	$1$	$3.046308799$	1.126822683	\( -\frac{72241514230136832}{6859} a^{2} + \frac{49766614320668672}{6859} a + \frac{232207325676879872}{6859} \)	\( \bigl[0\) , \( -a^{2} + 2 a + 1\) , \( a\) , \( 54 a^{2} + 87 a - 439\) , \( 548 a^{2} + 456 a - 3568\bigr] \)	${y}^2+a{y}={x}^{3}+\left(-a^{2}+2a+1\right){x}^{2}+\left(54a^{2}+87a-439\right){x}+548a^{2}+456a-3568$
361.2-c4	361.2-c	$4$	$6$	3.3.148.1	$3$	$[3, 0]$	361.2	\( 19^{2} \)	\( - 19^{7} \)	$2.90082$	$(-a^2-a-1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B	$1$	\( 2 \)	$1$	$27.41677919$	1.126822683	\( -\frac{16384}{19} a^{2} - \frac{319488}{19} a + \frac{737280}{19} \)	\( \bigl[0\) , \( -a^{2} + 2 a + 1\) , \( a\) , \( -6 a^{2} + 17 a - 9\) , \( 35 a^{2} - 84 a + 16\bigr] \)	${y}^2+a{y}={x}^{3}+\left(-a^{2}+2a+1\right){x}^{2}+\left(-6a^{2}+17a-9\right){x}+35a^{2}-84a+16$
361.2-d1	361.2-d	$1$	$1$	3.3.148.1	$3$	$[3, 0]$	361.2	\( 19^{2} \)	\( 19^{4} \)	$2.90082$	$(-a^2-a-1)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$				✓			$1$	\( 1 \)	$0.313278206$	$34.12653973$	2.636409308	\( 729 a^{2} + 985 a - 377 \)	\( \bigl[a^{2} - a - 1\) , \( a^{2} - a - 1\) , \( a^{2} - 1\) , \( -a\) , \( -2 a^{2} + 3 a - 1\bigr] \)	${y}^2+\left(a^{2}-a-1\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{2}-a-1\right){x}^{2}-a{x}-2a^{2}+3a-1$

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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.