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-b3	19.1-b	$4$	$10$	3.3.148.1	$3$	$[3, 0]$	19.1	\( 19 \)	\( -19 \)	$1.77580$	$(-a^2-a-1)$	$1$	$\Z/10\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 5$	2B, 5B.1.1	$1$	\( 1 \)	$0.505936340$	$363.3791571$	0.453363221	\( -\frac{2985984}{19} a^{2} + \frac{2048000}{19} a + \frac{9617408}{19} \)	\( \bigl[0\) , \( -a\) , \( 1\) , \( -2423600 a^{2} - 2835822 a + 1116822\) , \( 78861696894 a^{2} + 92275005848 a - 36340347438\bigr] \)	${y}^2+{y}={x}^{3}-a{x}^{2}+\left(-2423600a^{2}-2835822a+1116822\right){x}+78861696894a^{2}+92275005848a-36340347438$
304.1-g3	304.1-g	$4$	$10$	3.3.148.1	$3$	$[3, 0]$	304.1	\( 2^{4} \cdot 19 \)	\( - 2^{12} \cdot 19 \)	$2.81891$	$(a^2-a-2), (-a^2-a-1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 5$	2B, 5B.4.1	$1$	\( 1 \)	$1$	$100.4691768$	2.064628865	\( -\frac{2985984}{19} a^{2} + \frac{2048000}{19} a + \frac{9617408}{19} \)	\( \bigl[0\) , \( -a\) , \( 0\) , \( -27907 a^{2} - 32654 a + 12860\) , \( -97420996 a^{2} - 113990991 a + 44892679\bigr] \)	${y}^2={x}^{3}-a{x}^{2}+\left(-27907a^{2}-32654a+12860\right){x}-97420996a^{2}-113990991a+44892679$
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	\( -\frac{2985984}{19} a^{2} + \frac{2048000}{19} a + \frac{9617408}{19} \)	\( \bigl[0\) , \( -a^{2} + 3\) , \( a^{2} - 2\) , \( -4352941 a^{2} - 5093316 a + 2005886\) , \( -189816234978 a^{2} - 222101411490 a + 87469433199\bigr] \)	${y}^2+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(-4352941a^{2}-5093316a+2005886\right){x}-189816234978a^{2}-222101411490a+87469433199$
475.2-a3	475.2-a	$4$	$10$	3.3.148.1	$3$	$[3, 0]$	475.2	\( 5^{2} \cdot 19 \)	\( - 5^{6} \cdot 19 \)	$3.03658$	$(a^2-a-1), (-a^2-a-1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 5$	2B, 5B.4.1	$1$	\( 2 \)	$1$	$78.16372189$	3.212509180	\( -\frac{2985984}{19} a^{2} + \frac{2048000}{19} a + \frac{9617408}{19} \)	\( \bigl[0\) , \( a^{2} - 2 a - 3\) , \( a^{2} - 2\) , \( -27039517 a^{2} - 31638572 a + 12460114\) , \( 2938778407350 a^{2} + 3438624901627 a - 1354221790452\bigr] \)	${y}^2+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{2}-2a-3\right){x}^{2}+\left(-27039517a^{2}-31638572a+12460114\right){x}+2938778407350a^{2}+3438624901627a-1354221790452$

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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.