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
14.1-a1	14.1-a	$6$	$18$	\(\Q(\sqrt{7}) \)	$2$	$[2, 0]$	14.1	\( 2 \cdot 7 \)	\( 2^{36} \cdot 7^{2} \)	$0.91464$	$(a+3), (a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3B	$1$	\( 2^{2} \)	$1$	$7.027708105$	1.328111995	\( -\frac{548347731625}{1835008} \)	\( \bigl[a\) , \( 1\) , \( 0\) , \( -168\) , \( 704\bigr] \)	${y}^2+a{x}{y}={x}^{3}+{x}^{2}-168{x}+704$
14.1-b1	14.1-b	$6$	$18$	\(\Q(\sqrt{7}) \)	$2$	$[2, 0]$	14.1	\( 2 \cdot 7 \)	\( 2^{36} \cdot 7^{2} \)	$0.91464$	$(a+3), (a)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3B.1.2	$1$	\( 2^{2} \)	$3.507207167$	$0.436190660$	0.578214212	\( -\frac{548347731625}{1835008} \)	\( \bigl[1\) , \( 0\) , \( 1\) , \( -171\) , \( -874\bigr] \)	${y}^2+{x}{y}+{y}={x}^{3}-171{x}-874$
98.1-a1	98.1-a	$6$	$18$	\(\Q(\sqrt{7}) \)	$2$	$[2, 0]$	98.1	\( 2 \cdot 7^{2} \)	\( 2^{36} \cdot 7^{8} \)	$1.48773$	$(a+3), (a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 3$	2B, 3B	$1$	\( 2^{3} \cdot 3^{2} \)	$1$	$0.661753152$	2.251072633	\( -\frac{548347731625}{1835008} \)	\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( -57295 a - 151591\) , \( -12113116 a - 32048292\bigr] \)	${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-57295a-151591\right){x}-12113116a-32048292$
98.1-b1	98.1-b	$6$	$18$	\(\Q(\sqrt{7}) \)	$2$	$[2, 0]$	98.1	\( 2 \cdot 7^{2} \)	\( 2^{36} \cdot 7^{8} \)	$1.48773$	$(a+3), (a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 3$	2B, 3B	$1$	\( 2^{3} \cdot 3^{2} \)	$1$	$0.661753152$	2.251072633	\( -\frac{548347731625}{1835008} \)	\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( 57294 a - 151591\) , \( 12113115 a - 32048292\bigr] \)	${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(57294a-151591\right){x}+12113115a-32048292$

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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.