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
14.3-b2	14.3-b	$4$	$4$	\(\Q(\sqrt{65}) \)	$2$	$[2, 0]$	14.3	\( 2 \cdot 7 \)	\( 2^{3} \cdot 7 \)	$1.39357$	$(2,a), (7,a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2$	2B	$4$	\( 1 \)	$1$	$5.253622939$	0.651631726	\( -\frac{4618208311865}{56} a + \frac{20925697887873}{56} \)	\( \bigl[1\) , \( -a\) , \( a + 1\) , \( 9584 a - 43423\) , \( 1037540 a - 4701238\bigr] \)	${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(9584a-43423\right){x}+1037540a-4701238$
14.3-c2	14.3-c	$4$	$4$	\(\Q(\sqrt{65}) \)	$2$	$[2, 0]$	14.3	\( 2 \cdot 7 \)	\( 2^{15} \cdot 7 \)	$1.39357$	$(2,a), (7,a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2$	2B	$4$	\( 3 \)	$1$	$5.253622939$	1.954895180	\( -\frac{4618208311865}{56} a + \frac{20925697887873}{56} \)	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 2110 a - 9536\) , \( 104711 a - 474436\bigr] \)	${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(2110a-9536\right){x}+104711a-474436$
112.9-d2	112.9-d	$4$	$4$	\(\Q(\sqrt{65}) \)	$2$	$[2, 0]$	112.9	\( 2^{4} \cdot 7 \)	\( 2^{27} \cdot 7 \)	$2.34369$	$(2,a), (7,a+1)$	$0 \le r \le 2$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2^{2} \)	$1$	$11.38106603$	1.411647505	\( -\frac{4618208311865}{56} a + \frac{20925697887873}{56} \)	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 119503 a - 541493\) , \( -44845568 a + 203201043\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(119503a-541493\right){x}-44845568a+203201043$
112.9-e2	112.9-e	$4$	$4$	\(\Q(\sqrt{65}) \)	$2$	$[2, 0]$	112.9	\( 2^{4} \cdot 7 \)	\( 2^{15} \cdot 7 \)	$2.34369$	$(2,a), (7,a+1)$	$1$	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2 \)	$6.188536872$	$11.38106603$	2.184008159	\( -\frac{4618208311865}{56} a + \frac{20925697887873}{56} \)	\( \bigl[a\) , \( -a\) , \( a\) , \( -5 a - 75\) , \( -48 a - 102\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-5a-75\right){x}-48a-102$

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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.