Elliptic curve search results

Results (6 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
2600.4-a2	2600.4-a	$6$	$8$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	2600.4	$2^{3} \cdot 5^{2} \cdot 13$	$2^{8} \cdot 5^{9} \cdot 13$	$1.27618$	$(a+1), (-a-2), (2a+1), (2a+3)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{4}$	$1$	$1.598837415$	1.598837415	$\frac{329359844912}{5078125} a - \frac{470870678516}{5078125}$	$\bigl[i + 1$ , $-i - 1$ , $i + 1$ , $-24 i + 37$ , $75 i + 67\bigr]$	${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(-24i+37\right){x}+75i+67$
26000.4-d2	26000.4-d	$6$	$8$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	26000.4	$2^{4} \cdot 5^{3} \cdot 13$	$2^{8} \cdot 5^{15} \cdot 13$	$2.26940$	$(a+1), (-a-2), (2a+1), (2a+3)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{4}$	$0.568858194$	$0.715021829$	3.253968216	$\frac{329359844912}{5078125} a - \frac{470870678516}{5078125}$	$\bigl[i + 1$ , $i - 1$ , $i + 1$ , $-79 i - 204$ , $570 i + 1169\bigr]$	${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(i-1\right){x}^{2}+\left(-79i-204\right){x}+570i+1169$
26000.6-a2	26000.6-a	$6$	$8$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	26000.6	$2^{4} \cdot 5^{3} \cdot 13$	$2^{8} \cdot 5^{15} \cdot 13$	$2.26940$	$(a+1), (-a-2), (2a+1), (2a+3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{3}$	$1$	$0.715021829$	1.430043658	$\frac{329359844912}{5078125} a - \frac{470870678516}{5078125}$	$\bigl[i + 1$ , $0$ , $0$ , $217 i - 17$ , $-982 i - 803\bigr]$	${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(217i-17\right){x}-982i-803$
65000.6-f2	65000.6-f	$6$	$8$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	65000.6	$2^{3} \cdot 5^{4} \cdot 13$	$2^{8} \cdot 5^{21} \cdot 13$	$2.85362$	$(a+1), (-a-2), (2a+1), (2a+3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{5}$	$1$	$0.319767483$	2.558139865	$\frac{329359844912}{5078125} a - \frac{470870678516}{5078125}$	$\bigl[i + 1$ , $1$ , $0$ , $-583 i + 919$ , $9196 i + 10797\bigr]$	${y}^2+\left(i+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-583i+919\right){x}+9196i+10797$
67600.6-g2	67600.6-g	$6$	$8$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	67600.6	$2^{4} \cdot 5^{2} \cdot 13^{2}$	$2^{8} \cdot 5^{9} \cdot 13^{7}$	$2.88174$	$(a+1), (-a-2), (2a+1), (2a+3)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{4}$	$1.371256731$	$0.443437714$	4.864535603	$\frac{329359844912}{5078125} a - \frac{470870678516}{5078125}$	$\bigl[i + 1$ , $-1$ , $i + 1$ , $323 i + 464$ , $-3191 i + 3939\bigr]$	${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}-{x}^{2}+\left(323i+464\right){x}-3191i+3939$
83200.4-d2	83200.4-d	$6$	$8$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	83200.4	$2^{8} \cdot 5^{2} \cdot 13$	$2^{20} \cdot 5^{9} \cdot 13$	$3.03528$	$(a+1), (-a-2), (2a+1), (2a+3)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{3}$	$1.257124254$	$0.799418707$	4.019874589	$\frac{329359844912}{5078125} a - \frac{470870678516}{5078125}$	$\bigl[0$ , $i - 1$ , $0$ , $-94 i + 147$ , $-511 i - 683\bigr]$	${y}^2={x}^{3}+\left(i-1\right){x}^{2}+\left(-94i+147\right){x}-511i-683$

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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.