Elliptic curve search results

Results (14 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
200.2-a3	200.2-a	$10$	$16$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	200.2	$2^{3} \cdot 5^{2}$	$2^{8} \cdot 5^{8}$	$0.67209$	$(a+1), (-a-2), (2a+1)$	0	$\Z/4\Z\oplus\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	$2^{6}$	$1$	$2.996888981$	0.749222245	$\frac{237276}{625}$	$\bigl[i + 1$ , $i$ , $0$ , $-4$ , $-6 i\bigr]$	${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}-4{x}-6i$
2000.2-a3	2000.2-a	$10$	$16$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	2000.2	$2^{4} \cdot 5^{3}$	$2^{8} \cdot 5^{14}$	$1.19516$	$(a+1), (-a-2), (2a+1)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2Cs	$1$	$2^{4}$	$1$	$1.340249496$	1.340249496	$\frac{237276}{625}$	$\bigl[i + 1$ , $i$ , $i + 1$ , $12 i + 9$ , $51 i + 2\bigr]$	${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+i{x}^{2}+\left(12i+9\right){x}+51i+2$
2000.3-a3	2000.3-a	$10$	$16$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	2000.3	$2^{4} \cdot 5^{3}$	$2^{8} \cdot 5^{14}$	$1.19516$	$(a+1), (-a-2), (2a+1)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2Cs	$1$	$2^{4}$	$1$	$1.340249496$	1.340249496	$\frac{237276}{625}$	$\bigl[i + 1$ , $i$ , $i + 1$ , $-14 i + 9$ , $51 i - 2\bigr]$	${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+i{x}^{2}+\left(-14i+9\right){x}+51i-2$
5000.3-a3	5000.3-a	$10$	$16$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	5000.3	$2^{3} \cdot 5^{4}$	$2^{8} \cdot 5^{20}$	$1.50283$	$(a+1), (-a-2), (2a+1)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	$2^{5}$	$0.933393502$	$0.599377796$	2.237821363	$\frac{237276}{625}$	$\bigl[i + 1$ , $i$ , $0$ , $-82$ , $-572 i\bigr]$	${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}-82{x}-572i$
6400.2-a3	6400.2-a	$10$	$16$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	6400.2	$2^{8} \cdot 5^{2}$	$2^{20} \cdot 5^{8}$	$1.59850$	$(a+1), (-a-2), (2a+1)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	$2^{4}$	$0.722205338$	$1.498444490$	2.164369220	$\frac{237276}{625}$	$\bigl[0$ , $0$ , $0$ , $-13$ , $34 i\bigr]$	${y}^2={x}^{3}-13{x}+34i$
16200.2-a3	16200.2-a	$10$	$16$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	16200.2	$2^{3} \cdot 3^{4} \cdot 5^{2}$	$2^{8} \cdot 3^{12} \cdot 5^{8}$	$2.01626$	$(a+1), (-a-2), (2a+1), (3)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	$2^{5}$	$0.683761292$	$0.998962993$	2.732208912	$\frac{237276}{625}$	$\bigl[i + 1$ , $i$ , $0$ , $-30$ , $100 i\bigr]$	${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}-30{x}+100i$
25600.2-j3	25600.2-j	$10$	$16$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	25600.2	$2^{10} \cdot 5^{2}$	$2^{26} \cdot 5^{8}$	$2.26063$	$(a+1), (-a-2), (2a+1)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2Cs	$1$	$2^{5}$	$1$	$1.059560260$	2.119120521	$\frac{237276}{625}$	$\bigl[0$ , $0$ , $0$ , $-26 i$ , $68 i + 68\bigr]$	${y}^2={x}^{3}-26i{x}+68i+68$
25600.2-p3	25600.2-p	$10$	$16$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	25600.2	$2^{10} \cdot 5^{2}$	$2^{26} \cdot 5^{8}$	$2.26063$	$(a+1), (-a-2), (2a+1)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2Cs	$1$	$2^{5}$	$1$	$1.059560260$	2.119120521	$\frac{237276}{625}$	$\bigl[0$ , $0$ , $0$ , $26 i$ , $-68 i + 68\bigr]$	${y}^2={x}^{3}+26i{x}-68i+68$
32000.2-l3	32000.2-l	$10$	$16$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	32000.2	$2^{8} \cdot 5^{3}$	$2^{20} \cdot 5^{14}$	$2.39032$	$(a+1), (-a-2), (2a+1)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2Cs	$1$	$2^{6}$	$1$	$0.670124748$	2.680498993	$\frac{237276}{625}$	$\bigl[0$ , $0$ , $0$ , $52 i + 39$ , $374 i + 68\bigr]$	${y}^2={x}^{3}+\left(52i+39\right){x}+374i+68$
32000.3-l3	32000.3-l	$10$	$16$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	32000.3	$2^{8} \cdot 5^{3}$	$2^{20} \cdot 5^{14}$	$2.39032$	$(a+1), (-a-2), (2a+1)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2Cs	$1$	$2^{6}$	$1$	$0.670124748$	2.680498993	$\frac{237276}{625}$	$\bigl[0$ , $0$ , $0$ , $-52 i + 39$ , $-374 i + 68\bigr]$	${y}^2={x}^{3}+\left(-52i+39\right){x}-374i+68$
57800.4-e3	57800.4-e	$10$	$16$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	57800.4	$2^{3} \cdot 5^{2} \cdot 17^{2}$	$2^{8} \cdot 5^{8} \cdot 17^{6}$	$2.77109$	$(a+1), (-a-2), (2a+1), (a+4)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2Cs	$1$	$2^{6}$	$1$	$0.726852342$	2.907409369	$\frac{237276}{625}$	$\bigl[i + 1$ , $i$ , $0$ , $26 i + 48$ , $224 i + 208\bigr]$	${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(26i+48\right){x}+224i+208$
57800.6-d3	57800.6-d	$10$	$16$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	57800.6	$2^{3} \cdot 5^{2} \cdot 17^{2}$	$2^{8} \cdot 5^{8} \cdot 17^{6}$	$2.77109$	$(a+1), (-a-2), (2a+1), (a-4)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2Cs	$1$	$2^{6}$	$1$	$0.726852342$	2.907409369	$\frac{237276}{625}$	$\bigl[i + 1$ , $i$ , $0$ , $-26 i + 48$ , $224 i - 208\bigr]$	${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(-26i+48\right){x}+224i-208$
67600.4-d3	67600.4-d	$10$	$16$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	67600.4	$2^{4} \cdot 5^{2} \cdot 13^{2}$	$2^{8} \cdot 5^{8} \cdot 13^{6}$	$2.88174$	$(a+1), (-a-2), (2a+1), (-3a-2)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2Cs	$1$	$2^{6}$	$0.564622956$	$0.831187453$	3.754460134	$\frac{237276}{625}$	$\bigl[i + 1$ , $i$ , $0$ , $39 i - 17$ , $30 i - 215\bigr]$	${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(39i-17\right){x}+30i-215$
67600.6-f3	67600.6-f	$10$	$16$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	67600.6	$2^{4} \cdot 5^{2} \cdot 13^{2}$	$2^{8} \cdot 5^{8} \cdot 13^{6}$	$2.88174$	$(a+1), (-a-2), (2a+1), (2a+3)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2Cs	$1$	$2^{6}$	$0.564622956$	$0.831187453$	3.754460134	$\frac{237276}{625}$	$\bigl[i + 1$ , $i$ , $i + 1$ , $-40 i - 17$ , $-47 i - 176\bigr]$	${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+i{x}^{2}+\left(-40i-17\right){x}-47i-176$

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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.