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
1800.2-a2	1800.2-a	$4$	$4$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	1800.2	$2^{3} \cdot 3^{2} \cdot 5^{2}$	$2^{8} \cdot 3^{4} \cdot 5^{4}$	$1.16409$	$(a+1), (-a-2), (2a+1), (3)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	$2^{5}$	$0.111452642$	$3.481586885$	1.552128233	$\frac{470596}{225}$	$\bigl[i + 1$ , $-i$ , $0$ , $4$ , $-2 i\bigr]$	${y}^2+\left(i+1\right){x}{y}={x}^{3}-i{x}^{2}+4{x}-2i$
16200.2-d2	16200.2-d	$4$	$4$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	16200.2	$2^{3} \cdot 3^{4} \cdot 5^{2}$	$2^{8} \cdot 3^{16} \cdot 5^{4}$	$2.01626$	$(a+1), (-a-2), (2a+1), (3)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	$2^{5}$	$0.748768142$	$1.160528961$	3.475868462	$\frac{470596}{225}$	$\bigl[i + 1$ , $i$ , $i + 1$ , $-i + 36$ , $-18 i\bigr]$	${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+i{x}^{2}+\left(-i+36\right){x}-18i$
18000.2-g2	18000.2-g	$4$	$4$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	18000.2	$2^{4} \cdot 3^{2} \cdot 5^{3}$	$2^{8} \cdot 3^{4} \cdot 5^{10}$	$2.07008$	$(a+1), (-a-2), (2a+1), (3)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2Cs	$1$	$2^{5}$	$0.561055090$	$1.557012989$	3.494280255	$\frac{470596}{225}$	$\bigl[i + 1$ , $1$ , $0$ , $-16 i - 12$ , $-22 i - 4\bigr]$	${y}^2+\left(i+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-16i-12\right){x}-22i-4$
18000.3-f2	18000.3-f	$4$	$4$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	18000.3	$2^{4} \cdot 3^{2} \cdot 5^{3}$	$2^{8} \cdot 3^{4} \cdot 5^{10}$	$2.07008$	$(a+1), (-a-2), (2a+1), (3)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2Cs	$1$	$2^{5}$	$0.561055090$	$1.557012989$	3.494280255	$\frac{470596}{225}$	$\bigl[i + 1$ , $-i + 1$ , $0$ , $16 i - 12$ , $22 i - 4\bigr]$	${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(16i-12\right){x}+22i-4$
45000.3-o2	45000.3-o	$4$	$4$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	45000.3	$2^{3} \cdot 3^{2} \cdot 5^{4}$	$2^{8} \cdot 3^{4} \cdot 5^{16}$	$2.60299$	$(a+1), (-a-2), (2a+1), (3)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	$2^{6}$	$1$	$0.696317377$	2.785269508	$\frac{470596}{225}$	$\bigl[i + 1$ , $-i$ , $i + 1$ , $-i + 102$ , $148 i\bigr]$	${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}-i{x}^{2}+\left(-i+102\right){x}+148i$
57600.2-bb2	57600.2-bb	$4$	$4$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	57600.2	$2^{8} \cdot 3^{2} \cdot 5^{2}$	$2^{20} \cdot 3^{4} \cdot 5^{4}$	$2.76869$	$(a+1), (-a-2), (2a+1), (3)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	$2^{5}$	$1$	$1.740793442$	3.481586885	$\frac{470596}{225}$	$\bigl[0$ , $i$ , $0$ , $16$ , $16 i\bigr]$	${y}^2={x}^{3}+i{x}^{2}+16{x}+16i$

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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.