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
450.2-a7	450.2-a	$8$	$12$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	450.2	$2 \cdot 3^{2} \cdot 5^{2}$	$2^{2} \cdot 3^{6} \cdot 5^{8}$	$0.82314$	$(a+1), (-a-2), (2a+1), (3)$	0	$\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3B.1.1	$1$	$2^{3} \cdot 3$	$1$	$0.970717605$	0.647145070	$\frac{2656166199049}{33750}$	$\bigl[1$ , $0$ , $1$ , $-289$ , $1862\bigr]$	${y}^2+{x}{y}+{y}={x}^{3}-289{x}+1862$
4050.2-c7	4050.2-c	$8$	$12$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	4050.2	$2 \cdot 3^{4} \cdot 5^{2}$	$2^{2} \cdot 3^{18} \cdot 5^{8}$	$1.42571$	$(a+1), (-a-2), (2a+1), (3)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2, 3$	2B, 3B.1.2	$1$	$2^{7}$	$1$	$0.323572535$	2.588580280	$\frac{2656166199049}{33750}$	$\bigl[1$ , $-1$ , $1$ , $-2597$ , $-50281\bigr]$	${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-2597{x}-50281$
11250.3-g7	11250.3-g	$8$	$12$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	11250.3	$2 \cdot 3^{2} \cdot 5^{4}$	$2^{2} \cdot 3^{6} \cdot 5^{20}$	$1.84059$	$(a+1), (-a-2), (2a+1), (3)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2, 3$	2B, 3B	$1$	$2^{5} \cdot 3$	$0.448117683$	$0.194143521$	4.175958957	$\frac{2656166199049}{33750}$	$\bigl[i$ , $-1$ , $i$ , $-7212$ , $-232781\bigr]$	${y}^2+i{x}{y}+i{y}={x}^{3}-{x}^{2}-7212{x}-232781$
18000.2-f7	18000.2-f	$8$	$12$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	18000.2	$2^{4} \cdot 3^{2} \cdot 5^{3}$	$2^{14} \cdot 3^{6} \cdot 5^{14}$	$2.07008$	$(a+1), (-a-2), (2a+1), (3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 3$	2B, 3B	$1$	$2^{5}$	$1$	$0.217059055$	1.736472441	$\frac{2656166199049}{33750}$	$\bigl[i + 1$ , $1$ , $0$ , $-4616 i - 3462$ , $163878 i + 29796\bigr]$	${y}^2+\left(i+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-4616i-3462\right){x}+163878i+29796$
18000.3-g7	18000.3-g	$8$	$12$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	18000.3	$2^{4} \cdot 3^{2} \cdot 5^{3}$	$2^{14} \cdot 3^{6} \cdot 5^{14}$	$2.07008$	$(a+1), (-a-2), (2a+1), (3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 3$	2B, 3B	$1$	$2^{5}$	$1$	$0.217059055$	1.736472441	$\frac{2656166199049}{33750}$	$\bigl[i + 1$ , $-i + 1$ , $0$ , $4616 i - 3462$ , $-163878 i + 29796\bigr]$	${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(4616i-3462\right){x}-163878i+29796$
57600.2-ba7	57600.2-ba	$8$	$12$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	57600.2	$2^{8} \cdot 3^{2} \cdot 5^{2}$	$2^{26} \cdot 3^{6} \cdot 5^{8}$	$2.76869$	$(a+1), (-a-2), (2a+1), (3)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2, 3$	2B, 3B	$1$	$2^{6} \cdot 3$	$1$	$0.242679401$	2.912152815	$\frac{2656166199049}{33750}$	$\bigl[0$ , $i$ , $0$ , $4616$ , $-119184 i\bigr]$	${y}^2={x}^{3}+i{x}^{2}+4616{x}-119184i$

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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.