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
75.1-a6	75.1-a	$8$	$16$	\(\Q(\sqrt{-33}) \)	$2$	$[0, 1]$	75.1	\( 3 \cdot 5^{2} \)	\( 3^{28} \cdot 5^{4} \)	$3.02128$	$(3,a), (5)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2Cs	$4$	\( 2^{5} \)	$2.248976610$	$1.117850856$	7.002156534	\( \frac{272223782641}{164025} \)	\( \bigl[1\) , \( -1\) , \( 0\) , \( -1215\) , \( 16600\bigr] \)	${y}^2+{x}{y}={x}^3-{x}^2-1215{x}+16600$
75.1-b6	75.1-b	$8$	$16$	\(\Q(\sqrt{-33}) \)	$2$	$[0, 1]$	75.1	\( 3 \cdot 5^{2} \)	\( 3^{28} \cdot 5^{4} \)	$3.02128$	$(3,a), (5)$	$2$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2Cs	$4$	\( 2^{2} \)	$8.665669460$	$1.117850856$	6.745109504	\( \frac{272223782641}{164025} \)	\( \bigl[a\) , \( 0\) , \( a\) , \( -1176\) , \( -12967\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^3-1176{x}-12967$
75.1-c6	75.1-c	$8$	$16$	\(\Q(\sqrt{-33}) \)	$2$	$[0, 1]$	75.1	\( 3 \cdot 5^{2} \)	\( 3^{16} \cdot 5^{4} \)	$3.02128$	$(3,a), (5)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2Cs	$16$	\( 2^{2} \)	$1$	$1.117850856$	0.778371427	\( \frac{272223782641}{164025} \)	\( \bigl[1\) , \( 1\) , \( 1\) , \( -135\) , \( -660\bigr] \)	${y}^2+{x}{y}+{y}={x}^3+{x}^2-135{x}-660$
75.1-d6	75.1-d	$8$	$16$	\(\Q(\sqrt{-33}) \)	$2$	$[0, 1]$	75.1	\( 3 \cdot 5^{2} \)	\( 3^{16} \cdot 5^{4} \)	$3.02128$	$(3,a), (5)$	$1$	$\Z/2\Z\oplus\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2Cs	$4$	\( 2^{5} \)	$4.676439788$	$1.117850856$	3.640007112	\( \frac{272223782641}{164025} \)	\( \bigl[a\) , \( 1\) , \( a\) , \( -101\) , \( 924\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^3+{x}^2-101{x}+924$

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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.