Elliptic curve search results

Results (10 matches)

 

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
12.1-a9	12.1-a	$12$	$36$	\(\Q(\sqrt{33}) \)	$2$	$[2, 0]$	12.1	\( 2^{2} \cdot 3 \)	\( 2^{20} \cdot 3^{2} \)	$0.95541$	$(-a-2), (-a+3), (-2a+7)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓		$2, 3$	2Cs, 3B.1.2	$9$	\( 2^{3} \)	$1$	$1.746262515$	1.367933784	\( -\frac{257094293735125}{786432} a + \frac{110018396673875}{98304} \)	\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -1060 a - 2519\) , \( -30451 a - 72245\bigr] \)	${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-1060a-2519\right){x}-30451a-72245$
12.1-b9	12.1-b	$12$	$36$	\(\Q(\sqrt{33}) \)	$2$	$[2, 0]$	12.1	\( 2^{2} \cdot 3 \)	\( 2^{20} \cdot 3^{2} \)	$0.95541$	$(-a-2), (-a+3), (-2a+7)$	0	$\Z/2\Z\oplus\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓		$2, 3$	2Cs, 3B.1.1	$1$	\( 2^{3} \cdot 3^{2} \)	$1$	$15.71636264$	1.367933784	\( -\frac{257094293735125}{786432} a + \frac{110018396673875}{98304} \)	\( \bigl[1\) , \( a + 1\) , \( 0\) , \( 1752 a - 5904\) , \( -68268 a + 230220\bigr] \)	${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(1752a-5904\right){x}-68268a+230220$
288.3-e9	288.3-e	$12$	$36$	\(\Q(\sqrt{33}) \)	$2$	$[2, 0]$	288.3	\( 2^{5} \cdot 3^{2} \)	\( 2^{32} \cdot 3^{8} \)	$2.11468$	$(-a-2), (-a+3), (-2a+7)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 3$	2Cs, 3B	$1$	\( 2^{5} \)	$1$	$4.536923101$	1.579553877	\( -\frac{257094293735125}{786432} a + \frac{110018396673875}{98304} \)	\( \bigl[a\) , \( -1\) , \( 0\) , \( 4613 a - 15712\) , \( -290843 a + 981464\bigr] \)	${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(4613a-15712\right){x}-290843a+981464$
288.3-l9	288.3-l	$12$	$36$	\(\Q(\sqrt{33}) \)	$2$	$[2, 0]$	288.3	\( 2^{5} \cdot 3^{2} \)	\( 2^{32} \cdot 3^{8} \)	$2.11468$	$(-a-2), (-a+3), (-2a+7)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 3$	2Cs, 3B	$1$	\( 2^{5} \cdot 3^{2} \)	$1.549036229$	$0.504102566$	4.893572364	\( -\frac{257094293735125}{786432} a + \frac{110018396673875}{98304} \)	\( \bigl[a\) , \( -1\) , \( a\) , \( -57700 a - 136896\) , \( -12821577 a - 30416408\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-57700a-136896\right){x}-12821577a-30416408$
288.4-e9	288.4-e	$12$	$36$	\(\Q(\sqrt{33}) \)	$2$	$[2, 0]$	288.4	\( 2^{5} \cdot 3^{2} \)	\( 2^{32} \cdot 3^{8} \)	$2.11468$	$(-a-2), (-a+3), (-2a+7)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 3$	2Cs, 3B	$9$	\( 2^{5} \)	$1$	$0.504102566$	1.579553877	\( -\frac{257094293735125}{786432} a + \frac{110018396673875}{98304} \)	\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -2768 a - 6824\) , \( -137692 a - 328404\bigr] \)	${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-2768a-6824\right){x}-137692a-328404$
288.4-l9	288.4-l	$12$	$36$	\(\Q(\sqrt{33}) \)	$2$	$[2, 0]$	288.4	\( 2^{5} \cdot 3^{2} \)	\( 2^{32} \cdot 3^{8} \)	$2.11468$	$(-a-2), (-a+3), (-2a+7)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 3$	2Cs, 3B	$1$	\( 2^{5} \)	$1.549036229$	$4.536923101$	4.893572364	\( -\frac{257094293735125}{786432} a + \frac{110018396673875}{98304} \)	\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 95183 a - 321001\) , \( -27033214 a + 91163605\bigr] \)	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(95183a-321001\right){x}-27033214a+91163605$
384.5-c9	384.5-c	$12$	$36$	\(\Q(\sqrt{33}) \)	$2$	$[2, 0]$	384.5	\( 2^{7} \cdot 3 \)	\( 2^{38} \cdot 3^{2} \)	$2.27237$	$(-a-2), (-a+3), (-2a+7)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 3$	2Cs, 3B	$1$	\( 2^{4} \cdot 3^{2} \)	$1$	$1.634325113$	2.560495363	\( -\frac{257094293735125}{786432} a + \frac{110018396673875}{98304} \)	\( \bigl[a\) , \( -a\) , \( a\) , \( 9849 a - 33252\) , \( 915099 a - 3085896\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(9849a-33252\right){x}+915099a-3085896$
384.5-r9	384.5-r	$12$	$36$	\(\Q(\sqrt{33}) \)	$2$	$[2, 0]$	384.5	\( 2^{7} \cdot 3 \)	\( 2^{38} \cdot 3^{2} \)	$2.27237$	$(-a-2), (-a+3), (-2a+7)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 3$	2Cs, 3B	$1$	\( 2^{4} \)	$3.112082318$	$2.099100015$	2.274349657	\( -\frac{257094293735125}{786432} a + \frac{110018396673875}{98304} \)	\( \bigl[a\) , \( a - 1\) , \( a\) , \( -12068 a - 28657\) , \( -1244785 a - 2952911\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-12068a-28657\right){x}-1244785a-2952911$
384.6-c9	384.6-c	$12$	$36$	\(\Q(\sqrt{33}) \)	$2$	$[2, 0]$	384.6	\( 2^{7} \cdot 3 \)	\( 2^{38} \cdot 3^{2} \)	$2.27237$	$(-a-2), (-a+3), (-2a+7)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 3$	2Cs, 3B	$9$	\( 2^{4} \)	$1$	$1.634325113$	2.560495363	\( -\frac{257094293735125}{786432} a + \frac{110018396673875}{98304} \)	\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -5966 a - 14208\) , \( 418520 a + 992703\bigr] \)	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-5966a-14208\right){x}+418520a+992703$
384.6-r9	384.6-r	$12$	$36$	\(\Q(\sqrt{33}) \)	$2$	$[2, 0]$	384.6	\( 2^{7} \cdot 3 \)	\( 2^{38} \cdot 3^{2} \)	$2.27237$	$(-a-2), (-a+3), (-2a+7)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 3$	2Cs, 3B	$1$	\( 2^{4} \)	$3.112082318$	$2.099100015$	2.274349657	\( -\frac{257094293735125}{786432} a + \frac{110018396673875}{98304} \)	\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 19916 a - 67166\) , \( -2605629 a + 8786860\bigr] \)	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(19916a-67166\right){x}-2605629a+8786860$

 

  *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.