Elliptic curve search results

Results (12 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
63.1-a3	63.1-a	$8$	$16$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	63.1	\( 3^{2} \cdot 7 \)	\( 3^{8} \cdot 7^{4} \)	$0.66607$	$(-2a+1), (3)$	0	$\Z/2\Z\oplus\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2Cs	$1$	\( 2^{3} \)	$1$	$3.448307718$	0.325834452	\( \frac{7189057}{3969} \)	\( \bigl[1\) , \( 0\) , \( 0\) , \( -4\) , \( -1\bigr] \)	${y}^2+{x}{y}={x}^{3}-4{x}-1$
567.1-a3	567.1-a	$8$	$16$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	567.1	\( 3^{4} \cdot 7 \)	\( 3^{20} \cdot 7^{4} \)	$1.15367$	$(-2a+1), (3)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	\( 2^{3} \)	$2.638508823$	$1.149435906$	2.292578873	\( \frac{7189057}{3969} \)	\( \bigl[1\) , \( -1\) , \( 0\) , \( -36\) , \( 27\bigr] \)	${y}^2+{x}{y}={x}^{3}-{x}^{2}-36{x}+27$
4032.1-c3	4032.1-c	$8$	$16$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	4032.1	\( 2^{6} \cdot 3^{2} \cdot 7 \)	\( 2^{18} \cdot 3^{8} \cdot 7^{4} \)	$1.88394$	$(a), (-2a+1), (3)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2Cs	$1$	\( 2^{5} \)	$1$	$1.219160885$	1.843198006	\( \frac{7189057}{3969} \)	\( \bigl[a\) , \( 1\) , \( 0\) , \( -20 a - 8\) , \( -17 a + 6\bigr] \)	${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-20a-8\right){x}-17a+6$
4032.7-c3	4032.7-c	$8$	$16$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	4032.7	\( 2^{6} \cdot 3^{2} \cdot 7 \)	\( 2^{18} \cdot 3^{8} \cdot 7^{4} \)	$1.88394$	$(-a+1), (-2a+1), (3)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2Cs	$1$	\( 2^{5} \)	$1$	$1.219160885$	1.843198006	\( \frac{7189057}{3969} \)	\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 20 a - 28\) , \( 17 a - 11\bigr] \)	${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(20a-28\right){x}+17a-11$
7056.1-c3	7056.1-c	$8$	$16$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	7056.1	\( 2^{4} \cdot 3^{2} \cdot 7^{2} \)	\( 2^{12} \cdot 3^{8} \cdot 7^{10} \)	$2.16684$	$(a), (-2a+1), (3)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2Cs	$1$	\( 2^{6} \)	$1$	$0.651668904$	1.970461553	\( \frac{7189057}{3969} \)	\( \bigl[a\) , \( -a\) , \( 0\) , \( -84 a + 56\) , \( 63 a - 154\bigr] \)	${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(-84a+56\right){x}+63a-154$
7056.5-c3	7056.5-c	$8$	$16$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	7056.5	\( 2^{4} \cdot 3^{2} \cdot 7^{2} \)	\( 2^{12} \cdot 3^{8} \cdot 7^{10} \)	$2.16684$	$(-a+1), (-2a+1), (3)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2Cs	$1$	\( 2^{6} \)	$1$	$0.651668904$	1.970461553	\( \frac{7189057}{3969} \)	\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 84 a - 28\) , \( -63 a - 91\bigr] \)	${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(84a-28\right){x}-63a-91$
16128.5-i3	16128.5-i	$8$	$16$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	16128.5	\( 2^{8} \cdot 3^{2} \cdot 7 \)	\( 2^{24} \cdot 3^{8} \cdot 7^{4} \)	$2.66430$	$(a), (-a+1), (-2a+1), (3)$	$1$	$\Z/2\Z\oplus\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	\( 2^{8} \)	$0.746299208$	$0.862076929$	3.890719903	\( \frac{7189057}{3969} \)	\( \bigl[0\) , \( -1\) , \( 0\) , \( -64\) , \( 64\bigr] \)	${y}^2={x}^{3}-{x}^{2}-64{x}+64$
28224.1-d3	28224.1-d	$8$	$16$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	28224.1	\( 2^{6} \cdot 3^{2} \cdot 7^{2} \)	\( 2^{18} \cdot 3^{8} \cdot 7^{10} \)	$3.06438$	$(a), (-2a+1), (3)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2Cs	$1$	\( 2^{5} \)	$1.485887490$	$0.460799501$	2.070326753	\( \frac{7189057}{3969} \)	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 140 a + 56\) , \( 35 a - 434\bigr] \)	${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(140a+56\right){x}+35a-434$
28224.7-d3	28224.7-d	$8$	$16$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	28224.7	\( 2^{6} \cdot 3^{2} \cdot 7^{2} \)	\( 2^{18} \cdot 3^{8} \cdot 7^{10} \)	$3.06438$	$(-a+1), (-2a+1), (3)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2Cs	$1$	\( 2^{5} \)	$1.485887490$	$0.460799501$	2.070326753	\( \frac{7189057}{3969} \)	\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -140 a + 195\) , \( 21 a - 118\bigr] \)	${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(-140a+195\right){x}+21a-118$
36288.1-c3	36288.1-c	$8$	$16$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	36288.1	\( 2^{6} \cdot 3^{4} \cdot 7 \)	\( 2^{18} \cdot 3^{20} \cdot 7^{4} \)	$3.26308$	$(a), (-2a+1), (3)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2Cs	$1$	\( 2^{6} \)	$1$	$0.406386961$	1.228798671	\( \frac{7189057}{3969} \)	\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -180 a - 72\) , \( 459 a - 162\bigr] \)	${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-180a-72\right){x}+459a-162$
36288.7-c3	36288.7-c	$8$	$16$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	36288.7	\( 2^{6} \cdot 3^{4} \cdot 7 \)	\( 2^{18} \cdot 3^{20} \cdot 7^{4} \)	$3.26308$	$(-a+1), (-2a+1), (3)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2Cs	$1$	\( 2^{6} \)	$1$	$0.406386961$	1.228798671	\( \frac{7189057}{3969} \)	\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 180 a - 253\) , \( -279 a + 44\bigr] \)	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(180a-253\right){x}-279a+44$
39375.1-d3	39375.1-d	$8$	$16$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	39375.1	\( 3^{2} \cdot 5^{4} \cdot 7 \)	\( 3^{8} \cdot 5^{12} \cdot 7^{4} \)	$3.33037$	$(-2a+1), (3), (5)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	\( 2^{6} \)	$1.931482321$	$0.689661543$	8.055596601	\( \frac{7189057}{3969} \)	\( \bigl[1\) , \( 1\) , \( 0\) , \( -100\) , \( -125\bigr] \)	${y}^2+{x}{y}={x}^{3}+{x}^{2}-100{x}-125$

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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.