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
1.1-a2	1.1-a	$4$	$6$	4.4.2624.1	$4$	$[4, 0]$	1.1	\( 1 \)	\( 1 \)	$4.57742$	$\textsf{none}$	0	$\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓	✓	$2, 3$	2B, 3B.1.1	$1$	\( 1 \)	$1$	$869.9086354$	0.471725361	\( 8064 a^{3} + 9536 a^{2} - 7936 a - 3776 \)	\( \bigl[a^{3} - 2 a^{2} - 2 a + 1\) , \( a^{3} - 2 a^{2} - 3 a\) , \( a + 1\) , \( -a^{3} + a^{2} + 4 a + 1\) , \( -a - 1\bigr] \)	${y}^2+\left(a^{3}-2a^{2}-2a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{3}-2a^{2}-3a\right){x}^{2}+\left(-a^{3}+a^{2}+4a+1\right){x}-a-1$
49.3-a2	49.3-a	$4$	$6$	4.4.2624.1	$4$	$[4, 0]$	49.3	\( 7^{2} \)	\( 7^{6} \)	$7.44552$	$(-a^2+a+2)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$				✓	$2, 3$	2B, 3B	$1$	\( 2 \)	$0.038363631$	$937.6524294$	1.404460983	\( 8064 a^{3} + 9536 a^{2} - 7936 a - 3776 \)	\( \bigl[a^{2} - a - 1\) , \( a^{2} - 2 a - 2\) , \( a^{3} - 2 a^{2} - a + 2\) , \( -2 a^{2} + 3 a + 2\) , \( 2 a^{3} - 7 a^{2} + 2 a + 1\bigr] \)	${y}^2+\left(a^{2}-a-1\right){x}{y}+\left(a^{3}-2a^{2}-a+2\right){y}={x}^{3}+\left(a^{2}-2a-2\right){x}^{2}+\left(-2a^{2}+3a+2\right){x}+2a^{3}-7a^{2}+2a+1$
49.4-a4	49.4-a	$4$	$6$	4.4.2624.1	$4$	$[4, 0]$	49.4	\( 7^{2} \)	\( 7^{6} \)	$7.44552$	$(-a^3+3a^2+a-3)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$				✓	$2, 3$	2B, 3B	$1$	\( 2^{2} \)	$0.019181815$	$937.6524294$	1.404460983	\( 8064 a^{3} + 9536 a^{2} - 7936 a - 3776 \)	\( \bigl[a^{3} - 2 a^{2} - 2 a + 1\) , \( -a^{3} + 2 a^{2} + 3 a - 2\) , \( a^{2} - 2 a\) , \( -a^{3} + a^{2} + 3 a + 2\) , \( a^{3} - 2 a^{2} - 2 a - 1\bigr] \)	${y}^2+\left(a^{3}-2a^{2}-2a+1\right){x}{y}+\left(a^{2}-2a\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+3a-2\right){x}^{2}+\left(-a^{3}+a^{2}+3a+2\right){x}+a^{3}-2a^{2}-2a-1$
256.1-e1	256.1-e	$4$	$6$	4.4.2624.1	$4$	$[4, 0]$	256.1	\( 2^{8} \)	\( 2^{24} \)	$9.15483$	$(a^3-2a^2-2a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$				✓	$2, 3$	2B, 3B	$1$	\( 1 \)	$1$	$316.8820943$	1.546520898	\( 8064 a^{3} + 9536 a^{2} - 7936 a - 3776 \)	\( \bigl[0\) , \( -a^{3} + 2 a^{2} + 2 a - 2\) , \( 0\) , \( -a^{2} + 1\) , \( 2 a^{2} + a - 2\bigr] \)	${y}^2={x}^{3}+\left(-a^{3}+2a^{2}+2a-2\right){x}^{2}+\left(-a^{2}+1\right){x}+2a^{2}+a-2$
256.1-j4	256.1-j	$4$	$6$	4.4.2624.1	$4$	$[4, 0]$	256.1	\( 2^{8} \)	\( 2^{24} \)	$9.15483$	$(a^3-2a^2-2a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$				✓	$2, 3$	2B, 3B	$1$	\( 1 \)	$1$	$316.8820943$	1.546520898	\( 8064 a^{3} + 9536 a^{2} - 7936 a - 3776 \)	\( \bigl[0\) , \( a^{3} - 2 a^{2} - 2 a + 2\) , \( 0\) , \( -a^{2} + 1\) , \( -2 a^{2} - a + 2\bigr] \)	${y}^2={x}^{3}+\left(a^{3}-2a^{2}-2a+2\right){x}^{2}+\left(-a^{2}+1\right){x}-2a^{2}-a+2$
256.1-n4	256.1-n	$4$	$6$	4.4.2624.1	$4$	$[4, 0]$	256.1	\( 2^{8} \)	\( 2^{24} \)	$9.15483$	$(a^3-2a^2-2a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$				✓	$2, 3$	2B, 3B	$1$	\( 1 \)	$1$	$461.7232551$	2.253408053	\( 8064 a^{3} + 9536 a^{2} - 7936 a - 3776 \)	\( \bigl[0\) , \( a^{3} - 2 a^{2} - 3 a + 2\) , \( 0\) , \( -a^{2} + 2 a + 2\) , \( 2 a^{3} - 4 a^{2} - 5 a + 2\bigr] \)	${y}^2={x}^{3}+\left(a^{3}-2a^{2}-3a+2\right){x}^{2}+\left(-a^{2}+2a+2\right){x}+2a^{3}-4a^{2}-5a+2$
289.3-a4	289.3-a	$4$	$6$	4.4.2624.1	$4$	$[4, 0]$	289.3	\( 17^{2} \)	\( 17^{6} \)	$9.29464$	$(a^3-a^2-4a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$				✓	$2, 3$	2B, 3B	$1$	\( 2 \)	$1$	$307.4207872$	3.000691301	\( 8064 a^{3} + 9536 a^{2} - 7936 a - 3776 \)	\( \bigl[a^{3} - 2 a^{2} - 2 a + 1\) , \( -a^{3} + 2 a^{2} + 3 a\) , \( a^{2} - 2 a\) , \( -a^{3} + a^{2} + 5 a\) , \( 2 a^{3} - 7 a^{2} + 2 a + 4\bigr] \)	${y}^2+\left(a^{3}-2a^{2}-2a+1\right){x}{y}+\left(a^{2}-2a\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+3a\right){x}^{2}+\left(-a^{3}+a^{2}+5a\right){x}+2a^{3}-7a^{2}+2a+4$
289.4-a2	289.4-a	$4$	$6$	4.4.2624.1	$4$	$[4, 0]$	289.4	\( 17^{2} \)	\( 17^{6} \)	$9.29464$	$(-a^3+3a^2-3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$				✓	$2, 3$	2B, 3B	$1$	\( 2 \)	$1$	$307.4207872$	3.000691301	\( 8064 a^{3} + 9536 a^{2} - 7936 a - 3776 \)	\( \bigl[a^{2} - a - 1\) , \( a^{2} - 2 a - 1\) , \( a^{3} - a^{2} - 4 a + 1\) , \( -a^{3} + a^{2} + 2 a + 1\) , \( a^{3} - a^{2} - 5 a - 3\bigr] \)	${y}^2+\left(a^{2}-a-1\right){x}{y}+\left(a^{3}-a^{2}-4a+1\right){y}={x}^{3}+\left(a^{2}-2a-1\right){x}^{2}+\left(-a^{3}+a^{2}+2a+1\right){x}+a^{3}-a^{2}-5a-3$
625.2-a2	625.2-a	$4$	$6$	4.4.2624.1	$4$	$[4, 0]$	625.2	\( 5^{4} \)	\( 5^{12} \)	$10.23542$	$(a^3-a^2-5a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$				✓	$2, 3$	2B, 3B	$1$	\( 2 \)	$1$	$96.42847788$	0.941224884	\( 8064 a^{3} + 9536 a^{2} - 7936 a - 3776 \)	\( \bigl[a^{2} - a - 1\) , \( -a^{2} + 3 a\) , \( a + 1\) , \( -6 a^{3} + 9 a^{2} + 19 a + 5\) , \( 10 a^{3} - 12 a^{2} - 39 a - 14\bigr] \)	${y}^2+\left(a^{2}-a-1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+3a\right){x}^{2}+\left(-6a^{3}+9a^{2}+19a+5\right){x}+10a^{3}-12a^{2}-39a-14$
625.3-a4	625.3-a	$4$	$6$	4.4.2624.1	$4$	$[4, 0]$	625.3	\( 5^{4} \)	\( 5^{12} \)	$10.23542$	$(a^3-a^2-3a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$				✓	$2, 3$	2B, 3B	$1$	\( 2 \)	$1$	$96.42847788$	0.941224884	\( 8064 a^{3} + 9536 a^{2} - 7936 a - 3776 \)	\( \bigl[a^{3} - 2 a^{2} - 2 a + 1\) , \( a^{3} - a^{2} - 5 a\) , \( a^{3} - 2 a^{2} - a + 2\) , \( 4 a^{3} - 17 a^{2} + 10 a + 6\) , \( 18 a^{3} - 60 a^{2} + 17 a + 14\bigr] \)	${y}^2+\left(a^{3}-2a^{2}-2a+1\right){x}{y}+\left(a^{3}-2a^{2}-a+2\right){y}={x}^{3}+\left(a^{3}-a^{2}-5a\right){x}^{2}+\left(4a^{3}-17a^{2}+10a+6\right){x}+18a^{3}-60a^{2}+17a+14$

 

  *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.