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
8.1-a4	8.1-a	$6$	$8$	3.3.148.1	$3$	$[3, 0]$	8.1	\( 2^{3} \)	\( 2^{4} \)	$1.53739$	$(a^2-a-2)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$				✓	$2$	2Cs	$1$	\( 2 \)	$1$	$55.79706605$	0.573311322	\( -10821604 a^{2} + 6316064 a + 37257972 \)	\( \bigl[a + 1\) , \( a^{2} - 2 a - 1\) , \( a^{2} - a - 2\) , \( -83347907948 a^{2} - 97524260781 a + 38407643413\) , \( -13188165606368355 a^{2} - 15431294359397846 a + 6077253458627265\bigr] \)	${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(a^{2}-2a-1\right){x}^{2}+\left(-83347907948a^{2}-97524260781a+38407643413\right){x}-13188165606368355a^{2}-15431294359397846a+6077253458627265$
16.1-a2	16.1-a	$6$	$8$	3.3.148.1	$3$	$[3, 0]$	16.1	\( 2^{4} \)	\( 2^{4} \)	$1.72566$	$(a^2-a-2)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$				✓	$2$	2Cs	$1$	\( 1 \)	$1$	$158.7523358$	0.815585101	\( -10821604 a^{2} + 6316064 a + 37257972 \)	\( \bigl[a^{2} - a - 2\) , \( a^{2} - 2 a - 3\) , \( a^{2} - 1\) , \( -16 a^{2} - 19 a + 8\) , \( 49 a^{2} + 57 a - 23\bigr] \)	${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{2}-2a-3\right){x}^{2}+\left(-16a^{2}-19a+8\right){x}+49a^{2}+57a-23$
200.2-d4	200.2-d	$6$	$8$	3.3.148.1	$3$	$[3, 0]$	200.2	\( 2^{3} \cdot 5^{2} \)	\( 2^{4} \cdot 5^{6} \)	$2.62890$	$(a^2-a-2), (a^2-a-1)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$				✓	$2$	2Cs	$1$	\( 2^{3} \)	$0.093636490$	$168.1773413$	1.941659237	\( -10821604 a^{2} + 6316064 a + 37257972 \)	\( \bigl[a^{2} - a - 2\) , \( 0\) , \( 0\) , \( -10 a^{2} + 21 a - 6\) , \( 24 a^{2} - 62 a + 17\bigr] \)	${y}^2+\left(a^{2}-a-2\right){x}{y}={x}^{3}+\left(-10a^{2}+21a-6\right){x}+24a^{2}-62a+17$
256.1-b4	256.1-b	$6$	$8$	3.3.148.1	$3$	$[3, 0]$	256.1	\( 2^{8} \)	\( 2^{16} \)	$2.73932$	$(a^2-a-2)$	0	$\Z/2\Z\oplus\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$				✓	$2$	2Cs	$1$	\( 2^{2} \)	$1$	$220.5448617$	1.133042247	\( -10821604 a^{2} + 6316064 a + 37257972 \)	\( \bigl[a^{2} - 1\) , \( 0\) , \( 0\) , \( -5895730 a^{2} - 6898514 a + 2716818\) , \( 7839217703 a^{2} + 9172562700 a - 3612398746\bigr] \)	${y}^2+\left(a^{2}-1\right){x}{y}={x}^{3}+\left(-5895730a^{2}-6898514a+2716818\right){x}+7839217703a^{2}+9172562700a-3612398746$
256.1-e1	256.1-e	$6$	$8$	3.3.148.1	$3$	$[3, 0]$	256.1	\( 2^{8} \)	\( 2^{16} \)	$2.73932$	$(a^2-a-2)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$				✓	$2$	2Cs	$1$	\( 2^{2} \)	$1$	$77.51543401$	1.592932356	\( -10821604 a^{2} + 6316064 a + 37257972 \)	\( \bigl[a^{2} - 1\) , \( a^{2} - 2 a - 2\) , \( 0\) , \( -43275682 a^{2} - 50636292 a + 19941918\) , \( -156055514429 a^{2} - 182598448598 a + 71912117508\bigr] \)	${y}^2+\left(a^{2}-1\right){x}{y}={x}^{3}+\left(a^{2}-2a-2\right){x}^{2}+\left(-43275682a^{2}-50636292a+19941918\right){x}-156055514429a^{2}-182598448598a+71912117508$
400.2-a4	400.2-a	$6$	$8$	3.3.148.1	$3$	$[3, 0]$	400.2	\( 2^{4} \cdot 5^{2} \)	\( 2^{4} \cdot 5^{6} \)	$2.95084$	$(a^2-a-2), (a^2-a-1)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$				✓	$2$	2Cs	$1$	\( 2^{2} \)	$1$	$81.32192145$	1.671155191	\( -10821604 a^{2} + 6316064 a + 37257972 \)	\( \bigl[a + 1\) , \( -a^{2} + 2\) , \( 0\) , \( -8 a^{2} - 9 a + 2\) , \( 13 a^{2} + 16 a - 6\bigr] \)	${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}+\left(-8a^{2}-9a+2\right){x}+13a^{2}+16a-6$

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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.