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
1.1-a4	1.1-a	$6$	$50$	\(\Q(\zeta_{20})^+\)	$4$	$[4, 0]$	1.1	\( 1 \)	\( 1 \)	$3.99626$	$\textsf{none}$	0	$\Z/2\Z$	$\textsf{potential}$	$-100$	$N(\mathrm{U}(1))$	✓		✓	✓	$5$	5B.1.4[2]	$25$	\( 1 \)	$1$	$2.420130817$	0.338223563	\( -19691491018752 a^{2} + 71244477160128 \)	\( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a - 1\) , \( a^{2} + a - 2\) , \( 140 a^{3} + 150 a^{2} - 541 a - 619\) , \( 1727 a^{3} + 1963 a^{2} - 6449 a - 7491\bigr] \)	${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(140a^{3}+150a^{2}-541a-619\right){x}+1727a^{3}+1963a^{2}-6449a-7491$
1.1-a5	1.1-a	$6$	$50$	\(\Q(\zeta_{20})^+\)	$4$	$[4, 0]$	1.1	\( 1 \)	\( 1 \)	$3.99626$	$\textsf{none}$	0	$\Z/10\Z$	$\textsf{potential}$	$-100$	$N(\mathrm{U}(1))$	✓		✓	✓	$5$	5B.1.1[2]	$1$	\( 1 \)	$1$	$1512.581761$	0.338223563	\( -19691491018752 a^{2} + 71244477160128 \)	\( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a - 1\) , \( a^{2} + a - 2\) , \( 140 a^{3} + 150 a^{2} - 541 a - 619\) , \( -1577 a^{3} - 1803 a^{2} + 5829 a + 6789\bigr] \)	${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(140a^{3}+150a^{2}-541a-619\right){x}-1577a^{3}-1803a^{2}+5829a+6789$
256.1-f3	256.1-f	$6$	$50$	\(\Q(\zeta_{20})^+\)	$4$	$[4, 0]$	256.1	\( 2^{8} \)	\( 2^{24} \)	$7.99252$	$(a^3-a^2-3a+2)$	0	$\Z/2\Z$	$\textsf{potential}$	$-100$	$N(\mathrm{U}(1))$	✓			✓	$5$	5B.4.1[2]	$25$	\( 1 \)	$1$	$15.12581761$	2.113897274	\( -19691491018752 a^{2} + 71244477160128 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( 398 a^{3} - 275 a^{2} - 878 a - 88\) , \( -2744 a^{3} + 10808 a^{2} - 168 a - 19880\bigr] \)	${y}^2={x}^{3}+\left(398a^{3}-275a^{2}-878a-88\right){x}-2744a^{3}+10808a^{2}-168a-19880$
256.1-f4	256.1-f	$6$	$50$	\(\Q(\zeta_{20})^+\)	$4$	$[4, 0]$	256.1	\( 2^{8} \)	\( 2^{24} \)	$7.99252$	$(a^3-a^2-3a+2)$	0	$\Z/2\Z$	$\textsf{potential}$	$-100$	$N(\mathrm{U}(1))$	✓			✓	$5$	5B.4.1[2]	$25$	\( 1 \)	$1$	$15.12581761$	2.113897274	\( -19691491018752 a^{2} + 71244477160128 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( 398 a^{3} - 275 a^{2} - 878 a - 88\) , \( 2744 a^{3} - 10808 a^{2} + 168 a + 19880\bigr] \)	${y}^2={x}^{3}+\left(398a^{3}-275a^{2}-878a-88\right){x}+2744a^{3}-10808a^{2}+168a+19880$

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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.