Elliptic curve search results

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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
64.1-a4	64.1-a	$6$	$8$	\(\Q(\zeta_{24})^+\)	$4$	$[4, 0]$	64.1	\( 2^{6} \)	\( 2^{12} \)	$7.21360$	$(a^3-4a+1)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$2$	2Cs	$1$	\( 2 \)	$1$	$483.3447190$	1.258710205	\( -241408 a^{2} + 902848 \)	\( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( a^{3} + a^{2} - 4 a - 3\) , \( a^{3} + a^{2} - 3 a - 1\) , \( -5 a^{3} + a^{2} + 17 a - 7\) , \( -5 a^{3} + 2 a^{2} + 17 a - 11\bigr] \)	${y}^2+\left(a^{3}+a^{2}-3a-1\right){x}{y}+\left(a^{3}+a^{2}-3a-1\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-3\right){x}^{2}+\left(-5a^{3}+a^{2}+17a-7\right){x}-5a^{3}+2a^{2}+17a-11$
64.1-c4	64.1-c	$6$	$8$	\(\Q(\zeta_{24})^+\)	$4$	$[4, 0]$	64.1	\( 2^{6} \)	\( 2^{12} \)	$7.21360$	$(a^3-4a+1)$	0	$\Z/2\Z\oplus\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$2$	2Cs	$1$	\( 2 \)	$1$	$1933.378876$	1.258710205	\( -241408 a^{2} + 902848 \)	\( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( -a^{3} + a^{2} + 5 a - 1\) , \( 0\) , \( -2 a^{3} + 5 a^{2} + 14 a - 6\) , \( 11 a^{3} - 3 a^{2} - 37 a + 19\bigr] \)	${y}^2+\left(a^{3}+a^{2}-3a-1\right){x}{y}={x}^{3}+\left(-a^{3}+a^{2}+5a-1\right){x}^{2}+\left(-2a^{3}+5a^{2}+14a-6\right){x}+11a^{3}-3a^{2}-37a+19$
256.1-b4	256.1-b	$6$	$8$	\(\Q(\zeta_{24})^+\)	$4$	$[4, 0]$	256.1	\( 2^{8} \)	\( 2^{12} \)	$8.57847$	$(a^3-4a+1)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$2$	2Cs	$1$	\( 1 \)	$1$	$966.6894380$	1.258710205	\( -241408 a^{2} + 902848 \)	\( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( -a^{3} + a^{2} + 4 a - 1\) , \( 0\) , \( -5 a^{3} + 5 a^{2} + 25 a - 12\) , \( 21 a^{3} - 9 a^{2} - 72 a + 37\bigr] \)	${y}^2+\left(a^{3}+a^{2}-3a-1\right){x}{y}={x}^{3}+\left(-a^{3}+a^{2}+4a-1\right){x}^{2}+\left(-5a^{3}+5a^{2}+25a-12\right){x}+21a^{3}-9a^{2}-72a+37$
256.1-d4	256.1-d	$6$	$8$	\(\Q(\zeta_{24})^+\)	$4$	$[4, 0]$	256.1	\( 2^{8} \)	\( 2^{12} \)	$8.57847$	$(a^3-4a+1)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$2$	2Cs	$1$	\( 1 \)	$1$	$966.6894380$	1.258710205	\( -241408 a^{2} + 902848 \)	\( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( a^{3} + a^{2} - 3 a - 1\) , \( a^{3} + a^{2} - 3 a - 1\) , \( 8 a^{3} + 5 a^{2} - 28 a - 15\) , \( -16 a^{3} - 9 a^{2} + 58 a + 30\bigr] \)	${y}^2+\left(a^{3}+a^{2}-3a-1\right){x}{y}+\left(a^{3}+a^{2}-3a-1\right){y}={x}^{3}+\left(a^{3}+a^{2}-3a-1\right){x}^{2}+\left(8a^{3}+5a^{2}-28a-15\right){x}-16a^{3}-9a^{2}+58a+30$

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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.