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
5.2-a1	5.2-a	$6$	$8$	4.4.10025.1	$4$	$[4, 0]$	5.2	\( 5 \)	\( -5 \)	$10.94087$	$(a^3+2a^2-7a-9)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2$	2B	$4$	\( 1 \)	$1$	$181.2063861$	1.809803020	\( -\frac{91618345092}{5} a^{3} - \frac{128114688219}{5} a^{2} + 140045058222 a + 152848630727 \)	\( \bigl[\frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{5}{2} a - 8\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 4\) , \( a^{3} + 2 a^{2} - 7 a - 11\) , \( \frac{31}{2} a^{3} + \frac{51}{2} a^{2} - \frac{221}{2} a - 130\) , \( \frac{175}{2} a^{3} + \frac{281}{2} a^{2} - \frac{1191}{2} a - 678\bigr] \)	${y}^2+\left(\frac{1}{2}a^{3}+\frac{3}{2}a^{2}-\frac{5}{2}a-8\right){x}{y}+\left(a^{3}+2a^{2}-7a-11\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-4\right){x}^{2}+\left(\frac{31}{2}a^{3}+\frac{51}{2}a^{2}-\frac{221}{2}a-130\right){x}+\frac{175}{2}a^{3}+\frac{281}{2}a^{2}-\frac{1191}{2}a-678$
25.3-a4	25.3-a	$6$	$8$	4.4.10025.1	$4$	$[4, 0]$	25.3	\( 5^{2} \)	\( - 5^{7} \)	$13.37899$	$(a^3+2a^2-7a-9)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2^{2} \)	$1$	$214.4069067$	2.141393995	\( -\frac{91618345092}{5} a^{3} - \frac{128114688219}{5} a^{2} + 140045058222 a + 152848630727 \)	\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{7}{2} a - 3\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + \frac{9}{2} a + 3\) , \( a^{3} + 2 a^{2} - 7 a - 10\) , \( \frac{113}{2} a^{3} + \frac{183}{2} a^{2} - \frac{749}{2} a - 424\) , \( -\frac{3325}{2} a^{3} - \frac{5507}{2} a^{2} + \frac{21921}{2} a + 12505\bigr] \)	${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{7}{2}a-3\right){x}{y}+\left(a^{3}+2a^{2}-7a-10\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}-\frac{1}{2}a^{2}+\frac{9}{2}a+3\right){x}^{2}+\left(\frac{113}{2}a^{3}+\frac{183}{2}a^{2}-\frac{749}{2}a-424\right){x}-\frac{3325}{2}a^{3}-\frac{5507}{2}a^{2}+\frac{21921}{2}a+12505$
125.1-g1	125.1-g	$6$	$8$	4.4.10025.1	$4$	$[4, 0]$	125.1	\( 5^{3} \)	\( - 5^{7} \)	$16.36042$	$(-a^3-a^2+8a+5), (a^3+2a^2-7a-9)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$4$	\( 2 \)	$0.439097257$	$77.92257012$	2.733831787	\( -\frac{91618345092}{5} a^{3} - \frac{128114688219}{5} a^{2} + 140045058222 a + 152848630727 \)	\( \bigl[\frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{7}{2} a - 8\) , \( -\frac{1}{2} a^{3} - \frac{3}{2} a^{2} + \frac{9}{2} a + 7\) , \( 1\) , \( 161 a^{3} + 229 a^{2} - 1230 a - 1368\) , \( 1878 a^{3} + 2624 a^{2} - 14354 a - 15628\bigr] \)	${y}^2+\left(\frac{1}{2}a^{3}+\frac{3}{2}a^{2}-\frac{7}{2}a-8\right){x}{y}+{y}={x}^{3}+\left(-\frac{1}{2}a^{3}-\frac{3}{2}a^{2}+\frac{9}{2}a+7\right){x}^{2}+\left(161a^{3}+229a^{2}-1230a-1368\right){x}+1878a^{3}+2624a^{2}-14354a-15628$

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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.