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
40.2-a1
40.2-a
$1$
$1$
3.3.169.1
$3$
$[3, 0]$
40.2
\( 2^{3} \cdot 5 \)
\( - 2^{3} \cdot 5^{5} \)
$2.14829$
$(-a^2+a+2), (2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 1 \)
$1$
$14.96312317$
1.151009474
\( -\frac{284338841997}{6250} a^{2} + \frac{337965466269}{3125} a + \frac{103230411712}{3125} \)
\( \bigl[a^{2} - 3\) , \( -a^{2} + 2 a + 3\) , \( a^{2} - 3\) , \( -4 a^{2} + 9 a + 5\) , \( -4 a^{2} + 9 a + 4\bigr] \)
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{2}+2a+3\right){x}^{2}+\left(-4a^{2}+9a+5\right){x}-4a^{2}+9a+4$
40.2-b1
40.2-b
$2$
$3$
3.3.169.1
$3$
$[3, 0]$
40.2
\( 2^{3} \cdot 5 \)
\( - 2^{3} \cdot 5^{3} \)
$2.14829$
$(-a^2+a+2), (2)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.1
$1$
\( 3 \)
$1$
$48.74212197$
1.249797999
\( \frac{637969}{125} a^{2} - \frac{6852327}{250} a - \frac{11869721}{250} \)
\( \bigl[1\) , \( a^{2} - 2\) , \( 0\) , \( -3 a^{2} - 4 a\) , \( 3 a^{2} + 5 a + 1\bigr] \)
${y}^2+{x}{y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(-3a^{2}-4a\right){x}+3a^{2}+5a+1$
40.2-b2
40.2-b
$2$
$3$
3.3.169.1
$3$
$[3, 0]$
40.2
\( 2^{3} \cdot 5 \)
\( - 2^{9} \cdot 5 \)
$2.14829$
$(-a^2+a+2), (2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.2
$9$
\( 1 \)
$1$
$1.805263776$
1.249797999
\( \frac{406469232176341}{20} a^{2} - \frac{1035593670375963}{40} a - \frac{1484058408536867}{20} \)
\( \bigl[1\) , \( a^{2} - 2\) , \( 0\) , \( 7 a^{2} + 36 a + 5\) , \( 51 a^{2} + 145 a + 34\bigr] \)
${y}^2+{x}{y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(7a^{2}+36a+5\right){x}+51a^{2}+145a+34$
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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.