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
6.1-a1
6.1-a
$4$
$4$
3.3.1101.1
$3$
$[3, 0]$
6.1
\( 2 \cdot 3 \)
\( 2 \cdot 3^{8} \)
$3.99691$
$(a-2), (-a+3)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$0.162784343$
$173.8695930$
1.279481083
\( \frac{29923}{162} a^{2} - \frac{19195}{54} a - \frac{63187}{162} \)
\( \bigl[a^{2} + 2 a - 7\) , \( a + 1\) , \( a\) , \( -12815463 a^{2} + 52787238 a - 49305624\) , \( -50792903895 a^{2} + 209217326538 a - 195418286610\bigr] \)
${y}^2+\left(a^{2}+2a-7\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-12815463a^{2}+52787238a-49305624\right){x}-50792903895a^{2}+209217326538a-195418286610$
6.1-a2
6.1-a
$4$
$4$
3.3.1101.1
$3$
$[3, 0]$
6.1
\( 2 \cdot 3 \)
\( - 2^{4} \cdot 3^{2} \)
$3.99691$
$(a-2), (-a+3)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \)
$0.162784343$
$86.93479650$
1.279481083
\( -\frac{12427210626707}{48} a^{2} - \frac{1787973677179}{16} a + \frac{104165760846863}{48} \)
\( \bigl[1\) , \( a^{2} - 8\) , \( a^{2} + a - 7\) , \( -5 a^{2} + 52 a - 105\) , \( -186 a^{2} + 572 a - 196\bigr] \)
${y}^2+{x}{y}+\left(a^{2}+a-7\right){y}={x}^{3}+\left(a^{2}-8\right){x}^{2}+\left(-5a^{2}+52a-105\right){x}-186a^{2}+572a-196$
6.1-a3
6.1-a
$4$
$4$
3.3.1101.1
$3$
$[3, 0]$
6.1
\( 2 \cdot 3 \)
\( 2 \cdot 3^{2} \)
$3.99691$
$(a-2), (-a+3)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$0.651137374$
$43.46739825$
1.279481083
\( \frac{1669232982931}{6} a^{2} - \frac{2268686450851}{2} a + \frac{6322552321817}{6} \)
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -801934 a^{2} + 3303175 a - 3085301\) , \( -1420574725 a^{2} + 5851385188 a - 5465453961\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-801934a^{2}+3303175a-3085301\right){x}-1420574725a^{2}+5851385188a-5465453961$
6.1-a4
6.1-a
$4$
$4$
3.3.1101.1
$3$
$[3, 0]$
6.1
\( 2 \cdot 3 \)
\( 2^{2} \cdot 3^{4} \)
$3.99691$
$(a-2), (-a+3)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2^{2} \)
$0.325568687$
$173.8695930$
1.279481083
\( -\frac{3386197}{36} a^{2} - \frac{5821025}{12} a + \frac{75756205}{36} \)
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -50124 a^{2} + 206470 a - 192851\) , \( -22179850 a^{2} + 91359400 a - 85333743\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-50124a^{2}+206470a-192851\right){x}-22179850a^{2}+91359400a-85333743$
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Pari/GP
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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.