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-a1
1.1-a
$4$
$15$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
1.1
\( 1 \)
\( 1 \)
$0.48121$
$\textsf{none}$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$3, 5$
3B.1.2 , 5B
$1$
\( 1 \)
$1$
$2.044974771$
0.379742281
\( -1407628760845 a - 3086342051803 \)
\( \bigl[a\) , \( a + 1\) , \( a\) , \( -23 a - 53\) , \( -169 a - 372\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-23a-53\right){x}-169a-372$
1.1-a2
1.1-a
$4$
$15$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
1.1
\( 1 \)
\( 1 \)
$0.48121$
$\textsf{none}$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$3, 5$
3B.1.1 , 5B
$1$
\( 1 \)
$1$
$18.40477294$
0.379742281
\( -3515 a - 7688 \)
\( \bigl[a\) , \( a + 1\) , \( a\) , \( 2 a + 2\) , \( a + 1\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(2a+2\right){x}+a+1$
1.1-a3
1.1-a
$4$
$15$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
1.1
\( 1 \)
\( 1 \)
$0.48121$
$\textsf{none}$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$3, 5$
3B.1.2 , 5B
$1$
\( 1 \)
$1$
$2.044974771$
0.379742281
\( 1407628760845 a - 4493970812648 \)
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( 27 a - 74\) , \( 92 a - 284\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(27a-74\right){x}+92a-284$
1.1-a4
1.1-a
$4$
$15$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
1.1
\( 1 \)
\( 1 \)
$0.48121$
$\textsf{none}$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$3, 5$
3B.1.1 , 5B
$1$
\( 1 \)
$1$
$18.40477294$
0.379742281
\( 3515 a - 11203 \)
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( 2 a + 6\) , \( 2 a + 4\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(2a+6\right){x}+2a+4$
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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.