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
81.1-a1
81.1-a
$4$
$15$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
81.1
\( 3^{4} \)
\( 3^{12} \)
$1.44364$
$(3)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3, 5$
3B.1.1 , 5B
$9$
\( 1 \)
$1$
$12.14895586$
2.256004467
\( -1407628760845 a - 3086342051803 \)
\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( -229 a - 503\) , \( 3200 a + 7022\bigr] \)
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-229a-503\right){x}+3200a+7022$
81.1-a2
81.1-a
$4$
$15$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
81.1
\( 3^{4} \)
\( 3^{12} \)
$1.44364$
$(3)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3, 5$
3B.1.2 , 5B
$1$
\( 1 \)
$1$
$12.14895586$
2.256004467
\( -3515 a - 7688 \)
\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( -4 a - 8\) , \( 5 a + 11\bigr] \)
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-4a-8\right){x}+5a+11$
81.1-a3
81.1-a
$4$
$15$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
81.1
\( 3^{4} \)
\( 3^{12} \)
$1.44364$
$(3)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3, 5$
3B.1.1 , 5B
$9$
\( 1 \)
$1$
$12.14895586$
2.256004467
\( 1407628760845 a - 4493970812648 \)
\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( 229 a - 725\) , \( -2972 a + 9498\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(229a-725\right){x}-2972a+9498$
81.1-a4
81.1-a
$4$
$15$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
81.1
\( 3^{4} \)
\( 3^{12} \)
$1.44364$
$(3)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3, 5$
3B.1.2 , 5B
$1$
\( 1 \)
$1$
$12.14895586$
2.256004467
\( 3515 a - 11203 \)
\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( 4 a - 5\) , \( -2 a + 12\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(4a-5\right){x}-2a+12$
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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.