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
2.1-b1
2.1-b
$2$
$3$
5.5.195829.1
$5$
$[5, 0]$
2.1
\( 2 \)
\( - 2^{24} \)
$42.38186$
$(a^4-2a^3-5a^2+7a+5)$
$1$
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.1
$1$
\( 2 \)
$0.311089713$
$2223.414605$
1.73670115
\( -\frac{140854061737}{16777216} a^{4} + \frac{521974831409}{16777216} a^{3} - \frac{86178293541}{8388608} a^{2} - \frac{34744410679}{1048576} a - \frac{76866520719}{16777216} \)
\( \bigl[a^{2} - a - 1\) , \( -a^{2} + a + 2\) , \( -a^{4} + 3 a^{3} + 4 a^{2} - 9 a - 4\) , \( 4 a^{4} - 10 a^{3} - 19 a^{2} + 32 a + 27\) , \( 13 a^{4} - 30 a^{3} - 60 a^{2} + 95 a + 78\bigr] \)
${y}^2+\left(a^{2}-a-1\right){x}{y}+\left(-a^{4}+3a^{3}+4a^{2}-9a-4\right){y}={x}^{3}+\left(-a^{2}+a+2\right){x}^{2}+\left(4a^{4}-10a^{3}-19a^{2}+32a+27\right){x}+13a^{4}-30a^{3}-60a^{2}+95a+78$
16.2-c1
16.2-c
$2$
$3$
5.5.195829.1
$5$
$[5, 0]$
16.2
\( 2^{4} \)
\( - 2^{36} \)
$52.17820$
$(a^4-2a^3-5a^2+7a+5)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3$
3B
$1$
\( 2 \)
$1$
$156.9037704$
0.709128390
\( -\frac{140854061737}{16777216} a^{4} + \frac{521974831409}{16777216} a^{3} - \frac{86178293541}{8388608} a^{2} - \frac{34744410679}{1048576} a - \frac{76866520719}{16777216} \)
\( \bigl[a^{3} - 4 a - 1\) , \( -a^{4} + 3 a^{3} + 2 a^{2} - 8 a - 2\) , \( a + 1\) , \( -69 a^{4} + 19 a^{3} + 347 a^{2} + 203 a + 25\) , \( 1840 a^{4} - 119 a^{3} - 9475 a^{2} - 7259 a - 968\bigr] \)
${y}^2+\left(a^{3}-4a-1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{4}+3a^{3}+2a^{2}-8a-2\right){x}^{2}+\left(-69a^{4}+19a^{3}+347a^{2}+203a+25\right){x}+1840a^{4}-119a^{3}-9475a^{2}-7259a-968$
64.2-e1
64.2-e
$2$
$3$
5.5.195829.1
$5$
$[5, 0]$
64.2
\( 2^{6} \)
\( - 2^{42} \)
$59.93701$
$(a^4-2a^3-5a^2+7a+5)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3$
3B
$1$
\( 2^{2} \)
$0.436481549$
$204.1355770$
4.02694857
\( -\frac{140854061737}{16777216} a^{4} + \frac{521974831409}{16777216} a^{3} - \frac{86178293541}{8388608} a^{2} - \frac{34744410679}{1048576} a - \frac{76866520719}{16777216} \)
\( \bigl[a^{4} - 2 a^{3} - 4 a^{2} + 6 a + 3\) , \( a^{4} - 3 a^{3} - 3 a^{2} + 10 a + 4\) , \( a^{3} - 4 a - 1\) , \( -7 a^{4} + 10 a^{3} + 28 a^{2} - 16 a\) , \( -21 a^{4} - 5 a^{3} + 112 a^{2} + 112 a + 17\bigr] \)
${y}^2+\left(a^{4}-2a^{3}-4a^{2}+6a+3\right){x}{y}+\left(a^{3}-4a-1\right){y}={x}^{3}+\left(a^{4}-3a^{3}-3a^{2}+10a+4\right){x}^{2}+\left(-7a^{4}+10a^{3}+28a^{2}-16a\right){x}-21a^{4}-5a^{3}+112a^{2}+112a+17$
64.2-f1
64.2-f
$2$
$3$
5.5.195829.1
$5$
$[5, 0]$
64.2
\( 2^{6} \)
\( - 2^{42} \)
$59.93701$
$(a^4-2a^3-5a^2+7a+5)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3$
3B
$1$
\( 2 \)
$1$
$436.1559843$
1.97121197
\( -\frac{140854061737}{16777216} a^{4} + \frac{521974831409}{16777216} a^{3} - \frac{86178293541}{8388608} a^{2} - \frac{34744410679}{1048576} a - \frac{76866520719}{16777216} \)
\( \bigl[a^{2} - a - 2\) , \( a^{3} - 3 a - 3\) , \( a^{3} - 3 a - 2\) , \( -29 a^{4} + 80 a^{3} + 92 a^{2} - 244 a - 43\) , \( 6 a^{4} - 14 a^{3} - 18 a^{2} + 41 a + 5\bigr] \)
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{3}-3a-2\right){y}={x}^{3}+\left(a^{3}-3a-3\right){x}^{2}+\left(-29a^{4}+80a^{3}+92a^{2}-244a-43\right){x}+6a^{4}-14a^{3}-18a^{2}+41a+5$
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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.