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
37.1-a1
37.1-a
$2$
$5$
5.5.65657.1
$5$
$[5, 0]$
37.1
\( 37 \)
\( 37 \)
$32.85483$
$(a^4-a^3-3a^2+3a+2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$5$
5B.1.2
$625$
\( 1 \)
$1$
$0.516065317$
1.25876359
\( -\frac{1682103188678259782838444650496}{37} a^{4} + \frac{4570890135767342003193598513152}{37} a^{3} + \frac{560624301911253507213468364800}{37} a^{2} - \frac{4327003532745719478147674701824}{37} a - \frac{979466879795506810202756071424}{37} \)
\( \bigl[0\) , \( -3 a^{4} + 4 a^{3} + 13 a^{2} - 11 a - 10\) , \( a^{2} - a - 2\) , \( 345 a^{4} - 549 a^{3} - 1365 a^{2} + 1487 a + 783\) , \( 3135 a^{4} - 5551 a^{3} - 12034 a^{2} + 14521 a + 5015\bigr] \)
${y}^2+\left(a^{2}-a-2\right){y}={x}^{3}+\left(-3a^{4}+4a^{3}+13a^{2}-11a-10\right){x}^{2}+\left(345a^{4}-549a^{3}-1365a^{2}+1487a+783\right){x}+3135a^{4}-5551a^{3}-12034a^{2}+14521a+5015$
333.1-f1
333.1-f
$2$
$5$
5.5.65657.1
$5$
$[5, 0]$
333.1
\( 3^{2} \cdot 37 \)
\( 3^{6} \cdot 37 \)
$40.92828$
$(-a^4+a^3+4a^2-2a-2), (a^4-a^3-3a^2+3a+2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$5$
5B.4.2
$25$
\( 1 \)
$1$
$8.598645279$
0.838937339
\( -\frac{1682103188678259782838444650496}{37} a^{4} + \frac{4570890135767342003193598513152}{37} a^{3} + \frac{560624301911253507213468364800}{37} a^{2} - \frac{4327003532745719478147674701824}{37} a - \frac{979466879795506810202756071424}{37} \)
\( \bigl[0\) , \( -a^{4} + 2 a^{3} + 5 a^{2} - 7 a - 5\) , \( a^{4} - a^{3} - 4 a^{2} + 3 a + 2\) , \( 479 a^{4} - 732 a^{3} - 1900 a^{2} + 2017 a + 1192\) , \( 3876 a^{4} - 3092 a^{3} - 11081 a^{2} + 8266 a - 2500\bigr] \)
${y}^2+\left(a^{4}-a^{3}-4a^{2}+3a+2\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+5a^{2}-7a-5\right){x}^{2}+\left(479a^{4}-732a^{3}-1900a^{2}+2017a+1192\right){x}+3876a^{4}-3092a^{3}-11081a^{2}+8266a-2500$
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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.