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-a2
37.1-a
$2$
$5$
5.5.65657.1
$5$
$[5, 0]$
37.1
\( 37 \)
\( 37^{5} \)
$32.85483$
$(a^4-a^3-3a^2+3a+2)$
0
$\Z/5\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$5$
5B.1.1
$1$
\( 5 \)
$1$
$1612.704115$
1.25876359
\( -\frac{2507214671425536}{69343957} a^{4} + \frac{3099587870568448}{69343957} a^{3} + \frac{11795529019346944}{69343957} a^{2} - \frac{7777196659007488}{69343957} a - \frac{10702583291781120}{69343957} \)
\( \bigl[0\) , \( a^{4} - 2 a^{3} - 4 a^{2} + 7 a + 3\) , \( -a^{4} + a^{3} + 5 a^{2} - 3 a - 4\) , \( 49 a^{4} - 88 a^{3} - 178 a^{2} + 239 a + 64\) , \( 162 a^{4} - 287 a^{3} - 588 a^{2} + 779 a + 208\bigr] \)
${y}^2+\left(-a^{4}+a^{3}+5a^{2}-3a-4\right){y}={x}^{3}+\left(a^{4}-2a^{3}-4a^{2}+7a+3\right){x}^{2}+\left(49a^{4}-88a^{3}-178a^{2}+239a+64\right){x}+162a^{4}-287a^{3}-588a^{2}+779a+208$
333.1-f2
333.1-f
$2$
$5$
5.5.65657.1
$5$
$[5, 0]$
333.1
\( 3^{2} \cdot 37 \)
\( 3^{6} \cdot 37^{5} \)
$40.92828$
$(-a^4+a^3+4a^2-2a-2), (a^4-a^3-3a^2+3a+2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$5$
5B.4.1
$1$
\( 1 \)
$1$
$214.9661319$
0.838937339
\( -\frac{2507214671425536}{69343957} a^{4} + \frac{3099587870568448}{69343957} a^{3} + \frac{11795529019346944}{69343957} a^{2} - \frac{7777196659007488}{69343957} a - \frac{10702583291781120}{69343957} \)
\( \bigl[0\) , \( -3 a^{4} + 4 a^{3} + 13 a^{2} - 11 a - 9\) , \( a^{2} - 2\) , \( 63 a^{4} - 112 a^{3} - 234 a^{2} + 300 a + 91\) , \( 387 a^{4} - 692 a^{3} - 1407 a^{2} + 1876 a + 500\bigr] \)
${y}^2+\left(a^{2}-2\right){y}={x}^{3}+\left(-3a^{4}+4a^{3}+13a^{2}-11a-9\right){x}^{2}+\left(63a^{4}-112a^{3}-234a^{2}+300a+91\right){x}+387a^{4}-692a^{3}-1407a^{2}+1876a+500$
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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.