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
\( -\frac{1682103188678259782838444650496}{37} a^{4} + \frac{4570890135767342003193598513152}{37} a^{3} + \frac{560624301911253507213468364800}{37} a^{2} - \frac{4327003532745719478147674701824}{37} a - \frac{979466879795506810202756071424}{37} \)
\( \bigl[0\) , \( -3 a^{4} + 4 a^{3} + 13 a^{2} - 11 a - 10\) , \( a^{2} - a - 2\) , \( 345 a^{4} - 549 a^{3} - 1365 a^{2} + 1487 a + 783\) , \( 3135 a^{4} - 5551 a^{3} - 12034 a^{2} + 14521 a + 5015\bigr] \)
${y}^2+\left(a^{2}-a-2\right){y}={x}^{3}+\left(-3a^{4}+4a^{3}+13a^{2}-11a-10\right){x}^{2}+\left(345a^{4}-549a^{3}-1365a^{2}+1487a+783\right){x}+3135a^{4}-5551a^{3}-12034a^{2}+14521a+5015$
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
\( -\frac{2507214671425536}{69343957} a^{4} + \frac{3099587870568448}{69343957} a^{3} + \frac{11795529019346944}{69343957} a^{2} - \frac{7777196659007488}{69343957} a - \frac{10702583291781120}{69343957} \)
\( \bigl[0\) , \( a^{4} - 2 a^{3} - 4 a^{2} + 7 a + 3\) , \( -a^{4} + a^{3} + 5 a^{2} - 3 a - 4\) , \( 49 a^{4} - 88 a^{3} - 178 a^{2} + 239 a + 64\) , \( 162 a^{4} - 287 a^{3} - 588 a^{2} + 779 a + 208\bigr] \)
${y}^2+\left(-a^{4}+a^{3}+5a^{2}-3a-4\right){y}={x}^{3}+\left(a^{4}-2a^{3}-4a^{2}+7a+3\right){x}^{2}+\left(49a^{4}-88a^{3}-178a^{2}+239a+64\right){x}+162a^{4}-287a^{3}-588a^{2}+779a+208$
37.1-b1
37.1-b
$2$
$3$
5.5.65657.1
$5$
$[5, 0]$
37.1
\( 37 \)
\( 37^{3} \)
$32.85483$
$(a^4-a^3-3a^2+3a+2)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B
$1$
\( 1 \)
$0.020206397$
$4207.941219$
1.65915913
\( -\frac{18254600376320}{50653} a^{4} + \frac{49539534499840}{50653} a^{3} + \frac{6263292940288}{50653} a^{2} - \frac{47056864038912}{50653} a - \frac{10663276101632}{50653} \)
\( \bigl[0\) , \( -a^{3} + 4 a + 2\) , \( -2 a^{4} + 3 a^{3} + 9 a^{2} - 8 a - 7\) , \( -20 a^{4} + 24 a^{3} + 92 a^{2} - 55 a - 81\) , \( 136 a^{4} - 170 a^{3} - 637 a^{2} + 426 a + 579\bigr] \)
${y}^2+\left(-2a^{4}+3a^{3}+9a^{2}-8a-7\right){y}={x}^{3}+\left(-a^{3}+4a+2\right){x}^{2}+\left(-20a^{4}+24a^{3}+92a^{2}-55a-81\right){x}+136a^{4}-170a^{3}-637a^{2}+426a+579$
37.1-b2
37.1-b
$2$
$3$
5.5.65657.1
$5$
$[5, 0]$
37.1
\( 37 \)
\( 37 \)
$32.85483$
$(a^4-a^3-3a^2+3a+2)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B
$1$
\( 1 \)
$0.006735465$
$12623.82365$
1.65915913
\( \frac{2371584}{37} a^{4} + \frac{970752}{37} a^{3} - \frac{10678272}{37} a^{2} - \frac{10203136}{37} a - \frac{1785856}{37} \)
\( \bigl[0\) , \( a^{4} - 2 a^{3} - 5 a^{2} + 6 a + 5\) , \( -a^{4} + 2 a^{3} + 5 a^{2} - 7 a - 4\) , \( 5 a^{4} - 8 a^{3} - 19 a^{2} + 22 a + 10\) , \( -5 a^{4} + 9 a^{3} + 17 a^{2} - 24 a - 6\bigr] \)
${y}^2+\left(-a^{4}+2a^{3}+5a^{2}-7a-4\right){y}={x}^{3}+\left(a^{4}-2a^{3}-5a^{2}+6a+5\right){x}^{2}+\left(5a^{4}-8a^{3}-19a^{2}+22a+10\right){x}-5a^{4}+9a^{3}+17a^{2}-24a-6$
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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.