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-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
\( -\frac{18254600376320}{50653} a^{4} + \frac{49539534499840}{50653} a^{3} + \frac{6263292940288}{50653} a^{2} - \frac{47056864038912}{50653} a - \frac{10663276101632}{50653} \)
\( \bigl[0\) , \( -a^{3} + 4 a + 2\) , \( -2 a^{4} + 3 a^{3} + 9 a^{2} - 8 a - 7\) , \( -20 a^{4} + 24 a^{3} + 92 a^{2} - 55 a - 81\) , \( 136 a^{4} - 170 a^{3} - 637 a^{2} + 426 a + 579\bigr] \)
${y}^2+\left(-2a^{4}+3a^{3}+9a^{2}-8a-7\right){y}={x}^{3}+\left(-a^{3}+4a+2\right){x}^{2}+\left(-20a^{4}+24a^{3}+92a^{2}-55a-81\right){x}+136a^{4}-170a^{3}-637a^{2}+426a+579$
333.1-d1
333.1-d
$2$
$3$
5.5.65657.1
$5$
$[5, 0]$
333.1
\( 3^{2} \cdot 37 \)
\( 3^{6} \cdot 37^{3} \)
$40.92828$
$(-a^4+a^3+4a^2-2a-2), (a^4-a^3-3a^2+3a+2)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3$
3B.1.2
$1$
\( 3 \)
$2.897981652$
$33.41740335$
5.66916469
\( -\frac{18254600376320}{50653} a^{4} + \frac{49539534499840}{50653} a^{3} + \frac{6263292940288}{50653} a^{2} - \frac{47056864038912}{50653} a - \frac{10663276101632}{50653} \)
\( \bigl[0\) , \( -a^{4} + 5 a^{2} - 4\) , \( -a^{4} + a^{3} + 5 a^{2} - 2 a - 3\) , \( -32 a^{4} + 40 a^{3} + 152 a^{2} - 99 a - 139\) , \( -296 a^{4} + 365 a^{3} + 1393 a^{2} - 917 a - 1264\bigr] \)
${y}^2+\left(-a^{4}+a^{3}+5a^{2}-2a-3\right){y}={x}^{3}+\left(-a^{4}+5a^{2}-4\right){x}^{2}+\left(-32a^{4}+40a^{3}+152a^{2}-99a-139\right){x}-296a^{4}+365a^{3}+1393a^{2}-917a-1264$
Download
displayed columns for
results
to
Text
Pari/GP
SageMath
Magma
Oscar
CSV
*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.