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
1.1-a1
1.1-a
$4$
$39$
6.6.434581.1
$6$
$[6, 0]$
1.1
\( 1 \)
\( 1 \)
$58.90795$
$\textsf{none}$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3, 13$
3B , 13B.1.2
$28561$
\( 1 \)
$1$
$0.014802157$
0.641303
\( 14273264587780952609125805373809022 a^{5} - 33978664183724880412077066535252082 a^{4} - 44161420314998729136586656312921749 a^{3} + 88173325697661842578861191186611639 a^{2} + 23535955393860563533538162020788064 a - 37503869415369575938251635322944654 \)
\( \bigl[3 a^{5} - 7 a^{4} - 8 a^{3} + 15 a^{2} + a - 3\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 2 a + 2\) , \( 2 a^{5} - 5 a^{4} - 5 a^{3} + 12 a^{2} - 3\) , \( -2015 a^{5} + 2317 a^{4} + 10491 a^{3} - 2078 a^{2} - 11628 a - 4340\) , \( -87669 a^{5} + 112368 a^{4} + 435832 a^{3} - 134018 a^{2} - 464939 a - 144427\bigr] \)
${y}^2+\left(3a^{5}-7a^{4}-8a^{3}+15a^{2}+a-3\right){x}{y}+\left(2a^{5}-5a^{4}-5a^{3}+12a^{2}-3\right){y}={x}^{3}+\left(a^{4}-2a^{3}-3a^{2}+2a+2\right){x}^{2}+\left(-2015a^{5}+2317a^{4}+10491a^{3}-2078a^{2}-11628a-4340\right){x}-87669a^{5}+112368a^{4}+435832a^{3}-134018a^{2}-464939a-144427$
169.4-b1
169.4-b
$4$
$39$
6.6.434581.1
$6$
$[6, 0]$
169.4
\( 13^{2} \)
\( 13^{6} \)
$90.32982$
$(-a^2+a+2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3, 13$
3B , 13B.12.2
$169$
\( 1 \)
$1$
$6.191483410$
1.58725
\( 14273264587780952609125805373809022 a^{5} - 33978664183724880412077066535252082 a^{4} - 44161420314998729136586656312921749 a^{3} + 88173325697661842578861191186611639 a^{2} + 23535955393860563533538162020788064 a - 37503869415369575938251635322944654 \)
\( \bigl[2 a^{5} - 4 a^{4} - 7 a^{3} + 9 a^{2} + 4 a - 2\) , \( a^{5} - 3 a^{4} - 2 a^{3} + 7 a^{2} - 3\) , \( 3 a^{5} - 6 a^{4} - 10 a^{3} + 12 a^{2} + 4 a - 2\) , \( 1677 a^{5} - 5031 a^{4} - 3478 a^{3} + 10398 a^{2} + 2133 a - 4472\) , \( 69075 a^{5} - 153507 a^{4} - 126786 a^{3} + 297677 a^{2} + 54889 a - 110958\bigr] \)
${y}^2+\left(2a^{5}-4a^{4}-7a^{3}+9a^{2}+4a-2\right){x}{y}+\left(3a^{5}-6a^{4}-10a^{3}+12a^{2}+4a-2\right){y}={x}^{3}+\left(a^{5}-3a^{4}-2a^{3}+7a^{2}-3\right){x}^{2}+\left(1677a^{5}-5031a^{4}-3478a^{3}+10398a^{2}+2133a-4472\right){x}+69075a^{5}-153507a^{4}-126786a^{3}+297677a^{2}+54889a-110958$
169.5-b1
169.5-b
$4$
$39$
6.6.434581.1
$6$
$[6, 0]$
169.5
\( 13^{2} \)
\( 13^{6} \)
$90.32982$
$(-2a^5+5a^4+5a^3-11a^2-2a+2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3, 13$
3B , 13B.12.2
$169$
\( 1 \)
$1$
$6.191483410$
1.58725
\( 14273264587780952609125805373809022 a^{5} - 33978664183724880412077066535252082 a^{4} - 44161420314998729136586656312921749 a^{3} + 88173325697661842578861191186611639 a^{2} + 23535955393860563533538162020788064 a - 37503869415369575938251635322944654 \)
\( \bigl[3 a^{5} - 6 a^{4} - 10 a^{3} + 12 a^{2} + 4 a - 2\) , \( -2 a^{5} + 6 a^{4} + 3 a^{3} - 14 a^{2} + a + 5\) , \( 2 a^{5} - 4 a^{4} - 7 a^{3} + 9 a^{2} + 4 a - 2\) , \( -988 a^{5} + 363 a^{4} + 6458 a^{3} + 2268 a^{2} - 8360 a - 5598\) , \( -93198 a^{5} + 141197 a^{4} + 423237 a^{3} - 233591 a^{2} - 410935 a - 59295\bigr] \)
${y}^2+\left(3a^{5}-6a^{4}-10a^{3}+12a^{2}+4a-2\right){x}{y}+\left(2a^{5}-4a^{4}-7a^{3}+9a^{2}+4a-2\right){y}={x}^{3}+\left(-2a^{5}+6a^{4}+3a^{3}-14a^{2}+a+5\right){x}^{2}+\left(-988a^{5}+363a^{4}+6458a^{3}+2268a^{2}-8360a-5598\right){x}-93198a^{5}+141197a^{4}+423237a^{3}-233591a^{2}-410935a-59295$
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.