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
43.3-a1
43.3-a
$2$
$7$
\(\Q(\zeta_{11})^+\)
$5$
$[5, 0]$
43.3
\( 43 \)
\( - 43^{7} \)
$15.74965$
$(a^3+a^2-4a-2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$7$
7B.1.3
$49$
\( 7 \)
$1$
$0.339304693$
0.961830659
\( -\frac{346480612818557831035095564492}{271818611107} a^{4} + \frac{247862002283140572960026511999}{271818611107} a^{3} + \frac{1456471349605584774275478512978}{271818611107} a^{2} - \frac{14532257307132343958115316054}{6321363049} a - \frac{1217303334006333416200315022669}{271818611107} \)
\( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( a^{4} - 5 a^{2} + a + 4\) , \( a^{3} + a^{2} - 3 a - 1\) , \( 201 a^{4} - 446 a^{3} - 237 a^{2} + 764 a - 199\) , \( -340 a^{4} + 1924 a^{3} - 3845 a^{2} + 2952 a - 615\bigr] \)
${y}^2+\left(a^{3}+a^{2}-3a-1\right){x}{y}+\left(a^{3}+a^{2}-3a-1\right){y}={x}^{3}+\left(a^{4}-5a^{2}+a+4\right){x}^{2}+\left(201a^{4}-446a^{3}-237a^{2}+764a-199\right){x}-340a^{4}+1924a^{3}-3845a^{2}+2952a-615$
43.3-a2
43.3-a
$2$
$7$
\(\Q(\zeta_{11})^+\)
$5$
$[5, 0]$
43.3
\( 43 \)
\( -43 \)
$15.74965$
$(a^3+a^2-4a-2)$
0
$\Z/7\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$7$
7B.1.1
$1$
\( 1 \)
$1$
$5702.693977$
0.961830659
\( -\frac{91210781}{43} a^{4} + \frac{244652383}{43} a^{3} - \frac{46805862}{43} a^{2} - 4530150 a + \frac{54191702}{43} \)
\( \bigl[a^{3} + a^{2} - 2 a - 2\) , \( a^{4} + a^{3} - 5 a^{2} - 4 a + 5\) , \( a^{4} + a^{3} - 3 a^{2} - 2 a + 1\) , \( -a^{4} + 8\) , \( a^{4} + a^{3} - 5 a^{2} - 4 a + 4\bigr] \)
${y}^2+\left(a^{3}+a^{2}-2a-2\right){x}{y}+\left(a^{4}+a^{3}-3a^{2}-2a+1\right){y}={x}^{3}+\left(a^{4}+a^{3}-5a^{2}-4a+5\right){x}^{2}+\left(-a^{4}+8\right){x}+a^{4}+a^{3}-5a^{2}-4a+4$
43.3-b1
43.3-b
$2$
$5$
\(\Q(\zeta_{11})^+\)
$5$
$[5, 0]$
43.3
\( 43 \)
\( - 43^{5} \)
$15.74965$
$(a^3+a^2-4a-2)$
0
$\Z/5\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$5$
5B.1.1
$1$
\( 5 \)
$1$
$537.8461822$
0.889001954
\( \frac{3173577425795}{147008443} a^{4} + \frac{1914042488207}{147008443} a^{3} - \frac{12939727176325}{147008443} a^{2} - \frac{136964266029}{3418801} a + \frac{2615991439281}{147008443} \)
\( \bigl[a^{4} - 3 a^{2} + a + 1\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( a^{3} - 2 a\) , \( 7 a^{3} - 2 a^{2} - 10 a + 2\) , \( 3 a^{4} + 7 a^{3} - 12 a^{2} - 6 a + 4\bigr] \)
${y}^2+\left(a^{4}-3a^{2}+a+1\right){x}{y}+\left(a^{3}-2a\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-2\right){x}^{2}+\left(7a^{3}-2a^{2}-10a+2\right){x}+3a^{4}+7a^{3}-12a^{2}-6a+4$
43.3-b2
43.3-b
$2$
$5$
\(\Q(\zeta_{11})^+\)
$5$
$[5, 0]$
43.3
\( 43 \)
\( -43 \)
$15.74965$
$(a^3+a^2-4a-2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$5$
5B.1.2
$625$
\( 1 \)
$1$
$0.172110778$
0.889001954
\( -\frac{1066176219167207113178088}{43} a^{4} + \frac{2860188915894901647487633}{43} a^{3} - \frac{547882844077769355159450}{43} a^{2} - 52956224025397325384387 a + \frac{633565967983653513966306}{43} \)
\( \bigl[a^{4} - 4 a^{2} + a + 3\) , \( a^{4} - 5 a^{2} + 3\) , \( a^{4} - 4 a^{2} + 2\) , \( -21 a^{4} - 275 a^{3} + 41 a^{2} + 674 a - 204\) , \( -200 a^{4} - 2874 a^{3} + 60 a^{2} + 6329 a - 1829\bigr] \)
${y}^2+\left(a^{4}-4a^{2}+a+3\right){x}{y}+\left(a^{4}-4a^{2}+2\right){y}={x}^{3}+\left(a^{4}-5a^{2}+3\right){x}^{2}+\left(-21a^{4}-275a^{3}+41a^{2}+674a-204\right){x}-200a^{4}-2874a^{3}+60a^{2}+6329a-1829$
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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.