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
43.1-a1
43.1-a
$2$
$7$
\(\Q(\zeta_{11})^+\)
$5$
$[5, 0]$
43.1
\( 43 \)
\( -43 \)
$15.74965$
$(-a^3-a^2+2a+3)$
0
$\Z/7\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$7$
7B.1.1
$1$
\( 1 \)
$1$
$5702.693977$
0.961830659
\( -\frac{166996603}{43} a^{4} - \frac{153441602}{43} a^{3} + \frac{373478096}{43} a^{2} + \frac{215672423}{43} a - \frac{87008899}{43} \)
\( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( -a^{3} + a^{2} + 2 a - 2\) , \( a^{2} - 2\) , \( -a^{4} + 3 a^{2} - 2 a - 1\) , \( a^{4} - 3 a^{2} - a\bigr] \)
${y}^2+\left(a^{3}+a^{2}-3a-1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+2a-2\right){x}^{2}+\left(-a^{4}+3a^{2}-2a-1\right){x}+a^{4}-3a^{2}-a$
43.1-a2
43.1-a
$2$
$7$
\(\Q(\zeta_{11})^+\)
$5$
$[5, 0]$
43.1
\( 43 \)
\( - 43^{7} \)
$15.74965$
$(-a^3-a^2+2a+3)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$7$
7B.1.3
$49$
\( 7 \)
$1$
$0.339304693$
0.961830659
\( \frac{318410900614494023095122767009}{271818611107} a^{4} + \frac{98618610535417258075069052493}{271818611107} a^{3} - \frac{1144480542817566448101585501712}{271818611107} a^{2} - \frac{543717833889392347185233669478}{271818611107} a + \frac{243113372524798476732529529704}{271818611107} \)
\( \bigl[a^{4} - 4 a^{2} + 3\) , \( -a^{4} + a^{3} + 3 a^{2} - 2 a - 1\) , \( a^{3} - 2 a\) , \( 294 a^{4} - 510 a^{3} - 733 a^{2} + 1419 a - 379\) , \( 4714 a^{4} - 8577 a^{3} - 11707 a^{2} + 23701 a - 5755\bigr] \)
${y}^2+\left(a^{4}-4a^{2}+3\right){x}{y}+\left(a^{3}-2a\right){y}={x}^{3}+\left(-a^{4}+a^{3}+3a^{2}-2a-1\right){x}^{2}+\left(294a^{4}-510a^{3}-733a^{2}+1419a-379\right){x}+4714a^{4}-8577a^{3}-11707a^{2}+23701a-5755$
43.1-b1
43.1-b
$2$
$5$
\(\Q(\zeta_{11})^+\)
$5$
$[5, 0]$
43.1
\( 43 \)
\( -43 \)
$15.74965$
$(-a^3-a^2+2a+3)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$5$
5B.1.2
$625$
\( 1 \)
$1$
$0.172110778$
0.889001954
\( -\frac{1952398804851696160384169}{43} a^{4} - \frac{1794012696727694534309545}{43} a^{3} + \frac{4366335020709066338090051}{43} a^{2} + \frac{2521849174288181955441002}{43} a - \frac{1017345331588181941808577}{43} \)
\( \bigl[a^{3} - 2 a\) , \( a^{4} + a^{3} - 4 a^{2} - 2 a + 2\) , \( a^{2} + a - 1\) , \( -273 a^{4} + 380 a^{3} + 846 a^{2} - 1091 a - 235\) , \( 2716 a^{4} - 6086 a^{3} - 5200 a^{2} + 16501 a - 8269\bigr] \)
${y}^2+\left(a^{3}-2a\right){x}{y}+\left(a^{2}+a-1\right){y}={x}^{3}+\left(a^{4}+a^{3}-4a^{2}-2a+2\right){x}^{2}+\left(-273a^{4}+380a^{3}+846a^{2}-1091a-235\right){x}+2716a^{4}-6086a^{3}-5200a^{2}+16501a-8269$
43.1-b2
43.1-b
$2$
$5$
\(\Q(\zeta_{11})^+\)
$5$
$[5, 0]$
43.1
\( 43 \)
\( - 43^{5} \)
$15.74965$
$(-a^3-a^2+2a+3)$
0
$\Z/5\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$5$
5B.1.1
$1$
\( 5 \)
$1$
$537.8461822$
0.889001954
\( \frac{1668625015062}{147008443} a^{4} - \frac{5087619914002}{147008443} a^{3} - \frac{4613121597415}{147008443} a^{2} + \frac{13348817253799}{147008443} a - \frac{3093462765934}{147008443} \)
\( \bigl[a^{4} + a^{3} - 3 a^{2} - 3 a + 1\) , \( -a^{4} - a^{3} + 4 a^{2} + 2 a - 2\) , \( a^{4} + a^{3} - 4 a^{2} - 3 a + 2\) , \( -a^{4} - 4 a^{3} + a^{2} + 7 a + 1\) , \( -5 a^{4} - 4 a^{3} + 12 a^{2} + 5 a - 4\bigr] \)
${y}^2+\left(a^{4}+a^{3}-3a^{2}-3a+1\right){x}{y}+\left(a^{4}+a^{3}-4a^{2}-3a+2\right){y}={x}^{3}+\left(-a^{4}-a^{3}+4a^{2}+2a-2\right){x}^{2}+\left(-a^{4}-4a^{3}+a^{2}+7a+1\right){x}-5a^{4}-4a^{3}+12a^{2}+5a-4$
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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.