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
43.2-a1
43.2-a
$2$
$7$
\(\Q(\zeta_{11})^+\)
$5$
$[5, 0]$
43.2
\( 43 \)
\( -43 \)
$15.74965$
$(-a^4+2a^2+a+1)$
0
$\Z/7\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$7$
7B.1.1
$1$
\( 1 \)
$1$
$5702.693977$
0.961830659
\( \frac{411648986}{43} a^{4} + \frac{127511713}{43} a^{3} - 34409287 a^{2} - \frac{702973344}{43} a + \frac{314269044}{43} \)
\( \bigl[a^{3} + a^{2} - 2 a - 1\) , \( -a^{4} + a^{3} + 3 a^{2} - 2 a - 1\) , \( a^{4} - 4 a^{2} + 3\) , \( 2 a^{4} + 2 a^{3} - 5 a^{2} - 3 a + 2\) , \( 2 a^{4} + 3 a^{3} - 5 a^{2} - 4 a + 1\bigr] \)
${y}^2+\left(a^{3}+a^{2}-2a-1\right){x}{y}+\left(a^{4}-4a^{2}+3\right){y}={x}^{3}+\left(-a^{4}+a^{3}+3a^{2}-2a-1\right){x}^{2}+\left(2a^{4}+2a^{3}-5a^{2}-3a+2\right){x}+2a^{4}+3a^{3}-5a^{2}-4a+1$
43.2-a2
43.2-a
$2$
$7$
\(\Q(\zeta_{11})^+\)
$5$
$[5, 0]$
43.2
\( 43 \)
\( - 43^{7} \)
$15.74965$
$(-a^4+2a^2+a+1)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$7$
7B.1.3
$49$
\( 7 \)
$1$
$0.339304693$
0.961830659
\( -\frac{70548898331353450135096255010}{271818611107} a^{4} + \frac{189247840974084378816217200685}{271818611107} a^{3} - \frac{842216448583260989645063883}{6321363049} a^{2} - \frac{150714011772341855278459782553}{271818611107} a + \frac{41930794528416841925025385323}{271818611107} \)
\( \bigl[a^{4} + a^{3} - 3 a^{2} - 3 a + 1\) , \( -a^{4} + 4 a^{2} + a - 3\) , \( a^{4} + a^{3} - 3 a^{2} - 3 a + 1\) , \( -30 a^{4} + 30 a^{3} + 25 a^{2} + 160 a - 215\) , \( -226 a^{4} + 563 a^{3} - 458 a^{2} + 913 a - 1012\bigr] \)
${y}^2+\left(a^{4}+a^{3}-3a^{2}-3a+1\right){x}{y}+\left(a^{4}+a^{3}-3a^{2}-3a+1\right){y}={x}^{3}+\left(-a^{4}+4a^{2}+a-3\right){x}^{2}+\left(-30a^{4}+30a^{3}+25a^{2}+160a-215\right){x}-226a^{4}+563a^{3}-458a^{2}+913a-1012$
43.2-b1
43.2-b
$2$
$5$
\(\Q(\zeta_{11})^+\)
$5$
$[5, 0]$
43.2
\( 43 \)
\( - 43^{5} \)
$15.74965$
$(-a^4+2a^2+a+1)$
0
$\Z/5\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$5$
5B.1.1
$1$
\( 5 \)
$1$
$537.8461822$
0.889001954
\( \frac{245417473145}{147008443} a^{4} - \frac{392753447771}{147008443} a^{3} - \frac{61634765294}{3418801} a^{2} - \frac{2240734555627}{147008443} a - \frac{148495909040}{147008443} \)
\( \bigl[a^{4} - 3 a^{2} + 1\) , \( -a^{4} - a^{3} + 3 a^{2} + 4 a + 1\) , \( a^{4} + a^{3} - 3 a^{2} - 2 a + 1\) , \( -6 a^{4} - a^{3} + 20 a^{2} + 4 a - 8\) , \( -6 a^{4} + a^{3} + 23 a^{2} - 3 a - 15\bigr] \)
${y}^2+\left(a^{4}-3a^{2}+1\right){x}{y}+\left(a^{4}+a^{3}-3a^{2}-2a+1\right){y}={x}^{3}+\left(-a^{4}-a^{3}+3a^{2}+4a+1\right){x}^{2}+\left(-6a^{4}-a^{3}+20a^{2}+4a-8\right){x}-6a^{4}+a^{3}+23a^{2}-3a-15$
43.2-b2
43.2-b
$2$
$5$
\(\Q(\zeta_{11})^+\)
$5$
$[5, 0]$
43.2
\( 43 \)
\( -43 \)
$15.74965$
$(-a^4+2a^2+a+1)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$5$
5B.1.2
$625$
\( 1 \)
$1$
$0.172110778$
0.889001954
\( \frac{4812587720746597807871802}{43} a^{4} + \frac{1490861393846022143062456}{43} a^{3} - 402277955305458024909373 a^{2} - \frac{8218995683117457123881082}{43} a + \frac{3673708517361273227425946}{43} \)
\( \bigl[a^{3} - 2 a + 1\) , \( -a^{3} + 3 a\) , \( a^{4} - 4 a^{2} + 2\) , \( 42 a^{4} - 193 a^{3} + 148 a^{2} + 559 a - 755\) , \( 589 a^{4} - 2716 a^{3} + 1086 a^{2} + 7676 a - 7875\bigr] \)
${y}^2+\left(a^{3}-2a+1\right){x}{y}+\left(a^{4}-4a^{2}+2\right){y}={x}^{3}+\left(-a^{3}+3a\right){x}^{2}+\left(42a^{4}-193a^{3}+148a^{2}+559a-755\right){x}+589a^{4}-2716a^{3}+1086a^{2}+7676a-7875$
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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.