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
43.4-a1
43.4-a
$2$
$7$
\(\Q(\zeta_{11})^+\)
$5$
$[5, 0]$
43.4
\( 43 \)
\( - 43^{7} \)
$15.74965$
$(a^4+a^3-3a^2-3a+2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$7$
7B.1.3
$49$
\( 7 \)
$1$
$0.339304693$
0.961830659
\( -\frac{129163059640409644278905566324}{271818611107} a^{4} - \frac{118698942642730928681120945675}{271818611107} a^{3} + \frac{288870568385811674761647646479}{271818611107} a^{2} + \frac{166848986954108407227145636340}{271818611107} a - \frac{67308147992945409028672333004}{271818611107} \)
\( \bigl[a^{4} - 3 a^{2} + a + 1\) , \( -a^{3} + 3 a\) , \( a^{3} - 3 a\) , \( -281 a^{4} + 780 a^{3} - 124 a^{2} - 737 a + 173\) , \( -7165 a^{4} + 19524 a^{3} - 4247 a^{2} - 15318 a + 4221\bigr] \)
${y}^2+\left(a^{4}-3a^{2}+a+1\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(-a^{3}+3a\right){x}^{2}+\left(-281a^{4}+780a^{3}-124a^{2}-737a+173\right){x}-7165a^{4}+19524a^{3}-4247a^{2}-15318a+4221$
43.4-a2
43.4-a
$2$
$7$
\(\Q(\zeta_{11})^+\)
$5$
$[5, 0]$
43.4
\( 43 \)
\( -43 \)
$15.74965$
$(a^4+a^3-3a^2-3a+2)$
0
$\Z/7\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$7$
7B.1.1
$1$
\( 1 \)
$1$
$5702.693977$
0.961830659
\( \frac{294508316}{43} a^{4} - \frac{539160699}{43} a^{3} - \frac{730083346}{43} a^{2} + \frac{1489970384}{43} a - \frac{354407213}{43} \)
\( \bigl[a^{3} - 2 a\) , \( -a^{4} + a^{3} + 3 a^{2} - 2 a - 1\) , \( a^{4} + a^{3} - 3 a^{2} - 3 a + 1\) , \( -a^{3} - a^{2} + a + 1\) , \( -a^{4} - a^{3} + 2 a^{2} + a - 1\bigr] \)
${y}^2+\left(a^{3}-2a\right){x}{y}+\left(a^{4}+a^{3}-3a^{2}-3a+1\right){y}={x}^{3}+\left(-a^{4}+a^{3}+3a^{2}-2a-1\right){x}^{2}+\left(-a^{3}-a^{2}+a+1\right){x}-a^{4}-a^{3}+2a^{2}+a-1$
43.4-b1
43.4-b
$2$
$5$
\(\Q(\zeta_{11})^+\)
$5$
$[5, 0]$
43.4
\( 43 \)
\( -43 \)
$15.74965$
$(a^4+a^3-3a^2-3a+2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$5$
5B.1.2
$625$
\( 1 \)
$1$
$0.172110778$
0.889001954
\( \frac{3443260198697718303446625}{43} a^{4} - \frac{6303449114592619950934258}{43} a^{3} - \frac{8535767899365460376030330}{43} a^{2} + \frac{17419485949931837709740318}{43} a - \frac{4143833314037896993105954}{43} \)
\( \bigl[a^{4} + a^{3} - 4 a^{2} - 2 a + 2\) , \( a^{2} - 3\) , \( a^{2} - 2\) , \( 124 a^{4} + 151 a^{3} - 668 a^{2} - 260 a + 194\) , \( 581 a^{4} + 2293 a^{3} - 4817 a^{2} - 3846 a + 946\bigr] \)
${y}^2+\left(a^{4}+a^{3}-4a^{2}-2a+2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(124a^{4}+151a^{3}-668a^{2}-260a+194\right){x}+581a^{4}+2293a^{3}-4817a^{2}-3846a+946$
43.4-b2
43.4-b
$2$
$5$
\(\Q(\zeta_{11})^+\)
$5$
$[5, 0]$
43.4
\( 43 \)
\( - 43^{5} \)
$15.74965$
$(a^4+a^3-3a^2-3a+2)$
0
$\Z/5\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$5$
5B.1.1
$1$
\( 5 \)
$1$
$537.8461822$
0.889001954
\( -\frac{2061378462833}{147008443} a^{4} + \frac{147335974626}{147008443} a^{3} + \frac{11271755302501}{147008443} a^{2} - \frac{49254476107}{147008443} a - \frac{14544574161229}{147008443} \)
\( \bigl[a^{4} + a^{3} - 4 a^{2} - 2 a + 2\) , \( a^{2} - 3\) , \( a^{2} - 2\) , \( -a^{4} + a^{3} + 7 a^{2} - 5 a - 6\) , \( 6 a^{4} - 4 a^{3} - 24 a^{2} + 10 a + 19\bigr] \)
${y}^2+\left(a^{4}+a^{3}-4a^{2}-2a+2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(-a^{4}+a^{3}+7a^{2}-5a-6\right){x}+6a^{4}-4a^{3}-24a^{2}+10a+19$
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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.