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
73.1-a1 73.1-a $2$
$2$
5.5.24217.1 $5$
$[5, 0]$
73.1
\( 73 \)
\( - 73^{2} \)
$21.35655$
$(-2a^4+2a^3+10a^2-5a-5)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2B $1$
\( 2 \)
$1$
$532.7413066$
1.71169430
\( -\frac{13676805271923}{5329} a^{4} + \frac{9479789620397}{5329} a^{3} + \frac{62312937090438}{5329} a^{2} - \frac{30875880058182}{5329} a - \frac{19195743311669}{5329} \)
\( \bigl[a^{3} - 3 a\) , \( 2 a^{4} - 9 a^{2} + 1\) , \( a^{2} + a - 2\) , \( -2 a^{4} - 4 a^{3} + 13 a^{2} + 18 a - 18\) , \( -30 a^{4} + 5 a^{3} + 152 a^{2} - 104\bigr] \) ${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(2a^{4}-9a^{2}+1\right){x}^{2}+\left(-2a^{4}-4a^{3}+13a^{2}+18a-18\right){x}-30a^{4}+5a^{3}+152a^{2}-104$
73.1-a2 73.1-a $2$
$2$
5.5.24217.1 $5$
$[5, 0]$
73.1
\( 73 \)
\( 73 \)
$21.35655$
$(-2a^4+2a^3+10a^2-5a-5)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2B $1$
\( 1 \)
$1$
$1065.482613$
1.71169430
\( \frac{77128415}{73} a^{4} - \frac{29275704}{73} a^{3} - \frac{374531013}{73} a^{2} + \frac{65385001}{73} a + \frac{205557366}{73} \)
\( \bigl[-2 a^{4} + a^{3} + 10 a^{2} - 2 a - 4\) , \( -2 a^{4} + 2 a^{3} + 9 a^{2} - 7 a - 3\) , \( a^{4} - a^{3} - 4 a^{2} + 4 a + 2\) , \( -5 a^{4} + 5 a^{3} + 22 a^{2} - 17 a - 8\) , \( -a^{4} + 4 a^{2} + a\bigr] \) ${y}^2+\left(-2a^{4}+a^{3}+10a^{2}-2a-4\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+4a+2\right){y}={x}^{3}+\left(-2a^{4}+2a^{3}+9a^{2}-7a-3\right){x}^{2}+\left(-5a^{4}+5a^{3}+22a^{2}-17a-8\right){x}-a^{4}+4a^{2}+a$
73.1-b1 73.1-b $2$
$2$
5.5.24217.1 $5$
$[5, 0]$
73.1
\( 73 \)
\( 73 \)
$21.35655$
$(-2a^4+2a^3+10a^2-5a-5)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2B $1$
\( 1 \)
$0.013585443$
$16315.17680$
1.78039127
\( \frac{25541025}{73} a^{4} - \frac{10499403}{73} a^{3} - \frac{123078275}{73} a^{2} + \frac{24749415}{73} a + \frac{65407672}{73} \)
\( \bigl[-a^{4} + 5 a^{2} + a - 1\) , \( -3 a^{4} + a^{3} + 14 a^{2} - 2 a - 5\) , \( -a^{4} + 5 a^{2} + a - 1\) , \( -2 a^{4} + 9 a^{2} - 2\) , \( a^{4} - a^{3} - 5 a^{2} + 2 a + 4\bigr] \) ${y}^2+\left(-a^{4}+5a^{2}+a-1\right){x}{y}+\left(-a^{4}+5a^{2}+a-1\right){y}={x}^{3}+\left(-3a^{4}+a^{3}+14a^{2}-2a-5\right){x}^{2}+\left(-2a^{4}+9a^{2}-2\right){x}+a^{4}-a^{3}-5a^{2}+2a+4$
73.1-b2 73.1-b $2$
$2$
5.5.24217.1 $5$
$[5, 0]$
73.1
\( 73 \)
\( - 73^{2} \)
$21.35655$
$(-2a^4+2a^3+10a^2-5a-5)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2B $1$
\( 2 \)
$0.027170887$
$4078.794201$
1.78039127
\( \frac{897914919792598}{5329} a^{4} - \frac{325870982359061}{5329} a^{3} - \frac{4373494381863622}{5329} a^{2} + \frac{691699015294266}{5329} a + \frac{2451613630132198}{5329} \)
\( \bigl[-a^{4} + 5 a^{2} + a - 1\) , \( -3 a^{4} + a^{3} + 14 a^{2} - 2 a - 5\) , \( -a^{4} + 5 a^{2} + a - 1\) , \( -22 a^{4} + 10 a^{3} + 104 a^{2} - 20 a - 57\) , \( 68 a^{4} - 24 a^{3} - 329 a^{2} + 46 a + 178\bigr] \) ${y}^2+\left(-a^{4}+5a^{2}+a-1\right){x}{y}+\left(-a^{4}+5a^{2}+a-1\right){y}={x}^{3}+\left(-3a^{4}+a^{3}+14a^{2}-2a-5\right){x}^{2}+\left(-22a^{4}+10a^{3}+104a^{2}-20a-57\right){x}+68a^{4}-24a^{3}-329a^{2}+46a+178$
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Pari/GP
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Magma
Oscar
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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.
