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
97.1-a1
97.1-a
$4$
$4$
5.5.24217.1
$5$
$[5, 0]$
97.1
\( 97 \)
\( 97 \)
$21.97232$
$(a^4-a^3-5a^2+5a+4)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 1 \)
$1$
$2396.428605$
0.962463662
\( -\frac{761279}{97} a^{4} - \frac{433426}{97} a^{3} + \frac{3272354}{97} a^{2} + \frac{2641857}{97} a + \frac{440084}{97} \)
\( \bigl[-a^{4} + a^{3} + 5 a^{2} - 3 a - 2\) , \( a^{3} - a^{2} - 4 a\) , \( a^{4} - 4 a^{2} + a\) , \( -2 a^{4} + 2 a^{3} + 9 a^{2} - 10 a - 5\) , \( -a^{2} - a - 1\bigr] \)
${y}^2+\left(-a^{4}+a^{3}+5a^{2}-3a-2\right){x}{y}+\left(a^{4}-4a^{2}+a\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a\right){x}^{2}+\left(-2a^{4}+2a^{3}+9a^{2}-10a-5\right){x}-a^{2}-a-1$
97.1-a2
97.1-a
$4$
$4$
5.5.24217.1
$5$
$[5, 0]$
97.1
\( 97 \)
\( 97^{2} \)
$21.97232$
$(a^4-a^3-5a^2+5a+4)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$4$
\( 2 \)
$1$
$299.5535756$
0.962463662
\( -\frac{2699246979785}{9409} a^{4} - \frac{2388620148409}{9409} a^{3} + \frac{11413457143722}{9409} a^{2} + \frac{12792778212781}{9409} a + \frac{3119261293489}{9409} \)
\( \bigl[-a^{4} + a^{3} + 5 a^{2} - 3 a - 2\) , \( a^{3} - a^{2} - 4 a\) , \( a^{4} - 4 a^{2} + a\) , \( 13 a^{4} + 22 a^{3} - 51 a^{2} - 110 a - 45\) , \( 72 a^{4} + 75 a^{3} - 298 a^{2} - 393 a - 125\bigr] \)
${y}^2+\left(-a^{4}+a^{3}+5a^{2}-3a-2\right){x}{y}+\left(a^{4}-4a^{2}+a\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a\right){x}^{2}+\left(13a^{4}+22a^{3}-51a^{2}-110a-45\right){x}+72a^{4}+75a^{3}-298a^{2}-393a-125$
97.1-a3
97.1-a
$4$
$4$
5.5.24217.1
$5$
$[5, 0]$
97.1
\( 97 \)
\( - 97^{4} \)
$21.97232$
$(a^4-a^3-5a^2+5a+4)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$16$
\( 2^{2} \)
$1$
$9.361049240$
0.962463662
\( \frac{298244004312035170314}{88529281} a^{4} - \frac{224778495680070789765}{88529281} a^{3} - \frac{1183654637007985475374}{88529281} a^{2} + \frac{271982011051561202569}{88529281} a + \frac{648707452832843494777}{88529281} \)
\( \bigl[a + 1\) , \( 2 a^{4} - a^{3} - 9 a^{2} + 4 a + 2\) , \( a^{4} - 4 a^{2} + a\) , \( 5 a^{4} + 5 a^{3} - 25 a^{2} - 21 a - 5\) , \( 222 a^{4} - 145 a^{3} - 1003 a^{2} + 419 a + 280\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a^{4}-4a^{2}+a\right){y}={x}^{3}+\left(2a^{4}-a^{3}-9a^{2}+4a+2\right){x}^{2}+\left(5a^{4}+5a^{3}-25a^{2}-21a-5\right){x}+222a^{4}-145a^{3}-1003a^{2}+419a+280$
97.1-a4
97.1-a
$4$
$4$
5.5.24217.1
$5$
$[5, 0]$
97.1
\( 97 \)
\( 97 \)
$21.97232$
$(a^4-a^3-5a^2+5a+4)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$16$
\( 1 \)
$1$
$37.44419696$
0.962463662
\( -\frac{59222861174558797002}{97} a^{4} - \frac{52003291912703292187}{97} a^{3} + \frac{250450480086938815342}{97} a^{2} + \frac{279142148582207331991}{97} a + \frac{67444715102322126455}{97} \)
\( \bigl[-a^{4} + a^{3} + 5 a^{2} - 2 a - 2\) , \( 3 a^{4} - a^{3} - 14 a^{2} + 2 a + 4\) , \( -a^{4} + a^{3} + 5 a^{2} - 3 a - 2\) , \( -242 a^{4} + 89 a^{3} + 1173 a^{2} - 192 a - 659\) , \( -1145 a^{4} + 417 a^{3} + 5555 a^{2} - 907 a - 3091\bigr] \)
${y}^2+\left(-a^{4}+a^{3}+5a^{2}-2a-2\right){x}{y}+\left(-a^{4}+a^{3}+5a^{2}-3a-2\right){y}={x}^{3}+\left(3a^{4}-a^{3}-14a^{2}+2a+4\right){x}^{2}+\left(-242a^{4}+89a^{3}+1173a^{2}-192a-659\right){x}-1145a^{4}+417a^{3}+5555a^{2}-907a-3091$
Download
displayed columns for
results
to
Text
Pari/GP
SageMath
Magma
Oscar
CSV
*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.