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
11.1-a4
11.1-a
$4$
$4$
5.5.89417.1
$5$
$[5, 0]$
11.1
\( 11 \)
\( 11^{16} \)
$33.96158$
$(a^3-a^2-3a+2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$4$
\( 2 \)
$0.839459932$
$91.08356335$
2.55699535
\( \frac{476417640375476377168321}{45949729863572161} a^{4} - \frac{921552595192807794564289}{45949729863572161} a^{3} - \frac{1018805365320562990606080}{45949729863572161} a^{2} + \frac{1637467232063013399273925}{45949729863572161} a + \frac{751306184458928265884514}{45949729863572161} \)
\( \bigl[a^{2} - 1\) , \( a^{3} - a^{2} - 4 a + 2\) , \( a^{4} - a^{3} - 5 a^{2} + 3 a + 6\) , \( -34 a^{4} - 106 a^{3} - 82 a^{2} - 9 a - 5\) , \( -1108 a^{4} - 2689 a^{3} + 484 a^{2} + 3592 a + 1217\bigr] \)
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+3a+6\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a+2\right){x}^{2}+\left(-34a^{4}-106a^{3}-82a^{2}-9a-5\right){x}-1108a^{4}-2689a^{3}+484a^{2}+3592a+1217$
11.1-b4
11.1-b
$4$
$4$
5.5.89417.1
$5$
$[5, 0]$
11.1
\( 11 \)
\( 11^{16} \)
$33.96158$
$(a^3-a^2-3a+2)$
$0 \le r \le 1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
\( 2 \)
$1$
$292.6395581$
1.87789849
\( \frac{476417640375476377168321}{45949729863572161} a^{4} - \frac{921552595192807794564289}{45949729863572161} a^{3} - \frac{1018805365320562990606080}{45949729863572161} a^{2} + \frac{1637467232063013399273925}{45949729863572161} a + \frac{751306184458928265884514}{45949729863572161} \)
\( \bigl[a^{4} - 4 a^{2} + a + 3\) , \( a^{4} - a^{3} - 4 a^{2} + 4 a + 3\) , \( a^{4} - 5 a^{2} + 4\) , \( 19 a^{4} - 67 a^{3} - 120 a^{2} + 207 a + 88\) , \( -36 a^{4} - 539 a^{3} - 321 a^{2} + 1448 a + 587\bigr] \)
${y}^2+\left(a^{4}-4a^{2}+a+3\right){x}{y}+\left(a^{4}-5a^{2}+4\right){y}={x}^{3}+\left(a^{4}-a^{3}-4a^{2}+4a+3\right){x}^{2}+\left(19a^{4}-67a^{3}-120a^{2}+207a+88\right){x}-36a^{4}-539a^{3}-321a^{2}+1448a+587$
121.3-a4
121.3-a
$4$
$4$
5.5.89417.1
$5$
$[5, 0]$
121.3
\( 11^{2} \)
\( 11^{22} \)
$43.16454$
$(a^3-a^2-3a+2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$4$
\( 2^{2} \)
$1$
$117.0462420$
1.56569592
\( \frac{476417640375476377168321}{45949729863572161} a^{4} - \frac{921552595192807794564289}{45949729863572161} a^{3} - \frac{1018805365320562990606080}{45949729863572161} a^{2} + \frac{1637467232063013399273925}{45949729863572161} a + \frac{751306184458928265884514}{45949729863572161} \)
\( \bigl[a^{3} - 2 a\) , \( -a^{4} + 6 a^{2} + a - 6\) , \( a\) , \( -193 a^{4} + 54 a^{3} + 1121 a^{2} - 190 a - 1463\) , \( 2483 a^{4} - 997 a^{3} - 14375 a^{2} + 3381 a + 18137\bigr] \)
${y}^2+\left(a^{3}-2a\right){x}{y}+a{y}={x}^{3}+\left(-a^{4}+6a^{2}+a-6\right){x}^{2}+\left(-193a^{4}+54a^{3}+1121a^{2}-190a-1463\right){x}+2483a^{4}-997a^{3}-14375a^{2}+3381a+18137$
121.3-b4
121.3-b
$4$
$4$
5.5.89417.1
$5$
$[5, 0]$
121.3
\( 11^{2} \)
\( 11^{22} \)
$43.16454$
$(a^3-a^2-3a+2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$4$
\( 2^{2} \)
$1$
$131.2034146$
1.75507258
\( \frac{476417640375476377168321}{45949729863572161} a^{4} - \frac{921552595192807794564289}{45949729863572161} a^{3} - \frac{1018805365320562990606080}{45949729863572161} a^{2} + \frac{1637467232063013399273925}{45949729863572161} a + \frac{751306184458928265884514}{45949729863572161} \)
\( \bigl[1\) , \( a^{2} + a - 1\) , \( a^{4} - a^{3} - 5 a^{2} + 3 a + 5\) , \( 131 a^{4} + 91 a^{3} - 524 a^{2} - 442 a - 99\) , \( -1292 a^{4} - 1287 a^{3} + 4999 a^{2} + 5888 a + 1504\bigr] \)
${y}^2+{x}{y}+\left(a^{4}-a^{3}-5a^{2}+3a+5\right){y}={x}^{3}+\left(a^{2}+a-1\right){x}^{2}+\left(131a^{4}+91a^{3}-524a^{2}-442a-99\right){x}-1292a^{4}-1287a^{3}+4999a^{2}+5888a+1504$
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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.