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
28.1-a8
28.1-a
$12$
$24$
4.4.7168.1
$4$
$[4, 0]$
28.1
\( 2^{2} \cdot 7 \)
\( 2^{8} \cdot 7^{3} \)
$11.47446$
$(a^2-a-2), (-a)$
$1$
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 3 \)
$4.582391323$
$69.05238521$
2.803064709
\( -\frac{3914388170038407466610901238990}{49} a^{3} - 100598188385994848717558770176 a^{2} + \frac{17278945348576339145325144222568}{49} a + 444061887523622038076420848360 \)
\( \bigl[a^{3} - 4 a + 1\) , \( a^{2} + a - 3\) , \( a^{3} - 3 a\) , \( -893 a^{3} + 1279 a^{2} + 3280 a - 4390\) , \( 15899 a^{3} - 18838 a^{2} - 73669 a + 90907\bigr] \)
${y}^2+\left(a^{3}-4a+1\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(a^{2}+a-3\right){x}^{2}+\left(-893a^{3}+1279a^{2}+3280a-4390\right){x}+15899a^{3}-18838a^{2}-73669a+90907$
28.1-b11
28.1-b
$12$
$24$
4.4.7168.1
$4$
$[4, 0]$
28.1
\( 2^{2} \cdot 7 \)
\( 2^{8} \cdot 7^{3} \)
$11.47446$
$(a^2-a-2), (-a)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B.1.2
$144$
\( 3 \)
$1$
$1.161481534$
1.481620801
\( -\frac{3914388170038407466610901238990}{49} a^{3} - 100598188385994848717558770176 a^{2} + \frac{17278945348576339145325144222568}{49} a + 444061887523622038076420848360 \)
\( \bigl[a + 1\) , \( a^{2} - 2\) , \( a^{2} + a - 2\) , \( -3880 a^{3} + 4939 a^{2} + 17013 a - 21585\) , \( -245033 a^{3} + 308773 a^{2} + 1081266 a - 1362224\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(-3880a^{3}+4939a^{2}+17013a-21585\right){x}-245033a^{3}+308773a^{2}+1081266a-1362224$
112.1-c5
112.1-c
$12$
$24$
4.4.7168.1
$4$
$[4, 0]$
112.1
\( 2^{4} \cdot 7 \)
\( 2^{8} \cdot 7^{3} \)
$13.64551$
$(a^2-a-2), (-a)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$16$
\( 3 \)
$14.38711602$
$0.497774362$
4.060210127
\( -\frac{3914388170038407466610901238990}{49} a^{3} - 100598188385994848717558770176 a^{2} + \frac{17278945348576339145325144222568}{49} a + 444061887523622038076420848360 \)
\( \bigl[a^{2} + a - 2\) , \( -a^{3} - a^{2} + 5 a + 3\) , \( 0\) , \( -894 a^{3} + 1277 a^{2} + 3285 a - 4378\) , \( -15515 a^{3} + 18036 a^{2} + 72567 a - 89037\bigr] \)
${y}^2+\left(a^{2}+a-2\right){x}{y}={x}^{3}+\left(-a^{3}-a^{2}+5a+3\right){x}^{2}+\left(-894a^{3}+1277a^{2}+3285a-4378\right){x}-15515a^{3}+18036a^{2}+72567a-89037$
112.1-f3
112.1-f
$12$
$24$
4.4.7168.1
$4$
$[4, 0]$
112.1
\( 2^{4} \cdot 7 \)
\( 2^{8} \cdot 7^{3} \)
$13.64551$
$(a^2-a-2), (-a)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$16$
\( 1 \)
$1$
$29.59367501$
1.398169722
\( -\frac{3914388170038407466610901238990}{49} a^{3} - 100598188385994848717558770176 a^{2} + \frac{17278945348576339145325144222568}{49} a + 444061887523622038076420848360 \)
\( \bigl[a^{3} + a^{2} - 4 a - 2\) , \( -a^{2} - a + 2\) , \( a^{2} - 3\) , \( -3879 a^{3} + 4937 a^{2} + 17009 a - 21579\) , \( 241153 a^{3} - 303835 a^{2} - 1064253 a + 1340641\bigr] \)
${y}^2+\left(a^{3}+a^{2}-4a-2\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{2}-a+2\right){x}^{2}+\left(-3879a^{3}+4937a^{2}+17009a-21579\right){x}+241153a^{3}-303835a^{2}-1064253a+1340641$
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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.