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
363.1-a3
363.1-a
$4$
$4$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
363.1
\( 3 \cdot 11^{2} \)
\( 3^{6} \cdot 11^{2} \)
$1.78741$
$(-a+2), (11)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 2 \cdot 3 \)
$1$
$30.13204906$
2.465757066
\( \frac{30664297}{297} \)
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 35 a - 87\) , \( -151 a + 428\bigr] \)
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(35a-87\right){x}-151a+428$
363.1-b3
363.1-b
$4$
$4$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
363.1
\( 3 \cdot 11^{2} \)
\( 3^{6} \cdot 11^{2} \)
$1.78741$
$(-a+2), (11)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 2 \)
$0.759802923$
$8.936252827$
1.481653873
\( \frac{30664297}{297} \)
\( \bigl[1\) , \( 1\) , \( 0\) , \( -6\) , \( -9\bigr] \)
${y}^2+{x}{y}={x}^{3}+{x}^{2}-6{x}-9$
1089.1-a3
1089.1-a
$4$
$4$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
1089.1
\( 3^{2} \cdot 11^{2} \)
\( 3^{12} \cdot 11^{2} \)
$2.35237$
$(-a+2), (11)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$2.162460007$
$9.473957439$
4.470641716
\( \frac{30664297}{297} \)
\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( 23 a - 52\) , \( 73 a - 196\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(23a-52\right){x}+73a-196$
1089.1-b3
1089.1-b
$4$
$4$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
1089.1
\( 3^{2} \cdot 11^{2} \)
\( 3^{12} \cdot 11^{2} \)
$2.35237$
$(-a+2), (11)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$2.162460007$
$9.473957439$
4.470641716
\( \frac{30664297}{297} \)
\( \bigl[a\) , \( a\) , \( 0\) , \( -18 a - 36\) , \( -108 a - 189\bigr] \)
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(-18a-36\right){x}-108a-189$
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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.