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
221.2-a1
221.2-a
$2$
$3$
\(\Q(\sqrt{13}) \)
$2$
$[2, 0]$
221.2
\( 13 \cdot 17 \)
\( 13^{3} \cdot 17 \)
$1.24225$
$(-2a+1), (a+4)$
$1$
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.1
$1$
\( 3 \)
$0.271715905$
$29.38258856$
1.476189729
\( \frac{52737753971}{2873} a - \frac{122739016195}{2873} \)
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -7 a - 22\) , \( 8 a + 28\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-7a-22\right){x}+8a+28$
221.2-a2
221.2-a
$2$
$3$
\(\Q(\sqrt{13}) \)
$2$
$[2, 0]$
221.2
\( 13 \cdot 17 \)
\( 13^{9} \cdot 17^{3} \)
$1.24225$
$(-2a+1), (a+4)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.2
$1$
\( 3^{2} \)
$0.090571968$
$3.264732062$
1.476189729
\( \frac{174270883997}{1824162509} a + \frac{174989742368}{1824162509} \)
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 18 a + 18\) , \( 116 a + 189\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(18a+18\right){x}+116a+189$
221.2-b1
221.2-b
$1$
$1$
\(\Q(\sqrt{13}) \)
$2$
$[2, 0]$
221.2
\( 13 \cdot 17 \)
\( 13^{2} \cdot 17^{5} \)
$1.24225$
$(-2a+1), (a+4)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 2 \cdot 5 \)
$0.023669495$
$13.43704502$
1.764213293
\( -\frac{325452722176}{18458141} a - \frac{427798695936}{18458141} \)
\( \bigl[0\) , \( a\) , \( a\) , \( 10 a - 23\) , \( -77 a + 176\bigr] \)
${y}^2+a{y}={x}^{3}+a{x}^{2}+\left(10a-23\right){x}-77a+176$
221.2-c1
221.2-c
$1$
$1$
\(\Q(\sqrt{13}) \)
$2$
$[2, 0]$
221.2
\( 13 \cdot 17 \)
\( 13 \cdot 17 \)
$1.24225$
$(-2a+1), (a+4)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 1 \)
$0.078912461$
$22.20344126$
0.971905854
\( \frac{57973}{221} a - \frac{98088}{221} \)
\( \bigl[1\) , \( a - 1\) , \( a\) , \( 2\) , \( -a - 2\bigr] \)
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+2{x}-a-2$
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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.