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
44.1-a1
44.1-a
$2$
$3$
\(\Q(\sqrt{22}) \)
$2$
$[2, 0]$
44.1
\( 2^{2} \cdot 11 \)
\( 2^{4} \cdot 11^{6} \)
$2.15895$
$(-3a-14), (7a-33)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3B
$1$
\( 2 \cdot 3 \)
$0.172006545$
$18.65468372$
4.104618276
\( -\frac{199794688}{1331} \)
\( \bigl[0\) , \( 1\) , \( a\) , \( -19\) , \( 21\bigr] \)
${y}^2+a{y}={x}^{3}+{x}^{2}-19{x}+21$
44.1-a2
44.1-a
$2$
$3$
\(\Q(\sqrt{22}) \)
$2$
$[2, 0]$
44.1
\( 2^{2} \cdot 11 \)
\( 2^{4} \cdot 11^{2} \)
$2.15895$
$(-3a-14), (7a-33)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3B
$1$
\( 2 \)
$0.516019637$
$18.65468372$
4.104618276
\( \frac{8192}{11} \)
\( \bigl[0\) , \( 1\) , \( a\) , \( 1\) , \( -5\bigr] \)
${y}^2+a{y}={x}^{3}+{x}^{2}+{x}-5$
44.1-b1
44.1-b
$2$
$3$
\(\Q(\sqrt{22}) \)
$2$
$[2, 0]$
44.1
\( 2^{2} \cdot 11 \)
\( 2^{4} \cdot 11^{6} \)
$2.15895$
$(-3a-14), (7a-33)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3B.1.2
$1$
\( 2 \)
$8.539905566$
$1.294911296$
4.715326211
\( -\frac{199794688}{1331} \)
\( \bigl[0\) , \( 1\) , \( a\) , \( 319928 a - 1500595\) , \( 214658661 a - 1006838372\bigr] \)
${y}^2+a{y}={x}^{3}+{x}^{2}+\left(319928a-1500595\right){x}+214658661a-1006838372$
44.1-b2
44.1-b
$2$
$3$
\(\Q(\sqrt{22}) \)
$2$
$[2, 0]$
44.1
\( 2^{2} \cdot 11 \)
\( 2^{4} \cdot 11^{2} \)
$2.15895$
$(-3a-14), (7a-33)$
$1$
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3B.1.1
$1$
\( 2 \cdot 3 \)
$2.846635188$
$11.65420166$
4.715326211
\( \frac{8192}{11} \)
\( \bigl[0\) , \( 1\) , \( a\) , \( -11032 a + 51745\) , \( 1565921 a - 7344826\bigr] \)
${y}^2+a{y}={x}^{3}+{x}^{2}+\left(-11032a+51745\right){x}+1565921a-7344826$
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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.