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
109744.2-a1
109744.2-a
$1$
$1$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
109744.2
\( 2^{4} \cdot 19^{3} \)
\( 2^{8} \cdot 19^{4} \)
$2.81705$
$(-5a+3), (-5a+2), (2)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2Cn
$1$
\( 2 \cdot 3 \)
$0.063197259$
$2.989516029$
2.617880053
\( \frac{1161216}{361} a + \frac{2218752}{361} \)
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 9 a - 1\) , \( -7 a - 3\bigr] \)
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(9a-1\right){x}-7a-3$
109744.2-b1
109744.2-b
$2$
$7$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
109744.2
\( 2^{4} \cdot 19^{3} \)
\( 2^{16} \cdot 19^{14} \)
$2.81705$
$(-5a+3), (-5a+2), (2)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$7$
7B
$1$
\( 2 \cdot 3 \cdot 7 \)
$0.178687083$
$0.168309805$
2.917099425
\( \frac{3517118889984}{893871739} a - \frac{927876390912}{893871739} \)
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -2231 a + 944\) , \( -22322 a + 36357\bigr] \)
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-2231a+944\right){x}-22322a+36357$
109744.2-b2
109744.2-b
$2$
$7$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
109744.2
\( 2^{4} \cdot 19^{3} \)
\( 2^{16} \cdot 19^{14} \)
$2.81705$
$(-5a+3), (-5a+2), (2)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$7$
7B
$1$
\( 2 \cdot 3 \)
$1.250809581$
$0.168309805$
2.917099425
\( -\frac{3517118889984}{893871739} a + \frac{2589242499072}{893871739} \)
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 57 a + 1912\) , \( 36310 a - 12259\bigr] \)
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(57a+1912\right){x}+36310a-12259$
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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.