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
72.1-a3
72.1-a
$8$
$16$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
72.1
\( 2^{3} \cdot 3^{2} \)
\( 2^{8} \cdot 3^{2} \)
$0.73624$
$(a), (3)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2 \)
$1$
$18.60223895$
0.822110581
\( \frac{2048}{3} \)
\( \bigl[0\) , \( -1\) , \( 0\) , \( 1\) , \( 0\bigr] \)
${y}^2={x}^{3}-{x}^{2}+{x}$
144.1-b3
144.1-b
$8$
$16$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
144.1
\( 2^{4} \cdot 3^{2} \)
\( 2^{8} \cdot 3^{2} \)
$0.87554$
$(a), (3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 1 \)
$1$
$11.36701703$
1.004711853
\( \frac{2048}{3} \)
\( \bigl[0\) , \( 1\) , \( 0\) , \( 1\) , \( 0\bigr] \)
${y}^2={x}^{3}+{x}^{2}+{x}$
648.1-a3
648.1-a
$8$
$16$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
648.1
\( 2^{3} \cdot 3^{4} \)
\( 2^{8} \cdot 3^{14} \)
$1.27520$
$(a), (3)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{4} \)
$1$
$3.789005678$
1.339615804
\( \frac{2048}{3} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( 6\) , \( -7\bigr] \)
${y}^2={x}^{3}+6{x}-7$
1296.1-b3
1296.1-b
$8$
$16$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
1296.1
\( 2^{4} \cdot 3^{4} \)
\( 2^{8} \cdot 3^{14} \)
$1.51647$
$(a), (3)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$0.539636932$
$6.200746317$
2.366086572
\( \frac{2048}{3} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( 6\) , \( 7\bigr] \)
${y}^2={x}^{3}+6{x}+7$
2304.1-c3
2304.1-c
$8$
$16$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
2304.1
\( 2^{8} \cdot 3^{2} \)
\( 2^{8} \cdot 3^{2} \)
$1.75107$
$(a), (3)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 1 \)
$1.070944103$
$14.54138807$
2.752945917
\( \frac{2048}{3} \)
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -2 a + 3\) , \( 0\bigr] \)
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-2a+3\right){x}$
2304.1-s3
2304.1-s
$8$
$16$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
2304.1
\( 2^{8} \cdot 3^{2} \)
\( 2^{8} \cdot 3^{2} \)
$1.75107$
$(a), (3)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 1 \)
$1.070944103$
$14.54138807$
2.752945917
\( \frac{2048}{3} \)
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -2 a + 3\) , \( 0\bigr] \)
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2a+3\right){x}$
3528.2-d3
3528.2-d
$8$
$16$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
3528.2
\( 2^{3} \cdot 3^{2} \cdot 7^{2} \)
\( 2^{8} \cdot 3^{2} \cdot 7^{6} \)
$1.94790$
$(a), (-2a+1), (3)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{4} \)
$0.197277226$
$5.496128079$
3.066752947
\( \frac{2048}{3} \)
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -2 a + 7\) , \( 7 a - 6\bigr] \)
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-2a+7\right){x}+7a-6$
3528.3-d3
3528.3-d
$8$
$16$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
3528.3
\( 2^{3} \cdot 3^{2} \cdot 7^{2} \)
\( 2^{8} \cdot 3^{2} \cdot 7^{6} \)
$1.94790$
$(a), (2a+1), (3)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{4} \)
$0.197277226$
$5.496128079$
3.066752947
\( \frac{2048}{3} \)
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 2 a + 7\) , \( -7 a - 6\bigr] \)
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(2a+7\right){x}-7a-6$
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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.