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
16.1-a2
16.1-a
$4$
$6$
\(\Q(\sqrt{7}) \)
$2$
$[2, 0]$
16.1
\( 2^{4} \)
\( 2^{4} \)
$0.94569$
$(a+3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2B , 3B
$1$
\( 1 \)
$1$
$36.50601953$
1.724747304
\( 3264 a - 6928 \)
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 3 a + 4\) , \( 8\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(3a+4\right){x}+8$
16.1-b2
16.1-b
$4$
$6$
\(\Q(\sqrt{7}) \)
$2$
$[2, 0]$
16.1
\( 2^{4} \)
\( 2^{4} \)
$0.94569$
$(a+3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2B , 3B
$1$
\( 1 \)
$1$
$11.49111446$
0.542904127
\( 3264 a - 6928 \)
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 2 a + 3\) , \( a + 2\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(2a+3\right){x}+a+2$
36.2-a2
36.2-a
$4$
$6$
\(\Q(\sqrt{7}) \)
$2$
$[2, 0]$
36.2
\( 2^{2} \cdot 3^{2} \)
\( 2^{4} \cdot 3^{6} \)
$1.15823$
$(a+3), (-a+2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2B , 3B
$1$
\( 2 \cdot 3 \)
$1$
$6.827191135$
1.935326774
\( 3264 a - 6928 \)
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( a + 4\) , \( 0\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+4\right){x}$
36.2-b2
36.2-b
$4$
$6$
\(\Q(\sqrt{7}) \)
$2$
$[2, 0]$
36.2
\( 2^{2} \cdot 3^{2} \)
\( 2^{4} \cdot 3^{6} \)
$1.15823$
$(a+3), (-a+2)$
0
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2B , 3B.1.1
$1$
\( 2 \cdot 3 \)
$1$
$20.48157340$
0.645108924
\( 3264 a - 6928 \)
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( a + 1\) , \( a + 2\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}+a+2$
36.3-a2
36.3-a
$4$
$6$
\(\Q(\sqrt{7}) \)
$2$
$[2, 0]$
36.3
\( 2^{2} \cdot 3^{2} \)
\( 2^{4} \cdot 3^{6} \)
$1.15823$
$(a+3), (-a-2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2B , 3B
$1$
\( 2 \)
$1$
$20.48157340$
1.935326774
\( 3264 a - 6928 \)
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 65 a + 172\) , \( 0\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(65a+172\right){x}$
36.3-b2
36.3-b
$4$
$6$
\(\Q(\sqrt{7}) \)
$2$
$[2, 0]$
36.3
\( 2^{2} \cdot 3^{2} \)
\( 2^{4} \cdot 3^{6} \)
$1.15823$
$(a+3), (-a-2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2B , 3B.1.2
$1$
\( 2 \)
$1$
$6.827191135$
0.645108924
\( 3264 a - 6928 \)
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 63 a + 169\) , \( 64 a + 170\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(63a+169\right){x}+64a+170$
256.1-a2
256.1-a
$4$
$6$
\(\Q(\sqrt{7}) \)
$2$
$[2, 0]$
256.1
\( 2^{8} \)
\( 2^{16} \)
$1.89137$
$(a+3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2B , 3B
$4$
\( 2^{2} \)
$1$
$5.745557232$
4.343233022
\( 3264 a - 6928 \)
\( \bigl[0\) , \( -1\) , \( 0\) , \( 4 a - 10\) , \( 6 a - 16\bigr] \)
${y}^2={x}^{3}-{x}^{2}+\left(4a-10\right){x}+6a-16$
256.1-e2
256.1-e
$4$
$6$
\(\Q(\sqrt{7}) \)
$2$
$[2, 0]$
256.1
\( 2^{8} \)
\( 2^{16} \)
$1.89137$
$(a+3)$
$2$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2B , 3B
$1$
\( 2^{2} \)
$0.145223206$
$18.25300976$
2.003786675
\( 3264 a - 6928 \)
\( \bigl[0\) , \( 1\) , \( 0\) , \( 4 a - 10\) , \( -6 a + 16\bigr] \)
${y}^2={x}^{3}+{x}^{2}+\left(4a-10\right){x}-6a+16$
Download
displayed columns for
results
to
Text
Pari/GP
SageMath
Magma
Oscar
CSV
*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.