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
$4$
$6$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
16.1
\( 2^{4} \)
\( - 2^{12} \)
$0.73687$
$(-a+2), (-a-1)$
0
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2B , 3B.1.1
$1$
\( 3^{2} \)
$1$
$13.66488855$
0.828555571
\( -1552 a + 4288 \)
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 2 a + 3\) , \( 0\bigr] \)
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(2a+3\right){x}$
64.2-a2
64.2-a
$4$
$6$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
64.2
\( 2^{6} \)
\( - 2^{12} \)
$1.04210$
$(-a+2), (-a-1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2B , 3B
$1$
\( 1 \)
$1$
$18.89585243$
1.145729345
\( -1552 a + 4288 \)
\( \bigl[0\) , \( -a\) , \( 0\) , \( 4 a - 8\) , \( -3 a + 7\bigr] \)
${y}^2={x}^{3}-a{x}^{2}+\left(4a-8\right){x}-3a+7$
64.3-a2
64.3-a
$4$
$6$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
64.3
\( 2^{6} \)
\( - 2^{12} \)
$1.04210$
$(-a+2), (-a-1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2B , 3B
$1$
\( 1 \)
$1$
$18.89585243$
1.145729345
\( -1552 a + 4288 \)
\( \bigl[0\) , \( a\) , \( 0\) , \( 4 a - 8\) , \( 3 a - 7\bigr] \)
${y}^2={x}^{3}+a{x}^{2}+\left(4a-8\right){x}+3a-7$
256.1-d2
256.1-d
$4$
$6$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
256.1
\( 2^{8} \)
\( - 2^{12} \)
$1.47375$
$(-a+2), (-a-1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2B , 3B
$1$
\( 1 \)
$1$
$26.12924634$
1.584318273
\( -1552 a + 4288 \)
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 2 a + 3\) , \( 0\bigr] \)
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(2a+3\right){x}$
256.4-a2
256.4-a
$4$
$6$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
256.4
\( 2^{8} \)
\( - 2^{18} \)
$1.47375$
$(-a+2), (-a-1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2B , 3B
$1$
\( 2 \)
$1$
$13.36138539$
1.620305978
\( -1552 a + 4288 \)
\( \bigl[0\) , \( 1\) , \( 0\) , \( a - 1\) , \( a - 1\bigr] \)
${y}^2={x}^{3}+{x}^{2}+\left(a-1\right){x}+a-1$
256.4-d2
256.4-d
$4$
$6$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
256.4
\( 2^{8} \)
\( - 2^{18} \)
$1.47375$
$(-a+2), (-a-1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2B , 3B
$1$
\( 2 \cdot 3 \)
$0.163791520$
$18.47616728$
2.201912694
\( -1552 a + 4288 \)
\( \bigl[0\) , \( -a\) , \( 0\) , \( 20 a + 32\) , \( 128 a + 200\bigr] \)
${y}^2={x}^{3}-a{x}^{2}+\left(20a+32\right){x}+128a+200$
256.5-a2
256.5-a
$4$
$6$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
256.5
\( 2^{8} \)
\( - 2^{18} \)
$1.47375$
$(-a+2), (-a-1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2B , 3B
$1$
\( 2 \)
$1$
$13.36138539$
1.620305978
\( -1552 a + 4288 \)
\( \bigl[0\) , \( -1\) , \( 0\) , \( 12 a + 19\) , \( -73 a - 114\bigr] \)
${y}^2={x}^{3}-{x}^{2}+\left(12a+19\right){x}-73a-114$
256.5-d2
256.5-d
$4$
$6$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
256.5
\( 2^{8} \)
\( - 2^{18} \)
$1.47375$
$(-a+2), (-a-1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2B , 3B
$1$
\( 2^{2} \cdot 3 \)
$0.081895760$
$18.47616728$
2.201912694
\( -1552 a + 4288 \)
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( a - 1\) , \( 0\bigr] \)
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(a-1\right){x}$
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.