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
256.2-c3
256.2-c
$4$
$4$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
256.2
\( 2^{8} \)
\( 2^{23} \)
$1.47375$
$(-a+2), (-a-1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$1$
$13.48883347$
1.635761328
\( -910322 a + 2340632 \)
\( \bigl[0\) , \( -a\) , \( 0\) , \( 124 a - 316\) , \( -1012 a + 2592\bigr] \)
${y}^2={x}^{3}-a{x}^{2}+\left(124a-316\right){x}-1012a+2592$
256.2-d3
256.2-d
$4$
$4$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
256.2
\( 2^{8} \)
\( 2^{23} \)
$1.47375$
$(-a+2), (-a-1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$5.597829937$
1.357673182
\( -910322 a + 2340632 \)
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -6 a - 17\) , \( -27 a - 49\bigr] \)
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-6a-17\right){x}-27a-49$
512.1-d3
512.1-d
$4$
$4$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
512.1
\( 2^{9} \)
\( 2^{23} \)
$1.75259$
$(-a+2), (-a-1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$8.009701860$
1.942638047
\( -910322 a + 2340632 \)
\( \bigl[0\) , \( a\) , \( 0\) , \( 124 a - 316\) , \( 1012 a - 2592\bigr] \)
${y}^2={x}^{3}+a{x}^{2}+\left(124a-316\right){x}+1012a-2592$
512.1-g3
512.1-g
$4$
$4$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
512.1
\( 2^{9} \)
\( 2^{23} \)
$1.75259$
$(-a+2), (-a-1)$
$1$
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{4} \)
$0.289043013$
$19.30061037$
2.706070181
\( -910322 a + 2340632 \)
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -6 a - 17\) , \( 27 a + 49\bigr] \)
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-6a-17\right){x}+27a+49$
512.4-c3
512.4-c
$4$
$4$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
512.4
\( 2^{9} \)
\( 2^{17} \)
$1.75259$
$(-a+2), (-a-1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 1 \)
$1$
$27.29518495$
1.655013686
\( -910322 a + 2340632 \)
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 9 a - 24\) , \( -32 a + 82\bigr] \)
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(9a-24\right){x}-32a+82$
512.4-j3
512.4-j
$4$
$4$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
512.4
\( 2^{9} \)
\( 2^{17} \)
$1.75259$
$(-a+2), (-a-1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 1 \)
$1.962096349$
$11.32742900$
2.695238627
\( -910322 a + 2340632 \)
\( \bigl[0\) , \( -1\) , \( 0\) , \( -28 a - 44\) , \( 114 a + 178\bigr] \)
${y}^2={x}^{3}-{x}^{2}+\left(-28a-44\right){x}+114a+178$
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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.