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
8.3-a1
8.3-a
$6$
$8$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
8.3
\( 2^{3} \)
\( 2^{11} \)
$0.61963$
$(-a-1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 1 \)
$1$
$12.69057434$
0.769479095
\( -343 a + 1029 \)
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 4 a + 7\) , \( -34 a - 53\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(4a+7\right){x}-34a-53$
8.3-a2
8.3-a
$6$
$8$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
8.3
\( 2^{3} \)
\( - 2^{10} \)
$0.61963$
$(-a-1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$1$
$6.345287171$
0.769479095
\( -2701312025 a + 6919553753 \)
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 80 a + 125\) , \( 1186 a + 1852\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(80a+125\right){x}+1186a+1852$
8.3-a3
8.3-a
$6$
$8$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
8.3
\( 2^{3} \)
\( 2^{8} \)
$0.61963$
$(-a-1)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2 \)
$1$
$25.38114868$
0.769479095
\( -24225 a + 68453 \)
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 12 a - 37\) , \( 46 a - 121\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(12a-37\right){x}+46a-121$
8.3-a4
8.3-a
$6$
$8$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
8.3
\( 2^{3} \)
\( 2^{10} \)
$0.61963$
$(-a-1)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2 \)
$1$
$25.38114868$
0.769479095
\( 1995 a + 5021 \)
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( a + 3\) , \( 0\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(a+3\right){x}$
8.3-a5
8.3-a
$6$
$8$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
8.3
\( 2^{3} \)
\( - 2^{4} \)
$0.61963$
$(-a-1)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$1$
$25.38114868$
0.769479095
\( 7659605 a + 11960871 \)
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -5 a - 8\) , \( 2 a + 3\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-5a-8\right){x}+2a+3$
8.3-a6
8.3-a
$6$
$8$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
8.3
\( 2^{3} \)
\( 2^{11} \)
$0.61963$
$(-a-1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 1 \)
$1$
$12.69057434$
0.769479095
\( 21069823 a + 33751811 \)
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -4 a - 12\) , \( -29 a - 31\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-4a-12\right){x}-29a-31$
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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.