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
68.1-a3
68.1-a
$4$
$6$
\(\Q(\sqrt{85}) \)
$2$
$[2, 0]$
68.1
\( 2^{2} \cdot 17 \)
\( 2^{6} \cdot 3^{12} \cdot 17^{4} \)
$2.36578$
$(17,a+8), (2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2B , 3B
$1$
\( 2^{2} \cdot 3 \)
$1$
$20.21098874$
6.576568561
\( \frac{8805624625}{2312} \)
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 471 a - 2456\) , \( -11288 a + 57711\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(471a-2456\right){x}-11288a+57711$
68.1-b3
68.1-b
$4$
$6$
\(\Q(\sqrt{85}) \)
$2$
$[2, 0]$
68.1
\( 2^{2} \cdot 17 \)
\( 2^{6} \cdot 17^{4} \)
$2.36578$
$(17,a+8), (2)$
$1$
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2B , 3B.1.1
$1$
\( 2 \cdot 3 \)
$1.120326844$
$20.21098874$
0.818656255
\( \frac{8805624625}{2312} \)
\( \bigl[1\) , \( 0\) , \( 0\) , \( -43\) , \( 105\bigr] \)
${y}^2+{x}{y}={x}^{3}-43{x}+105$
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Pari/GP
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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.