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
34.1-a1
34.1-a
$4$
$6$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
34.1
\( 2 \cdot 17 \)
\( 2^{18} \cdot 17^{3} \)
$0.61031$
$(a), (-3a-1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B.1.2
$1$
\( 2 \)
$1$
$2.790055734$
0.493216832
\( -\frac{9756993259}{1257728} a - \frac{25455932221}{2515456} \)
\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( -16 a + 19\) , \( -25 a + 31\bigr] \)
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-16a+19\right){x}-25a+31$
34.1-a2
34.1-a
$4$
$6$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
34.1
\( 2 \cdot 17 \)
\( 2^{6} \cdot 17 \)
$0.61031$
$(a), (-3a-1)$
0
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B.1.1
$1$
\( 2 \)
$1$
$25.11050160$
0.493216832
\( \frac{2939047}{68} a - \frac{8089117}{136} \)
\( \bigl[1\) , \( a - 1\) , \( 0\) , \( 2 a + 4\) , \( 0\bigr] \)
${y}^2+{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(2a+4\right){x}$
34.1-a3
34.1-a
$4$
$6$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
34.1
\( 2 \cdot 17 \)
\( 2^{3} \cdot 17^{2} \)
$0.61031$
$(a), (-3a-1)$
0
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B.1.1
$1$
\( 2 \)
$1$
$25.11050160$
0.493216832
\( -\frac{6018090689657}{1156} a + \frac{4255433785057}{578} \)
\( \bigl[1\) , \( a - 1\) , \( 0\) , \( -8 a - 16\) , \( -10 a - 4\bigr] \)
${y}^2+{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-8a-16\right){x}-10a-4$
34.1-a4
34.1-a
$4$
$6$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
34.1
\( 2 \cdot 17 \)
\( 2^{9} \cdot 17^{6} \)
$0.61031$
$(a), (-3a-1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B.1.2
$1$
\( 2 \)
$1$
$2.790055734$
0.493216832
\( \frac{130087595511310753}{772402208} a + \frac{91987087285468997}{386201104} \)
\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( 64 a - 141\) , \( -457 a + 479\bigr] \)
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(64a-141\right){x}-457a+479$
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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.