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
17.2-a1
17.2-a
$2$
$2$
\(\Q(\sqrt{53}) \)
$2$
$[2, 0]$
17.2
\( 17 \)
\( 17 \)
$1.32096$
$(a-6)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 1 \)
$1$
$48.93243156$
1.680346598
\( \frac{34263}{17} a + \frac{138726}{17} \)
\( \bigl[1\) , \( -1\) , \( 0\) , \( a - 4\) , \( 0\bigr] \)
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(a-4\right){x}$
289.3-a1
289.3-a
$2$
$2$
\(\Q(\sqrt{53}) \)
$2$
$[2, 0]$
289.3
\( 17^{2} \)
\( 17^{7} \)
$2.68226$
$(a-6)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2 \)
$1$
$11.86785787$
0.815087825
\( \frac{34263}{17} a + \frac{138726}{17} \)
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 85 a - 346\) , \( 252 a - 1034\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(85a-346\right){x}+252a-1034$
833.3-e1
833.3-e
$2$
$2$
\(\Q(\sqrt{53}) \)
$2$
$[2, 0]$
833.3
\( 7^{2} \cdot 17 \)
\( 7^{6} \cdot 17 \)
$3.49492$
$(-a-2), (a-6)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$1.944538188$
$12.02402538$
6.423303189
\( \frac{34263}{17} a + \frac{138726}{17} \)
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 2 a - 4\) , \( 2 a - 4\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(2a-4\right){x}+2a-4$
833.4-c1
833.4-c
$2$
$2$
\(\Q(\sqrt{53}) \)
$2$
$[2, 0]$
833.4
\( 7^{2} \cdot 17 \)
\( 7^{6} \cdot 17 \)
$3.49492$
$(-a+3), (a-6)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2 \)
$1$
$19.71386615$
1.353953886
\( \frac{34263}{17} a + \frac{138726}{17} \)
\( \bigl[1\) , \( -1\) , \( 0\) , \( -22 a - 69\) , \( 107 a + 336\bigr] \)
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-22a-69\right){x}+107a+336$
1377.2-a1
1377.2-a
$2$
$2$
\(\Q(\sqrt{53}) \)
$2$
$[2, 0]$
1377.2
\( 3^{4} \cdot 17 \)
\( 3^{12} \cdot 17 \)
$3.96287$
$(a-6), (3)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2 \)
$4.341391037$
$11.30320686$
6.740508277
\( \frac{34263}{17} a + \frac{138726}{17} \)
\( \bigl[1\) , \( -1\) , \( 1\) , \( 9 a - 38\) , \( -9 a + 37\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(9a-38\right){x}-9a+37$
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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.