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
17.1-a1
17.1-a
$2$
$2$
\(\Q(\sqrt{53}) \)
$2$
$[2, 0]$
17.1
\( 17 \)
\( - 17^{2} \)
$1.32096$
$(a+5)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$1$
$24.46621578$
1.680346598
\( -\frac{9844754985}{289} a + \frac{40758297444}{289} \)
\( \bigl[1\) , \( -1\) , \( 0\) , \( 4 a + 12\) , \( -3 a - 9\bigr] \)
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(4a+12\right){x}-3a-9$
289.2-a1
289.2-a
$2$
$2$
\(\Q(\sqrt{53}) \)
$2$
$[2, 0]$
289.2
\( 17^{2} \)
\( - 17^{8} \)
$2.68226$
$(a+5)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$1$
$5.933928937$
0.815087825
\( -\frac{9844754985}{289} a + \frac{40758297444}{289} \)
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 325 a + 1025\) , \( -1594 a - 5004\bigr] \)
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(325a+1025\right){x}-1594a-5004$
833.5-c1
833.5-c
$2$
$2$
\(\Q(\sqrt{53}) \)
$2$
$[2, 0]$
833.5
\( 7^{2} \cdot 17 \)
\( - 7^{6} \cdot 17^{2} \)
$3.49492$
$(-a-2), (a+5)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$1$
$9.856933077$
1.353953886
\( -\frac{9844754985}{289} a + \frac{40758297444}{289} \)
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 148 a + 463\) , \( 829 a + 2602\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(148a+463\right){x}+829a+2602$
833.6-e1
833.6-e
$2$
$2$
\(\Q(\sqrt{53}) \)
$2$
$[2, 0]$
833.6
\( 7^{2} \cdot 17 \)
\( - 7^{6} \cdot 17^{2} \)
$3.49492$
$(-a+3), (a+5)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{3} \)
$3.889076377$
$3.006006345$
6.423303189
\( -\frac{9844754985}{289} a + \frac{40758297444}{289} \)
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 8 a + 4\) , \( 9 a - 69\bigr] \)
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(8a+4\right){x}+9a-69$
1377.1-a1
1377.1-a
$2$
$2$
\(\Q(\sqrt{53}) \)
$2$
$[2, 0]$
1377.1
\( 3^{4} \cdot 17 \)
\( - 3^{12} \cdot 17^{2} \)
$3.96287$
$(a+5), (3)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$8.682782074$
$2.825801715$
6.740508277
\( -\frac{9844754985}{289} a + \frac{40758297444}{289} \)
\( \bigl[1\) , \( -1\) , \( 1\) , \( 36 a + 106\) , \( 45 a + 136\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(36a+106\right){x}+45a+136$
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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.