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-a7
17.1-a
$8$
$16$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
17.1
\( 17 \)
\( 17^{2} \)
$0.74813$
$(-2a+1)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2Cs
$1$
\( 2 \)
$3.035256177$
$2.393455763$
0.440490254
\( \frac{82483294977}{17} \)
\( \bigl[1\) , \( -1\) , \( 1\) , \( -91\) , \( -310\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-91{x}-310$
272.4-a7
272.4-a
$8$
$16$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
272.4
\( 2^{4} \cdot 17 \)
\( 2^{12} \cdot 17^{2} \)
$1.49625$
$(-a-1), (-2a+1)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$4$
\( 2^{3} \)
$1$
$4.247877398$
2.060523199
\( \frac{82483294977}{17} \)
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 92 a - 451\) , \( 1640 a - 3240\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(92a-451\right){x}+1640a-3240$
272.5-a7
272.5-a
$8$
$16$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
272.5
\( 2^{4} \cdot 17 \)
\( 2^{12} \cdot 17^{2} \)
$1.49625$
$(-a+2), (-2a+1)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$4$
\( 2^{3} \)
$1$
$4.247877398$
2.060523199
\( \frac{82483294977}{17} \)
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -91 a - 364\) , \( -1549 a - 1240\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-91a-364\right){x}-1549a-1240$
289.1-a7
289.1-a
$8$
$16$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
289.1
\( 17^{2} \)
\( 17^{8} \)
$1.51910$
$(-2a+1)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$64$
\( 2^{2} \)
$1$
$0.580498289$
2.252664248
\( \frac{82483294977}{17} \)
\( \bigl[1\) , \( -1\) , \( 0\) , \( -24667 a - 38542\) , \( -3022719 a - 4720173\bigr] \)
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-24667a-38542\right){x}-3022719a-4720173$
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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.