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
18.1-a4
18.1-a
$6$
$8$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
18.1
\( 2 \cdot 3^{2} \)
\( 2^{4} \cdot 3^{4} \)
$0.75889$
$(-a+2), (3)$
0
$\Z/2\Z\oplus\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2^{3} \)
$1$
$26.89023731$
0.815230064
\( \frac{173375}{144} a + \frac{1033157}{144} \)
\( \bigl[1\) , \( a\) , \( a\) , \( 4 a - 9\) , \( -7 a + 17\bigr] \)
${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(4a-9\right){x}-7a+17$
144.4-d4
144.4-d
$6$
$8$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
144.4
\( 2^{4} \cdot 3^{2} \)
\( 2^{16} \cdot 3^{4} \)
$1.27630$
$(-a+2), (3)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2Cs
$1$
\( 2^{3} \)
$0.917668247$
$10.04123052$
2.234848983
\( \frac{173375}{144} a + \frac{1033157}{144} \)
\( \bigl[a\) , \( a\) , \( 0\) , \( 11 a - 23\) , \( 17 a - 42\bigr] \)
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(11a-23\right){x}+17a-42$
162.1-a4
162.1-a
$6$
$8$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
162.1
\( 2 \cdot 3^{4} \)
\( 2^{4} \cdot 3^{16} \)
$1.31444$
$(-a+2), (3)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2Cs
$1$
\( 2^{3} \)
$1$
$9.757425008$
1.183261586
\( \frac{173375}{144} a + \frac{1033157}{144} \)
\( \bigl[1\) , \( -1\) , \( 0\) , \( 36 a - 93\) , \( 131 a - 335\bigr] \)
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(36a-93\right){x}+131a-335$
288.3-c4
288.3-c
$6$
$8$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
288.3
\( 2^{5} \cdot 3^{2} \)
\( 2^{16} \cdot 3^{4} \)
$1.51779$
$(-a+2), (-a-1), (3)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2Cs
$1$
\( 2^{4} \)
$0.185028252$
$19.59765838$
1.758926798
\( \frac{173375}{144} a + \frac{1033157}{144} \)
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 26 a - 66\) , \( -64 a + 164\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(26a-66\right){x}-64a+164$
576.7-h4
576.7-h
$6$
$8$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
576.7
\( 2^{6} \cdot 3^{2} \)
\( 2^{22} \cdot 3^{4} \)
$1.80496$
$(-a+2), (3)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2Cs
$1$
\( 2^{3} \)
$1$
$13.85763714$
1.680485342
\( \frac{173375}{144} a + \frac{1033157}{144} \)
\( \bigl[a\) , \( a + 1\) , \( a\) , \( -9\) , \( -2 a + 3\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}-9{x}-2a+3$
576.7-k4
576.7-k
$6$
$8$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
576.7
\( 2^{6} \cdot 3^{2} \)
\( 2^{22} \cdot 3^{4} \)
$1.80496$
$(-a+2), (3)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2Cs
$1$
\( 2^{3} \)
$1$
$10.34931208$
1.255038437
\( \frac{173375}{144} a + \frac{1033157}{144} \)
\( \bigl[a\) , \( -1\) , \( a\) , \( 124 a - 321\) , \( 875 a - 2243\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(124a-321\right){x}+875a-2243$
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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.