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
52.2-b2
52.2-b
$8$
$12$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
52.2
\( 2^{2} \cdot 13 \)
\( - 2^{13} \cdot 13 \)
$0.98938$
$(-a+2), (-a-1), (2a+1)$
0
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B.1.1
$1$
\( 2^{2} \cdot 3 \)
$1$
$14.99565970$
1.212327233
\( -\frac{166375125}{53248} a + \frac{426241625}{53248} \)
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 2 a - 5\) , \( 5 a - 13\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(2a-5\right){x}+5a-13$
416.5-d2
416.5-d
$8$
$12$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
416.5
\( 2^{5} \cdot 13 \)
\( - 2^{25} \cdot 13 \)
$1.66393$
$(-a+2), (-a-1), (2a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 2^{2} \)
$1$
$11.22064599$
2.721406389
\( -\frac{166375125}{53248} a + \frac{426241625}{53248} \)
\( \bigl[a\) , \( 1\) , \( a\) , \( 6 a - 16\) , \( -7 a + 20\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(6a-16\right){x}-7a+20$
416.7-h2
416.7-h
$8$
$12$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
416.7
\( 2^{5} \cdot 13 \)
\( - 2^{25} \cdot 13 \)
$1.66393$
$(-a+2), (-a-1), (2a+1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 2^{2} \)
$0.929719721$
$4.479241409$
2.020049667
\( -\frac{166375125}{53248} a + \frac{426241625}{53248} \)
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 20 a - 36\) , \( 48 a - 112\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(20a-36\right){x}+48a-112$
676.5-g2
676.5-g
$8$
$12$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
676.5
\( 2^{2} \cdot 13^{2} \)
\( - 2^{13} \cdot 13^{7} \)
$1.87867$
$(-a+2), (-a-1), (2a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 2^{2} \)
$1$
$3.718305499$
0.901821548
\( -\frac{166375125}{53248} a + \frac{426241625}{53248} \)
\( \bigl[1\) , \( a\) , \( a + 1\) , \( 30 a + 47\) , \( -4839 a - 7556\bigr] \)
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(30a+47\right){x}-4839a-7556$
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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.