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
17.3-a1
17.3-a
$8$
$12$
\(\Q(\zeta_{9})^+\)
$3$
$[3, 0]$
17.3
\( 17 \)
\( 17^{3} \)
$1.28960$
$(a^2-2a-3)$
0
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B.1.1
$1$
\( 3 \)
$1$
$54.78446428$
0.507263558
\( -\frac{32318862738926135454}{4913} a^{2} + \frac{11224223245743811083}{4913} a + \frac{93058456412295170190}{4913} \)
\( \bigl[a^{2} - 2\) , \( -a^{2} - a + 1\) , \( a\) , \( 28433 a^{2} - 9539 a - 82497\) , \( -3025589 a^{2} + 1055150 a + 8703613\bigr] \)
${y}^2+\left(a^{2}-2\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}-a+1\right){x}^{2}+\left(28433a^{2}-9539a-82497\right){x}-3025589a^{2}+1055150a+8703613$
153.3-a1
153.3-a
$8$
$12$
\(\Q(\zeta_{9})^+\)
$3$
$[3, 0]$
153.3
\( 3^{2} \cdot 17 \)
\( 3^{6} \cdot 17^{3} \)
$1.85993$
$(-a^2+1), (a^2-2a-3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B.1.2
$4$
\( 2 \)
$1$
$4.696336808$
1.043630401
\( -\frac{32318862738926135454}{4913} a^{2} + \frac{11224223245743811083}{4913} a + \frac{93058456412295170190}{4913} \)
\( \bigl[a^{2} - 2\) , \( -a^{2} + 3\) , \( a^{2} + a - 2\) , \( 14228 a^{2} - 4939 a - 40984\) , \( 1079684 a^{2} - 374983 a - 3108816\bigr] \)
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(14228a^{2}-4939a-40984\right){x}+1079684a^{2}-374983a-3108816$
289.5-b1
289.5-b
$8$
$12$
\(\Q(\zeta_{9})^+\)
$3$
$[3, 0]$
289.5
\( 17^{2} \)
\( 17^{9} \)
$2.06791$
$(a^2-2a-3)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 2^{2} \)
$4.818686163$
$0.893356286$
1.434934525
\( -\frac{32318862738926135454}{4913} a^{2} + \frac{11224223245743811083}{4913} a + \frac{93058456412295170190}{4913} \)
\( \bigl[a^{2} + a - 1\) , \( a + 1\) , \( a\) , \( 135427 a^{2} - 45082 a - 393598\) , \( 31720876 a^{2} - 10955869 a - 91450639\bigr] \)
${y}^2+\left(a^{2}+a-1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(135427a^{2}-45082a-393598\right){x}+31720876a^{2}-10955869a-91450639$
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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.