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
145.3-a1
145.3-a
$8$
$12$
\(\Q(\zeta_{15})^+\)
$4$
$[4, 0]$
145.3
\( 5 \cdot 29 \)
\( 5 \cdot 29 \)
$5.58323$
$(-a-1), (-a^3+a^2+4a-2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B.1.2
$4$
\( 1 \)
$1$
$42.29533189$
1.261003163
\( -\frac{765623948004282479}{145} a^{3} - \frac{258980786426845107}{145} a^{2} + \frac{2715911939787230208}{145} a + \frac{572103573083015331}{145} \)
\( \bigl[a + 1\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( a^{3} - 3 a + 1\) , \( 767 a^{3} + 261 a^{2} - 2731 a - 600\) , \( 14439 a^{3} + 4899 a^{2} - 51204 a - 10817\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-2\right){x}^{2}+\left(767a^{3}+261a^{2}-2731a-600\right){x}+14439a^{3}+4899a^{2}-51204a-10817$
145.3-c5
145.3-c
$8$
$12$
\(\Q(\zeta_{15})^+\)
$4$
$[4, 0]$
145.3
\( 5 \cdot 29 \)
\( 5 \cdot 29 \)
$5.58323$
$(-a-1), (-a^3+a^2+4a-2)$
0
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B.1.1
$4$
\( 1 \)
$1$
$292.0890134$
0.967601317
\( -\frac{765623948004282479}{145} a^{3} - \frac{258980786426845107}{145} a^{2} + \frac{2715911939787230208}{145} a + \frac{572103573083015331}{145} \)
\( \bigl[a\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( a^{3} + a^{2} - 2 a - 1\) , \( -166 a^{3} - 146 a^{2} + 393 a + 78\) , \( -2158 a^{3} - 1772 a^{2} + 5412 a + 1214\bigr] \)
${y}^2+a{x}{y}+\left(a^{3}+a^{2}-2a-1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-2\right){x}^{2}+\left(-166a^{3}-146a^{2}+393a+78\right){x}-2158a^{3}-1772a^{2}+5412a+1214$
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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.