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
147.1-a5
147.1-a
$6$
$8$
\(\Q(\sqrt{15}) \)
$2$
$[2, 0]$
147.1
\( 3 \cdot 7^{2} \)
\( 2^{12} \cdot 3^{4} \cdot 7^{8} \)
$2.41015$
$(3,a), (7,a+1), (7,a+6)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2Cs
$1$
\( 2^{4} \)
$1.444790239$
$14.60752776$
5.449239426
\( \frac{13027640977}{21609} \)
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -1570 a - 6072\) , \( 65406 a + 253320\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-1570a-6072\right){x}+65406a+253320$
147.1-g5
147.1-g
$6$
$8$
\(\Q(\sqrt{15}) \)
$2$
$[2, 0]$
147.1
\( 3 \cdot 7^{2} \)
\( 2^{12} \cdot 3^{4} \cdot 7^{8} \)
$2.41015$
$(3,a), (7,a+1), (7,a+6)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2Cs
$4$
\( 2^{5} \)
$1$
$3.256081743$
3.362866764
\( \frac{13027640977}{21609} \)
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -1568 a - 6077\) , \( -70112 a - 271549\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-1568a-6077\right){x}-70112a-271549$
147.1-h5
147.1-h
$6$
$8$
\(\Q(\sqrt{15}) \)
$2$
$[2, 0]$
147.1
\( 3 \cdot 7^{2} \)
\( 3^{4} \cdot 7^{8} \)
$2.41015$
$(3,a), (7,a+1), (7,a+6)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2Cs
$1$
\( 2^{4} \)
$2.856034248$
$3.256081743$
2.401115663
\( \frac{13027640977}{21609} \)
\( \bigl[1\) , \( 0\) , \( 0\) , \( -49\) , \( -136\bigr] \)
${y}^2+{x}{y}={x}^{3}-49{x}-136$
147.1-k5
147.1-k
$6$
$8$
\(\Q(\sqrt{15}) \)
$2$
$[2, 0]$
147.1
\( 3 \cdot 7^{2} \)
\( 3^{4} \cdot 7^{8} \)
$2.41015$
$(3,a), (7,a+1), (7,a+6)$
$2$
$\Z/2\Z\oplus\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2Cs
$1$
\( 2^{5} \)
$0.705364543$
$14.60752776$
2.660386384
\( \frac{13027640977}{21609} \)
\( \bigl[a\) , \( -1\) , \( a\) , \( -54\) , \( 84\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-54{x}+84$
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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.