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
15.1-a3
15.1-a
$10$
$32$
\(\Q(\sqrt{15}) \)
$2$
$[2, 0]$
15.1
\( 3 \cdot 5 \)
\( 3^{2} \cdot 5^{2} \)
$1.36219$
$(3,a), (5,a)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$4$
\( 2^{2} \)
$1$
$10.19195692$
1.315775981
\( -\frac{1}{15} \)
\( \bigl[a\) , \( 1\) , \( a\) , \( 0\) , \( 0\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}$
15.1-b3
15.1-b
$10$
$32$
\(\Q(\sqrt{15}) \)
$2$
$[2, 0]$
15.1
\( 3 \cdot 5 \)
\( 2^{12} \cdot 3^{2} \cdot 5^{2} \)
$1.36219$
$(3,a), (5,a)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$10.19195692$
1.315775981
\( -\frac{1}{15} \)
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( a + 7\) , \( -94 a - 363\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(a+7\right){x}-94a-363$
15.1-c3
15.1-c
$10$
$32$
\(\Q(\sqrt{15}) \)
$2$
$[2, 0]$
15.1
\( 3 \cdot 5 \)
\( 3^{2} \cdot 5^{2} \)
$1.36219$
$(3,a), (5,a)$
$1$
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$0.600243838$
$31.38702211$
1.216108162
\( -\frac{1}{15} \)
\( \bigl[1\) , \( 1\) , \( 1\) , \( 0\) , \( 0\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}$
15.1-d3
15.1-d
$10$
$32$
\(\Q(\sqrt{15}) \)
$2$
$[2, 0]$
15.1
\( 3 \cdot 5 \)
\( 2^{12} \cdot 3^{2} \cdot 5^{2} \)
$1.36219$
$(3,a), (5,a)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$0.325078210$
$31.38702211$
2.634464464
\( -\frac{1}{15} \)
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -3 a - 4\) , \( 92 a + 362\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-3a-4\right){x}+92a+362$
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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.