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-a8
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
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2Cs
$16$
\( 2^{2} \)
$1$
$2.547989231$
1.315775981
\( \frac{56667352321}{15} \)
\( \bigl[a\) , \( 1\) , \( a\) , \( -80\) , \( -402\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-80{x}-402$
15.1-b8
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
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2Cs
$16$
\( 2^{2} \)
$1$
$2.547989231$
1.315775981
\( \frac{56667352321}{15} \)
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -2559 a - 9913\) , \( -144782 a - 560747\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-2559a-9913\right){x}-144782a-560747$
15.1-c8
15.1-c
$10$
$32$
\(\Q(\sqrt{15}) \)
$2$
$[2, 0]$
15.1
\( 3 \cdot 5 \)
\( 3^{2} \cdot 5^{2} \)
$1.36219$
$(3,a), (5,a)$
$1$
$\Z/2\Z\oplus\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2Cs
$1$
\( 2^{2} \)
$2.400975354$
$31.38702211$
1.216108162
\( \frac{56667352321}{15} \)
\( \bigl[1\) , \( 1\) , \( 1\) , \( -80\) , \( 242\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-80{x}+242$
15.1-d8
15.1-d
$10$
$32$
\(\Q(\sqrt{15}) \)
$2$
$[2, 0]$
15.1
\( 3 \cdot 5 \)
\( 2^{12} \cdot 3^{2} \cdot 5^{2} \)
$1.36219$
$(3,a), (5,a)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2Cs
$1$
\( 2^{2} \)
$1.300312843$
$31.38702211$
2.634464464
\( \frac{56667352321}{15} \)
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -2563 a - 9924\) , \( 137100 a + 530986\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-2563a-9924\right){x}+137100a+530986$
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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.