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-a9
15.1-a
$10$
$32$
\(\Q(\sqrt{15}) \)
$2$
$[2, 0]$
15.1
\( 3 \cdot 5 \)
\( 3^{8} \cdot 5^{2} \)
$1.36219$
$(3,a), (5,a)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 2^{4} \)
$1$
$10.19195692$
1.315775981
\( \frac{1114544804970241}{405} \)
\( \bigl[a\) , \( 1\) , \( a\) , \( -2160\) , \( 35220\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-2160{x}+35220$
15.1-b9
15.1-b
$10$
$32$
\(\Q(\sqrt{15}) \)
$2$
$[2, 0]$
15.1
\( 3 \cdot 5 \)
\( 2^{12} \cdot 3^{8} \cdot 5^{2} \)
$1.36219$
$(3,a), (5,a)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$4$
\( 2^{2} \)
$1$
$10.19195692$
1.315775981
\( \frac{1114544804970241}{405} \)
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -69119 a - 267833\) , \( 19314626 a + 74805717\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-69119a-267833\right){x}+19314626a+74805717$
15.1-c9
15.1-c
$10$
$32$
\(\Q(\sqrt{15}) \)
$2$
$[2, 0]$
15.1
\( 3 \cdot 5 \)
\( 3^{8} \cdot 5^{2} \)
$1.36219$
$(3,a), (5,a)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$9.603901418$
$0.490422220$
1.216108162
\( \frac{1114544804970241}{405} \)
\( \bigl[1\) , \( 1\) , \( 1\) , \( -2160\) , \( -39540\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-2160{x}-39540$
15.1-d9
15.1-d
$10$
$32$
\(\Q(\sqrt{15}) \)
$2$
$[2, 0]$
15.1
\( 3 \cdot 5 \)
\( 2^{12} \cdot 3^{8} \cdot 5^{2} \)
$1.36219$
$(3,a), (5,a)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 2^{4} \)
$5.201251375$
$0.490422220$
2.634464464
\( \frac{1114544804970241}{405} \)
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -69123 a - 267844\) , \( -19521988 a - 75609238\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-69123a-267844\right){x}-19521988a-75609238$
Download
displayed columns for
results
to
Text
Pari/GP
SageMath
Magma
Oscar
CSV
*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.