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-a4 15.1-a $10$
$32$
\(\Q(\sqrt{-15}) \) $2$
$[0, 1]$
15.1
\( 3 \cdot 5 \)
\( 3^{8} \cdot 5^{8} \)
$0.68109$
$(3,a+1), (5,a+2)$
0
$\Z/2\Z\oplus\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
✓
$2$
2Cs $1$
\( 2^{4} \)
$1$
$2.235701712$
0.288627850
\( \frac{111284641}{50625} \)
\( \bigl[1\) , \( 1\) , \( 1\) , \( -10\) , \( -10\bigr] \) ${y}^2+{x}{y}+{y}={x}^3+{x}^2-10{x}-10$
15.1-b4 15.1-b $10$
$32$
\(\Q(\sqrt{-15}) \) $2$
$[0, 1]$
15.1
\( 3 \cdot 5 \)
\( 2^{12} \cdot 3^{8} \cdot 5^{8} \)
$0.68109$
$(3,a+1), (5,a+2)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
✓
$2$
2Cs $1$
\( 2^{4} \)
$1$
$2.235701712$
1.154511400
\( \frac{111284641}{50625} \)
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 9 a + 27\) , \( 0\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^3+\left(a-1\right){x}^2+\left(9a+27\right){x}$
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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.
