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
30000.1-b1 30000.1-b $2$
$3$
\(\Q(\sqrt{-3}) \) $2$
$[0, 1]$
30000.1
\( 2^{4} \cdot 3 \cdot 5^{4} \)
\( 2^{16} \cdot 3^{2} \cdot 5^{4} \)
$2.03695$
$(-2a+1), (2), (5)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$2, 3$
2Cn , 3B[2] $1$
\( 2 \cdot 3 \)
$0.342467425$
$0.600235187$
2.848336760
\( -\frac{30866268160}{3} \)
\( \bigl[0\) , \( -1\) , \( 0\) , \( -1213\) , \( -15863\bigr] \) ${y}^2={x}^{3}-{x}^{2}-1213{x}-15863$
30000.1-c1 30000.1-c $2$
$3$
\(\Q(\sqrt{-3}) \) $2$
$[0, 1]$
30000.1
\( 2^{4} \cdot 3 \cdot 5^{4} \)
\( 2^{16} \cdot 3^{2} \cdot 5^{16} \)
$2.03695$
$(-2a+1), (2), (5)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$2, 3$
2Cn , 3B.1.1[2] $9$
\( 2 \cdot 3^{2} \)
$1$
$0.120047037$
2.495130817
\( -\frac{30866268160}{3} \)
\( \bigl[0\) , \( -a\) , \( 0\) , \( -30333 a + 30333\) , \( -2043537\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(-30333a+30333\right){x}-2043537$
Download
displayed columns for
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.
