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
30.1-a4
30.1-a
$8$
$12$
\(\Q(\sqrt{30}) \)
$2$
$[2, 0]$
30.1
\( 2 \cdot 3 \cdot 5 \)
\( 2^{14} \cdot 3^{24} \cdot 5^{2} \)
$2.29092$
$(2,a), (3,a), (a+5)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2B , 3B.1.2
$1$
\( 2^{3} \)
$1$
$5.367489134$
0.979964958
\( \frac{35578826569}{5314410} \)
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 12064 a - 66030\) , \( -1449060 a + 7936890\bigr] \)
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(12064a-66030\right){x}-1449060a+7936890$
30.1-d4
30.1-d
$8$
$12$
\(\Q(\sqrt{30}) \)
$2$
$[2, 0]$
30.1
\( 2 \cdot 3 \cdot 5 \)
\( 2^{2} \cdot 3^{24} \cdot 5^{2} \)
$2.29092$
$(2,a), (3,a), (a+5)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2B , 3B
$1$
\( 2^{3} \)
$5.016745697$
$2.808889283$
5.145482154
\( \frac{35578826569}{5314410} \)
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -3013 a - 16501\) , \( -193189 a - 1058137\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-3013a-16501\right){x}-193189a-1058137$
30.1-i4
30.1-i
$8$
$12$
\(\Q(\sqrt{30}) \)
$2$
$[2, 0]$
30.1
\( 2 \cdot 3 \cdot 5 \)
\( 2^{2} \cdot 3^{24} \cdot 5^{2} \)
$2.29092$
$(2,a), (3,a), (a+5)$
$1$
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2B , 3B.1.1
$1$
\( 2^{5} \cdot 3 \)
$1.693773937$
$2.808889283$
2.316317946
\( \frac{35578826569}{5314410} \)
\( \bigl[1\) , \( 0\) , \( 1\) , \( -69\) , \( -194\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-69{x}-194$
30.1-l4
30.1-l
$8$
$12$
\(\Q(\sqrt{30}) \)
$2$
$[2, 0]$
30.1
\( 2 \cdot 3 \cdot 5 \)
\( 2^{14} \cdot 3^{24} \cdot 5^{2} \)
$2.29092$
$(2,a), (3,a), (a+5)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2B , 3B
$1$
\( 2^{5} \cdot 3 \)
$1$
$5.367489134$
2.939894875
\( \frac{35578826569}{5314410} \)
\( \bigl[a\) , \( 1\) , \( a\) , \( -265\) , \( 743\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-265{x}+743$
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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.