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
$8$
$12$
\(\Q(\sqrt{15}) \)
$2$
$[2, 0]$
30.1
\( 2 \cdot 3 \cdot 5 \)
\( 2^{2} \cdot 3^{24} \cdot 5^{2} \)
$1.61992$
$(2,a+1), (3,a), (5,a)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2B , 3B
$1$
\( 2^{3} \)
$1$
$5.367489134$
1.385879735
\( \frac{35578826569}{5314410} \)
\( \bigl[a\) , \( -1\) , \( 0\) , \( -66\) , \( 126\bigr] \)
${y}^2+a{x}{y}={x}^{3}-{x}^{2}-66{x}+126$
30.1-b4
30.1-b
$8$
$12$
\(\Q(\sqrt{15}) \)
$2$
$[2, 0]$
30.1
\( 2 \cdot 3 \cdot 5 \)
\( 2^{2} \cdot 3^{24} \cdot 5^{2} \)
$1.61992$
$(2,a+1), (3,a), (5,a)$
$1$
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2B , 3B.1.1
$1$
\( 2^{5} \cdot 3 \)
$0.921859192$
$2.808889283$
1.782880826
\( \frac{35578826569}{5314410} \)
\( \bigl[1\) , \( 0\) , \( 1\) , \( -69\) , \( -194\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-69{x}-194$
30.1-c4
30.1-c
$8$
$12$
\(\Q(\sqrt{15}) \)
$2$
$[2, 0]$
30.1
\( 2 \cdot 3 \cdot 5 \)
\( 2^{14} \cdot 3^{24} \cdot 5^{2} \)
$1.61992$
$(2,a+1), (3,a), (5,a)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2B , 3B
$4$
\( 2^{3} \)
$1$
$2.808889283$
2.901008377
\( \frac{35578826569}{5314410} \)
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -2192 a - 8495\) , \( -99842 a - 386695\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-2192a-8495\right){x}-99842a-386695$
30.1-d4
30.1-d
$8$
$12$
\(\Q(\sqrt{15}) \)
$2$
$[2, 0]$
30.1
\( 2 \cdot 3 \cdot 5 \)
\( 2^{14} \cdot 3^{24} \cdot 5^{2} \)
$1.61992$
$(2,a+1), (3,a), (5,a)$
$1$
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2B , 3B.1.2
$1$
\( 2^{5} \cdot 3 \)
$0.448117683$
$5.367489134$
3.726223300
\( \frac{35578826569}{5314410} \)
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -2194 a - 8490\) , \( 93264 a + 361212\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-2194a-8490\right){x}+93264a+361212$
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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.