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-a2
30.1-a
$8$
$12$
\(\Q(\sqrt{30}) \)
$2$
$[2, 0]$
30.1
\( 2 \cdot 3 \cdot 5 \)
\( 2^{20} \cdot 3^{6} \cdot 5^{2} \)
$2.29092$
$(2,a), (3,a), (a+5)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2B , 3B.1.2
$1$
\( 2^{5} \)
$1$
$5.367489134$
0.979964958
\( \frac{357911}{2160} \)
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -256 a + 1450\) , \( 16348 a - 89478\bigr] \)
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-256a+1450\right){x}+16348a-89478$
30.1-d2
30.1-d
$8$
$12$
\(\Q(\sqrt{30}) \)
$2$
$[2, 0]$
30.1
\( 2 \cdot 3 \cdot 5 \)
\( 2^{8} \cdot 3^{6} \cdot 5^{2} \)
$2.29092$
$(2,a), (3,a), (a+5)$
$1$
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2B , 3B
$1$
\( 2^{5} \)
$1.254186424$
$11.23555713$
5.145482154
\( \frac{357911}{2160} \)
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 67 a + 369\) , \( 2307 a + 12639\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(67a+369\right){x}+2307a+12639$
30.1-i2
30.1-i
$8$
$12$
\(\Q(\sqrt{30}) \)
$2$
$[2, 0]$
30.1
\( 2 \cdot 3 \cdot 5 \)
\( 2^{8} \cdot 3^{6} \cdot 5^{2} \)
$2.29092$
$(2,a), (3,a), (a+5)$
$1$
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2B , 3B.1.1
$1$
\( 2^{3} \cdot 3 \)
$1.693773937$
$11.23555713$
2.316317946
\( \frac{357911}{2160} \)
\( \bigl[1\) , \( 0\) , \( 1\) , \( 1\) , \( 2\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+{x}+2$
30.1-l2
30.1-l
$8$
$12$
\(\Q(\sqrt{30}) \)
$2$
$[2, 0]$
30.1
\( 2 \cdot 3 \cdot 5 \)
\( 2^{20} \cdot 3^{6} \cdot 5^{2} \)
$2.29092$
$(2,a), (3,a), (a+5)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2B , 3B
$1$
\( 2^{3} \cdot 3 \)
$1$
$5.367489134$
2.939894875
\( \frac{357911}{2160} \)
\( \bigl[a\) , \( 1\) , \( a\) , \( 15\) , \( 15\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+15{x}+15$
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.