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-a3
15.1-a
$8$
$16$
\(\Q(\sqrt{30}) \)
$2$
$[2, 0]$
15.1
\( 3 \cdot 5 \)
\( 3^{4} \cdot 5^{16} \)
$1.92642$
$(3,a), (a+5)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 2^{6} \)
$1$
$1.961688882$
2.865230004
\( \frac{4733169839}{3515625} \)
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( 1536 a + 8452\) , \( -38388 a - 210217\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(1536a+8452\right){x}-38388a-210217$
15.1-b3
15.1-b
$8$
$16$
\(\Q(\sqrt{30}) \)
$2$
$[2, 0]$
15.1
\( 3 \cdot 5 \)
\( 2^{12} \cdot 3^{4} \cdot 5^{16} \)
$1.92642$
$(3,a), (a+5)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$4$
\( 2^{2} \)
$1$
$2.547989231$
0.930394118
\( \frac{4733169839}{3515625} \)
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -2967357 a + 16252869\) , \( -3478975110 a + 19055131440\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-2967357a+16252869\right){x}-3478975110a+19055131440$
15.1-c3
15.1-c
$8$
$16$
\(\Q(\sqrt{30}) \)
$2$
$[2, 0]$
15.1
\( 3 \cdot 5 \)
\( 2^{12} \cdot 3^{4} \cdot 5^{16} \)
$1.92642$
$(3,a), (a+5)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 2^{3} \)
$4.297783744$
$2.547989231$
3.998632720
\( \frac{4733169839}{3515625} \)
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -6162 a + 33754\) , \( -356336 a + 1951734\bigr] \)
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-6162a+33754\right){x}-356336a+1951734$
15.1-d3
15.1-d
$8$
$16$
\(\Q(\sqrt{30}) \)
$2$
$[2, 0]$
15.1
\( 3 \cdot 5 \)
\( 3^{4} \cdot 5^{16} \)
$1.92642$
$(3,a), (a+5)$
$1$
$\Z/8\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 2^{5} \)
$10.07379811$
$1.961688882$
1.803984289
\( \frac{4733169839}{3515625} \)
\( \bigl[1\) , \( 1\) , \( 1\) , \( 35\) , \( -28\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+35{x}-28$
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Pari/GP
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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.