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
$8$
$16$
\(\Q(\sqrt{105}) \)
$2$
$[2, 0]$
15.1
\( 3 \cdot 5 \)
\( 2^{12} \cdot 3^{4} \cdot 5^{16} \)
$1.80201$
$(3,a+1), (2a-11)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 2^{3} \)
$1.378356153$
$2.547989231$
1.370958724
\( \frac{4733169839}{3515625} \)
\( \bigl[a\) , \( 0\) , \( 0\) , \( 21867472 a + 101103728\) , \( 67141172125 a + 310425556510\bigr] \)
${y}^2+a{x}{y}={x}^{3}+\left(21867472a+101103728\right){x}+67141172125a+310425556510$
15.1-b3
15.1-b
$8$
$16$
\(\Q(\sqrt{105}) \)
$2$
$[2, 0]$
15.1
\( 3 \cdot 5 \)
\( 3^{4} \cdot 5^{16} \)
$1.80201$
$(3,a+1), (2a-11)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 2^{6} \)
$1$
$1.961688882$
3.063059717
\( \frac{4733169839}{3515625} \)
\( \bigl[1\) , \( a + 1\) , \( a\) , \( 22947 a + 106101\) , \( -2227705 a - 10299746\bigr] \)
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(22947a+106101\right){x}-2227705a-10299746$
15.1-c3
15.1-c
$8$
$16$
\(\Q(\sqrt{105}) \)
$2$
$[2, 0]$
15.1
\( 3 \cdot 5 \)
\( 3^{4} \cdot 5^{16} \)
$1.80201$
$(3,a+1), (2a-11)$
$1$
$\Z/8\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 2^{5} \)
$5.235832845$
$1.961688882$
1.002354292
\( \frac{4733169839}{3515625} \)
\( \bigl[1\) , \( 1\) , \( 1\) , \( 35\) , \( -28\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+35{x}-28$
15.1-d3
15.1-d
$8$
$16$
\(\Q(\sqrt{105}) \)
$2$
$[2, 0]$
15.1
\( 3 \cdot 5 \)
\( 2^{12} \cdot 3^{4} \cdot 5^{16} \)
$1.80201$
$(3,a+1), (2a-11)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$4$
\( 2^{2} \)
$1$
$2.547989231$
0.994633150
\( \frac{4733169839}{3515625} \)
\( \bigl[a\) , \( -a\) , \( 0\) , \( 3250 a + 15060\) , \( 124193 a + 574242\bigr] \)
${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(3250a+15060\right){x}+124193a+574242$
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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.