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-a6
15.1-a
$6$
$8$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
15.1
\( 3 \cdot 5 \)
\( 3^{8} \cdot 5^{2} \)
$0.80588$
$(-a+2), (-a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$4.078081616$
0.889910366
\( \frac{11403943879867}{2025} a + \frac{4085550627187}{405} \)
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 67 a - 177\) , \( 271 a - 757\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(67a-177\right){x}+271a-757$
15.1-b6
15.1-b
$6$
$8$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
15.1
\( 3 \cdot 5 \)
\( 3^{8} \cdot 5^{2} \)
$0.80588$
$(-a+2), (-a+1)$
0
$\Z/8\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{4} \)
$1$
$19.53039258$
1.065470266
\( \frac{11403943879867}{2025} a + \frac{4085550627187}{405} \)
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -15 a - 39\) , \( 72 a + 135\bigr] \)
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-15a-39\right){x}+72a+135$
45.2-a6
45.2-a
$6$
$8$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
45.2
\( 3^{2} \cdot 5 \)
\( 3^{14} \cdot 5^{2} \)
$1.06060$
$(-a+2), (-a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{3} \)
$1$
$2.955229559$
1.289767919
\( \frac{11403943879867}{2025} a + \frac{4085550627187}{405} \)
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 29 a - 132\) , \( -136 a + 264\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(29a-132\right){x}-136a+264$
45.2-b6
45.2-b
$6$
$8$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
45.2
\( 3^{2} \cdot 5 \)
\( 3^{14} \cdot 5^{2} \)
$1.06060$
$(-a+2), (-a+1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{3} \)
$0.160486773$
$8.983682810$
1.258473281
\( \frac{11403943879867}{2025} a + \frac{4085550627187}{405} \)
\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( -252 a - 459\) , \( 2770 a + 4957\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-252a-459\right){x}+2770a+4957$
1875.1-k6
1875.1-k
$6$
$8$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
1875.1
\( 3 \cdot 5^{4} \)
\( 3^{8} \cdot 5^{14} \)
$2.69463$
$(-a+2), (-a), (-a+1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{5} \)
$1.940369156$
$0.815616323$
5.525614808
\( \frac{11403943879867}{2025} a + \frac{4085550627187}{405} \)
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( 1605 a - 4571\) , \( 39293 a - 110027\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(1605a-4571\right){x}+39293a-110027$
1875.1-bj6
1875.1-bj
$6$
$8$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
1875.1
\( 3 \cdot 5^{4} \)
\( 3^{8} \cdot 5^{14} \)
$2.69463$
$(-a+2), (-a), (-a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{3} \)
$1$
$3.906078517$
1.704752426
\( \frac{11403943879867}{2025} a + \frac{4085550627187}{405} \)
\( \bigl[a\) , \( -a\) , \( a + 1\) , \( -378 a - 1000\) , \( 7634 a + 14991\bigr] \)
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-378a-1000\right){x}+7634a+14991$
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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.