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
15.2-a2
15.2-a
$6$
$8$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
15.2
\( 3 \cdot 5 \)
\( 3^{2} \cdot 5^{2} \)
$0.80588$
$(-a+2), (-a)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$16.31232646$
0.889910366
\( \frac{721}{75} a - \frac{242}{25} \)
\( \bigl[1\) , \( a - 1\) , \( a\) , \( 0\) , \( 3 a - 10\bigr] \)
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+3a-10$
15.2-b2
15.2-b
$6$
$8$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
15.2
\( 3 \cdot 5 \)
\( 3^{2} \cdot 5^{2} \)
$0.80588$
$(-a+2), (-a)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$19.53039258$
1.065470266
\( \frac{721}{75} a - \frac{242}{25} \)
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 0\) , \( 0\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}$
45.1-a2
45.1-a
$6$
$8$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
45.1
\( 3^{2} \cdot 5 \)
\( 3^{8} \cdot 5^{2} \)
$1.06060$
$(-a+2), (-a)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$1$
$5.910459118$
1.289767919
\( \frac{721}{75} a - \frac{242}{25} \)
\( \bigl[1\) , \( a\) , \( 1\) , \( a + 2\) , \( -2 a - 4\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(a+2\right){x}-2a-4$
45.1-b2
45.1-b
$6$
$8$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
45.1
\( 3^{2} \cdot 5 \)
\( 3^{8} \cdot 5^{2} \)
$1.06060$
$(-a+2), (-a)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$0.160486773$
$17.96736562$
1.258473281
\( \frac{721}{75} a - \frac{242}{25} \)
\( \bigl[a\) , \( a\) , \( 0\) , \( 2 a + 2\) , \( -a + 7\bigr] \)
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(2a+2\right){x}-a+7$
1875.1-e2
1875.1-e
$6$
$8$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
1875.1
\( 3 \cdot 5^{4} \)
\( 3^{2} \cdot 5^{14} \)
$2.69463$
$(-a+2), (-a), (-a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{3} \)
$1$
$3.906078517$
1.704752426
\( \frac{721}{75} a - \frac{242}{25} \)
\( \bigl[a + 1\) , \( -1\) , \( a\) , \( a - 2\) , \( -10 a + 1\bigr] \)
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-{x}^{2}+\left(a-2\right){x}-10a+1$
1875.1-bp2
1875.1-bp
$6$
$8$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
1875.1
\( 3 \cdot 5^{4} \)
\( 3^{2} \cdot 5^{14} \)
$2.69463$
$(-a+2), (-a), (-a+1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{3} \)
$1.940369156$
$3.262465293$
5.525614808
\( \frac{721}{75} a - \frac{242}{25} \)
\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( 17 a - 45\) , \( 456 a - 1278\bigr] \)
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(17a-45\right){x}+456a-1278$
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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.