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-a1
15.1-a
$6$
$8$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
15.1
\( 3 \cdot 5 \)
\( 3^{2} \cdot 5^{2} \)
$0.80588$
$(-a+2), (-a+1)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$16.31232646$
0.889910366
\( -\frac{721}{75} a - \frac{1}{15} \)
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -a\) , \( -4 a - 7\bigr] \)
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}-a{x}-4a-7$
15.1-b1
15.1-b
$6$
$8$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
15.1
\( 3 \cdot 5 \)
\( 3^{2} \cdot 5^{2} \)
$0.80588$
$(-a+2), (-a+1)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$19.53039258$
1.065470266
\( -\frac{721}{75} a - \frac{1}{15} \)
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 1\) , \( 0\bigr] \)
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+{x}$
45.2-a1
45.2-a
$6$
$8$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
45.2
\( 3^{2} \cdot 5 \)
\( 3^{8} \cdot 5^{2} \)
$1.06060$
$(-a+2), (-a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$1$
$5.910459118$
1.289767919
\( -\frac{721}{75} a - \frac{1}{15} \)
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -a + 3\) , \( 2 a - 6\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-a+3\right){x}+2a-6$
45.2-b1
45.2-b
$6$
$8$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
45.2
\( 3^{2} \cdot 5 \)
\( 3^{8} \cdot 5^{2} \)
$1.06060$
$(-a+2), (-a+1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$0.160486773$
$17.96736562$
1.258473281
\( -\frac{721}{75} a - \frac{1}{15} \)
\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( 3 a + 6\) , \( 4 a + 7\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(3a+6\right){x}+4a+7$
1875.1-k1
1875.1-k
$6$
$8$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
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
\( -\frac{721}{75} a - \frac{1}{15} \)
\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( -16 a - 28\) , \( -474 a - 849\bigr] \)
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-16a-28\right){x}-474a-849$
1875.1-bj1
1875.1-bj
$6$
$8$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
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
\( -\frac{721}{75} a - \frac{1}{15} \)
\( \bigl[a\) , \( -a\) , \( a + 1\) , \( -3 a\) , \( 9 a - 9\bigr] \)
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}-3a{x}+9a-9$
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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.