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-a4
15.1-a
$6$
$8$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
15.1
\( 3 \cdot 5 \)
\( 3^{4} \cdot 5^{4} \)
$0.80588$
$(-a+2), (-a+1)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2^{2} \)
$1$
$16.31232646$
0.889910366
\( \frac{169820651}{5625} a + \frac{28920482}{375} \)
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 27 a - 62\) , \( -106 a + 305\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(27a-62\right){x}-106a+305$
15.1-b4
15.1-b
$6$
$8$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
15.1
\( 3 \cdot 5 \)
\( 3^{4} \cdot 5^{4} \)
$0.80588$
$(-a+2), (-a+1)$
0
$\Z/2\Z\oplus\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2^{4} \)
$1$
$19.53039258$
1.065470266
\( \frac{169820651}{5625} a + \frac{28920482}{375} \)
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -4\) , \( 3 a - 1\bigr] \)
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}-4{x}+3a-1$
45.2-a4
45.2-a
$6$
$8$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
45.2
\( 3^{2} \cdot 5 \)
\( 3^{10} \cdot 5^{4} \)
$1.06060$
$(-a+2), (-a+1)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2Cs
$1$
\( 2^{4} \)
$1$
$5.910459118$
1.289767919
\( \frac{169820651}{5625} a + \frac{28920482}{375} \)
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 14 a - 42\) , \( 62 a - 174\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(14a-42\right){x}+62a-174$
45.2-b4
45.2-b
$6$
$8$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
45.2
\( 3^{2} \cdot 5 \)
\( 3^{10} \cdot 5^{4} \)
$1.06060$
$(-a+2), (-a+1)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2Cs
$1$
\( 2^{3} \)
$0.320973547$
$17.96736562$
1.258473281
\( \frac{169820651}{5625} a + \frac{28920482}{375} \)
\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( -12 a - 24\) , \( 16 a + 31\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-12a-24\right){x}+16a+31$
1875.1-k4
1875.1-k
$6$
$8$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
1875.1
\( 3 \cdot 5^{4} \)
\( 3^{4} \cdot 5^{16} \)
$2.69463$
$(-a+2), (-a), (-a+1)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2Cs
$1$
\( 2^{6} \)
$0.970184578$
$3.262465293$
5.525614808
\( \frac{169820651}{5625} a + \frac{28920482}{375} \)
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( 605 a - 1696\) , \( -11457 a + 31973\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(605a-1696\right){x}-11457a+31973$
1875.1-bj4
1875.1-bj
$6$
$8$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
1875.1
\( 3 \cdot 5^{4} \)
\( 3^{4} \cdot 5^{16} \)
$2.69463$
$(-a+2), (-a), (-a+1)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2Cs
$1$
\( 2^{5} \)
$1$
$3.906078517$
1.704752426
\( \frac{169820651}{5625} a + \frac{28920482}{375} \)
\( \bigl[a\) , \( -a\) , \( a + 1\) , \( -3 a - 125\) , \( 259 a - 134\bigr] \)
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-3a-125\right){x}+259a-134$
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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.