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-a4
15.2-a
$6$
$8$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
15.2
\( 3 \cdot 5 \)
\( 3^{4} \cdot 5^{4} \)
$0.80588$
$(-a+2), (-a)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2^{2} \)
$1$
$16.31232646$
0.889910366
\( -\frac{169820651}{5625} a + \frac{603627881}{5625} \)
\( \bigl[a\) , \( a - 1\) , \( 1\) , \( -24 a - 41\) , \( 65 a + 116\bigr] \)
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-24a-41\right){x}+65a+116$
15.2-b4
15.2-b
$6$
$8$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
15.2
\( 3 \cdot 5 \)
\( 3^{4} \cdot 5^{4} \)
$0.80588$
$(-a+2), (-a)$
0
$\Z/2\Z\oplus\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2^{4} \)
$1$
$19.53039258$
1.065470266
\( -\frac{169820651}{5625} a + \frac{603627881}{5625} \)
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -5\) , \( -3 a - 3\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}-5{x}-3a-3$
45.1-a4
45.1-a
$6$
$8$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
45.1
\( 3^{2} \cdot 5 \)
\( 3^{10} \cdot 5^{4} \)
$1.06060$
$(-a+2), (-a)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2Cs
$1$
\( 2^{4} \)
$1$
$5.910459118$
1.289767919
\( -\frac{169820651}{5625} a + \frac{603627881}{5625} \)
\( \bigl[1\) , \( a\) , \( 1\) , \( -14 a - 28\) , \( -62 a - 112\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-14a-28\right){x}-62a-112$
45.1-b4
45.1-b
$6$
$8$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
45.1
\( 3^{2} \cdot 5 \)
\( 3^{10} \cdot 5^{4} \)
$1.06060$
$(-a+2), (-a)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2Cs
$1$
\( 2^{3} \)
$0.320973547$
$17.96736562$
1.258473281
\( -\frac{169820651}{5625} a + \frac{603627881}{5625} \)
\( \bigl[a\) , \( a\) , \( 0\) , \( 17 a - 43\) , \( -58 a + 163\bigr] \)
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(17a-43\right){x}-58a+163$
1875.1-e4
1875.1-e
$6$
$8$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
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
\( -\frac{169820651}{5625} a + \frac{603627881}{5625} \)
\( \bigl[a + 1\) , \( -1\) , \( a\) , \( a - 127\) , \( -260 a + 126\bigr] \)
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-{x}^{2}+\left(a-127\right){x}-260a+126$
1875.1-bp4
1875.1-bp
$6$
$8$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
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
\( -\frac{169820651}{5625} a + \frac{603627881}{5625} \)
\( \bigl[a\) , \( 0\) , \( 1\) , \( -606 a - 1090\) , \( 11457 a + 20516\bigr] \)
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-606a-1090\right){x}+11457a+20516$
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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.