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
25.3-a1
25.3-a
$4$
$14$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
25.3
\( 5^{2} \)
\( 5^{6} \)
$0.91566$
$(-a+1)$
0
$\Z/2\Z$
$\textsf{potential}$
$-7$
$N(\mathrm{U}(1))$
✓
✓
$1$
\( 2 \)
$1$
$11.70083348$
1.276665598
\( -3375 \)
\( \bigl[1\) , \( -1\) , \( a\) , \( 2 a - 7\) , \( -5 a + 12\bigr] \)
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(2a-7\right){x}-5a+12$
25.3-a2
25.3-a
$4$
$14$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
25.3
\( 5^{2} \)
\( 5^{6} \)
$0.91566$
$(-a+1)$
0
$\Z/2\Z$
$\textsf{potential}$
$-7$
$N(\mathrm{U}(1))$
✓
✓
$1$
\( 2 \)
$1$
$11.70083348$
1.276665598
\( -3375 \)
\( \bigl[a + 1\) , \( 0\) , \( a\) , \( -a - 3\) , \( -1\bigr] \)
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a-3\right){x}-1$
25.3-a3
25.3-a
$4$
$14$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
25.3
\( 5^{2} \)
\( 5^{6} \)
$0.91566$
$(-a+1)$
0
$\Z/2\Z$
$\textsf{potential}$
$-28$
$N(\mathrm{U}(1))$
✓
✓
$1$
\( 2 \)
$1$
$11.70083348$
1.276665598
\( 16581375 \)
\( \bigl[1\) , \( -1\) , \( a\) , \( 42 a - 122\) , \( -246 a + 683\bigr] \)
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(42a-122\right){x}-246a+683$
25.3-a4
25.3-a
$4$
$14$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
25.3
\( 5^{2} \)
\( 5^{6} \)
$0.91566$
$(-a+1)$
0
$\Z/2\Z$
$\textsf{potential}$
$-28$
$N(\mathrm{U}(1))$
✓
✓
$1$
\( 2 \)
$1$
$11.70083348$
1.276665598
\( 16581375 \)
\( \bigl[a + 1\) , \( 0\) , \( a\) , \( -16 a - 38\) , \( 43 a + 66\bigr] \)
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-16a-38\right){x}+43a+66$
25.3-b1
25.3-b
$2$
$3$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
25.3
\( 5^{2} \)
\( 5^{4} \)
$0.91566$
$(-a+1)$
$1$
$\mathsf{trivial}$
$\textsf{potential}$
$-3$
$N(\mathrm{U}(1))$
✓
✓
$7$
7Ns.2.1
$1$
\( 1 \)
$0.139669982$
$16.42661250$
1.001316654
\( 0 \)
\( \bigl[0\) , \( -a - 1\) , \( a\) , \( a + 2\) , \( a + 1\bigr] \)
${y}^2+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+2\right){x}+a+1$
25.3-b2
25.3-b
$2$
$3$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
25.3
\( 5^{2} \)
\( 5^{4} \)
$0.91566$
$(-a+1)$
$1$
$\mathsf{trivial}$
$\textsf{potential}$
$-3$
$N(\mathrm{U}(1))$
✓
✓
$7$
7Ns.2.1
$1$
\( 3 \)
$0.046556660$
$16.42661250$
1.001316654
\( 0 \)
\( \bigl[0\) , \( a + 1\) , \( a\) , \( a + 2\) , \( 0\bigr] \)
${y}^2+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(a+2\right){x}$
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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.