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
$2$
$3$
\(\Q(\sqrt{51}) \)
$2$
$[2, 0]$
25.3
\( 5^{2} \)
\( 5^{10} \)
$2.85390$
$(5,a+4)$
0
$\mathsf{trivial}$
$\textsf{potential}$
$-3$
$N(\mathrm{U}(1))$
✓
✓
$1$
\( 1 \)
$1$
$7.346204439$
0.514337188
\( 0 \)
\( \bigl[0\) , \( -a\) , \( 1\) , \( 17\) , \( -a - 6\bigr] \)
${y}^2+{y}={x}^3-w{x}^2+17{x}-w-6$
25.3-a2
25.3-a
$2$
$3$
\(\Q(\sqrt{51}) \)
$2$
$[2, 0]$
25.3
\( 5^{2} \)
\( 3^{12} \cdot 5^{10} \)
$2.85390$
$(5,a+4)$
0
$\mathsf{trivial}$
$\textsf{potential}$
$-3$
$N(\mathrm{U}(1))$
✓
✓
$1$
\( 1 \)
$1$
$7.346204439$
0.514337188
\( 0 \)
\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( -24 a + 155\bigr] \)
${y}^2+{y}={x}^3-24w+155$
25.3-b1
25.3-b
$2$
$3$
\(\Q(\sqrt{51}) \)
$2$
$[2, 0]$
25.3
\( 5^{2} \)
\( 5^{10} \)
$2.85390$
$(5,a+4)$
0
$\mathsf{trivial}$
$\textsf{potential}$
$-3$
$N(\mathrm{U}(1))$
✓
✓
$9$
\( 1 \)
$1$
$7.346204439$
4.629034696
\( 0 \)
\( \bigl[0\) , \( a\) , \( a\) , \( 17\) , \( a - 7\bigr] \)
${y}^2+w{y}={x}^3+w{x}^2+17{x}+w-7$
25.3-b2
25.3-b
$2$
$3$
\(\Q(\sqrt{51}) \)
$2$
$[2, 0]$
25.3
\( 5^{2} \)
\( 3^{12} \cdot 5^{10} \)
$2.85390$
$(5,a+4)$
0
$\mathsf{trivial}$
$\textsf{potential}$
$-3$
$N(\mathrm{U}(1))$
✓
✓
$9$
\( 1 \)
$1$
$7.346204439$
4.629034696
\( 0 \)
\( \bigl[0\) , \( 0\) , \( a\) , \( 0\) , \( 24 a - 168\bigr] \)
${y}^2+w{y}={x}^3+24w-168$
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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.