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
25.2-a1
25.2-a
$4$
$15$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
25.2
\( 5^{2} \)
\( 5^{6} \)
$1.07603$
$(-a-1)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3, 5$
3B , 5B
$9$
\( 1 \)
$1$
$0.914540520$
1.528433200
\( -1407628760845 a - 3086342051803 \)
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -16 a - 38\) , \( -64 a - 195\bigr] \)
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-16a-38\right){x}-64a-195$
25.2-a2
25.2-a
$4$
$15$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
25.2
\( 5^{2} \)
\( 5^{6} \)
$1.07603$
$(-a-1)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3, 5$
3B , 5B
$1$
\( 1 \)
$1$
$8.230864683$
1.528433200
\( -3515 a - 7688 \)
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -a + 2\) , \( -a - 2\bigr] \)
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-a+2\right){x}-a-2$
25.2-a3
25.2-a
$4$
$15$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
25.2
\( 5^{2} \)
\( 5^{6} \)
$1.07603$
$(-a-1)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3, 5$
3B , 5B
$9$
\( 1 \)
$1$
$0.914540520$
1.528433200
\( 1407628760845 a - 4493970812648 \)
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -15 a - 40\) , \( -481 a - 1066\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-15a-40\right){x}-481a-1066$
25.2-a4
25.2-a
$4$
$15$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
25.2
\( 5^{2} \)
\( 5^{6} \)
$1.07603$
$(-a-1)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3, 5$
3B , 5B
$1$
\( 1 \)
$1$
$8.230864683$
1.528433200
\( 3515 a - 11203 \)
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 0\) , \( 17 a + 37\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+17a+37$
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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.