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
$1$
$1$
4.4.16997.1
$4$
$[4, 0]$
25.3
\( 5^{2} \)
\( 5^{8} \)
$17.42076$
$(-a^2-a+1)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$1$
\( 2^{2} \)
$1$
$61.37133238$
1.882952680
\( \frac{8133357}{25} a^{3} + \frac{7223444}{25} a^{2} - \frac{42380619}{25} a - \frac{9156051}{5} \)
\( \bigl[a^{2} + a - 3\) , \( -a + 1\) , \( a^{2} + a - 3\) , \( -a^{3} + 6 a - 6\) , \( -9 a^{3} + 6 a^{2} + 55 a - 48\bigr] \)
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-a^{3}+6a-6\right){x}-9a^{3}+6a^{2}+55a-48$
25.3-b1
25.3-b
$1$
$1$
4.4.16997.1
$4$
$[4, 0]$
25.3
\( 5^{2} \)
\( 5^{10} \)
$17.42076$
$(-a^2-a+1)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 1 \)
$1$
$352.0394050$
2.700257252
\( -1623 a^{3} + 1898 a^{2} + 4548 a - 114 \)
\( \bigl[a^{3} - a^{2} - 3 a + 3\) , \( a^{2} - 3\) , \( a^{3} - a^{2} - 3 a + 2\) , \( 3 a - 1\) , \( a^{3} + a^{2} - 2\bigr] \)
${y}^2+\left(a^{3}-a^{2}-3a+3\right){x}{y}+\left(a^{3}-a^{2}-3a+2\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(3a-1\right){x}+a^{3}+a^{2}-2$
25.3-c1
25.3-c
$1$
$1$
4.4.16997.1
$4$
$[4, 0]$
25.3
\( 5^{2} \)
\( 5^{4} \)
$17.42076$
$(-a^2-a+1)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 1 \)
$0.028174239$
$2233.566012$
1.930744681
\( -1623 a^{3} + 1898 a^{2} + 4548 a - 114 \)
\( \bigl[a^{3} - 3 a - 1\) , \( a + 1\) , \( a^{2} - 3\) , \( 3 a^{3} + 5 a^{2} - 12 a - 15\) , \( a^{3} + 3 a^{2} + a - 2\bigr] \)
${y}^2+\left(a^{3}-3a-1\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(3a^{3}+5a^{2}-12a-15\right){x}+a^{3}+3a^{2}+a-2$
25.3-d1
25.3-d
$2$
$5$
4.4.16997.1
$4$
$[4, 0]$
25.3
\( 5^{2} \)
\( 5^{8} \)
$17.42076$
$(-a^2-a+1)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$5$
5B.4.2
$25$
\( 2^{2} \)
$1$
$3.327658221$
2.552422574
\( \frac{5357496973442499987}{25} a^{3} + \frac{4190018497495156254}{25} a^{2} - \frac{29759807723130703029}{25} a - \frac{6303903372448402516}{5} \)
\( \bigl[1\) , \( a^{3} - 2 a^{2} - 5 a + 4\) , \( 1\) , \( 1574 a^{3} - 3343 a^{2} - 2624 a + 3703\) , \( 84078 a^{3} - 176952 a^{2} - 135976 a + 202333\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+\left(a^{3}-2a^{2}-5a+4\right){x}^{2}+\left(1574a^{3}-3343a^{2}-2624a+3703\right){x}+84078a^{3}-176952a^{2}-135976a+202333$
25.3-d2
25.3-d
$2$
$5$
4.4.16997.1
$4$
$[4, 0]$
25.3
\( 5^{2} \)
\( 5^{16} \)
$17.42076$
$(-a^2-a+1)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$5$
5B.4.1
$1$
\( 2^{2} \)
$1$
$83.19145553$
2.552422574
\( \frac{3364042267}{9765625} a^{3} + \frac{1964925889}{9765625} a^{2} - \frac{25655280414}{9765625} a - \frac{3815938726}{1953125} \)
\( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( a^{3} - 2 a^{2} - 3 a + 4\) , \( a\) , \( 180 a^{3} + 156 a^{2} - 937 a - 997\) , \( -3246 a^{3} - 2885 a^{2} + 16915 a + 18278\bigr] \)
${y}^2+\left(a^{3}-a^{2}-3a+2\right){x}{y}+a{y}={x}^{3}+\left(a^{3}-2a^{2}-3a+4\right){x}^{2}+\left(180a^{3}+156a^{2}-937a-997\right){x}-3246a^{3}-2885a^{2}+16915a+18278$
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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.