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
30625.1-a1
30625.1-a
$2$
$5$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
30625.1
\( 5^{4} \cdot 7^{2} \)
\( 5^{6} \cdot 7^{10} \)
$3.34351$
$(5), (7)$
$2$
$\Z/5\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$5$
5B.1.1
$1$
\( 2 \cdot 5 \)
$2.137492530$
$0.897281548$
2.169893045
\( -\frac{2887553024}{16807} \)
\( \bigl[0\) , \( -1\) , \( 1\) , \( -148\) , \( 748\bigr] \)
${y}^2+{y}={x}^{3}-{x}^{2}-148{x}+748$
30625.1-a2
30625.1-a
$2$
$5$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
30625.1
\( 5^{4} \cdot 7^{2} \)
\( 5^{6} \cdot 7^{2} \)
$3.34351$
$(5), (7)$
$2$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$5$
5B.1.2
$1$
\( 2 \)
$0.085499701$
$4.486407744$
2.169893045
\( \frac{4096}{7} \)
\( \bigl[0\) , \( -1\) , \( 1\) , \( 2\) , \( -2\bigr] \)
${y}^2+{y}={x}^{3}-{x}^{2}+2{x}-2$
30625.1-b1
30625.1-b
$3$
$9$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
30625.1
\( 5^{4} \cdot 7^{2} \)
\( 5^{30} \cdot 7^{2} \)
$3.34351$
$(5), (7)$
$2$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3B
$1$
\( 2^{2} \)
$2.180275799$
$0.154995040$
3.823263413
\( -\frac{250523582464}{13671875} \)
\( \bigl[0\) , \( -1\) , \( 1\) , \( -3283\) , \( -74657\bigr] \)
${y}^2+{y}={x}^{3}-{x}^{2}-3283{x}-74657$
30625.1-b2
30625.1-b
$3$
$9$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
30625.1
\( 5^{4} \cdot 7^{2} \)
\( 5^{14} \cdot 7^{2} \)
$3.34351$
$(5), (7)$
$2$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3B
$1$
\( 2^{2} \)
$0.242252866$
$1.394955364$
3.823263413
\( -\frac{262144}{35} \)
\( \bigl[0\) , \( -1\) , \( 1\) , \( -33\) , \( 93\bigr] \)
${y}^2+{y}={x}^{3}-{x}^{2}-33{x}+93$
30625.1-b3
30625.1-b
$3$
$9$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
30625.1
\( 5^{4} \cdot 7^{2} \)
\( 5^{18} \cdot 7^{6} \)
$3.34351$
$(5), (7)$
$2$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3Cs
$1$
\( 2^{2} \cdot 3 \)
$0.242252866$
$0.464985121$
3.823263413
\( \frac{71991296}{42875} \)
\( \bigl[0\) , \( -1\) , \( 1\) , \( 217\) , \( -282\bigr] \)
${y}^2+{y}={x}^{3}-{x}^{2}+217{x}-282$
30625.1-c1
30625.1-c
$2$
$5$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
30625.1
\( 5^{4} \cdot 7^{2} \)
\( 5^{18} \cdot 7^{10} \)
$3.34351$
$(5), (7)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$5$
5B.1.4
$4$
\( 2 \cdot 5 \)
$1$
$0.179456309$
5.075790943
\( -\frac{2887553024}{16807} \)
\( \bigl[0\) , \( 1\) , \( 1\) , \( -3708\) , \( 86119\bigr] \)
${y}^2+{y}={x}^{3}+{x}^{2}-3708{x}+86119$
30625.1-c2
30625.1-c
$2$
$5$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
30625.1
\( 5^{4} \cdot 7^{2} \)
\( 5^{18} \cdot 7^{2} \)
$3.34351$
$(5), (7)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$5$
5B.1.3
$4$
\( 2 \)
$1$
$0.897281548$
5.075790943
\( \frac{4096}{7} \)
\( \bigl[0\) , \( 1\) , \( 1\) , \( 42\) , \( -131\bigr] \)
${y}^2+{y}={x}^{3}+{x}^{2}+42{x}-131$
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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.