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
225.1-a7
225.1-a
$8$
$16$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
225.1
\( 3^{2} \cdot 5^{2} \)
\( 3^{2} \cdot 5^{2} \)
$0.91566$
$(3), (5)$
$1$
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 1 \)
$2.756712307$
$2.235701712$
0.582366377
\( \frac{56667352321}{15} \)
\( \bigl[1\) , \( 1\) , \( 1\) , \( -80\) , \( 242\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-80{x}+242$
2025.1-a7
2025.1-a
$8$
$16$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
2025.1
\( 3^{4} \cdot 5^{2} \)
\( 3^{14} \cdot 5^{2} \)
$1.58597$
$(3), (5)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$4$
\( 2^{2} \)
$1$
$0.745233904$
2.253375518
\( \frac{56667352321}{15} \)
\( \bigl[1\) , \( -1\) , \( 0\) , \( -720\) , \( -7259\bigr] \)
${y}^2+{x}{y}={x}^{3}-{x}^{2}-720{x}-7259$
5625.1-b7
5625.1-b
$8$
$16$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
5625.1
\( 3^{2} \cdot 5^{4} \)
\( 3^{2} \cdot 5^{14} \)
$2.04747$
$(3), (5)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$4$
\( 2^{2} \)
$1$
$0.447140342$
1.352025311
\( \frac{56667352321}{15} \)
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2001\) , \( 34273\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-2001{x}+34273$
14400.1-d7
14400.1-d
$8$
$16$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
14400.1
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \)
\( 2^{18} \cdot 3^{2} \cdot 5^{2} \)
$2.58987$
$(a), (3), (5)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \)
$3.819002024$
$0.790439920$
4.563832806
\( \frac{56667352321}{15} \)
\( \bigl[a\) , \( a\) , \( 0\) , \( -400 a - 161\) , \( 4517 a - 1293\bigr] \)
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(-400a-161\right){x}+4517a-1293$
14400.7-d7
14400.7-d
$8$
$16$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
14400.7
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \)
\( 2^{18} \cdot 3^{2} \cdot 5^{2} \)
$2.58987$
$(-a+1), (3), (5)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \)
$3.819002024$
$0.790439920$
4.563832806
\( \frac{56667352321}{15} \)
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 402 a - 562\) , \( -4677 a + 2423\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(402a-562\right){x}-4677a+2423$
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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.