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-a2
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
$1$
\( 1 \)
$0.689178076$
$8.942806850$
0.582366377
\( -\frac{1}{15} \)
\( \bigl[1\) , \( 1\) , \( 1\) , \( 0\) , \( 0\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}$
2025.1-a2
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
$1$
\( 2^{2} \)
$1$
$2.980935616$
2.253375518
\( -\frac{1}{15} \)
\( \bigl[1\) , \( -1\) , \( 0\) , \( 0\) , \( -5\bigr] \)
${y}^2+{x}{y}={x}^{3}-{x}^{2}-5$
5625.1-b2
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
$1$
\( 2^{2} \)
$1$
$1.788561370$
1.352025311
\( -\frac{1}{15} \)
\( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( 23\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-{x}+23$
14400.1-d2
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
$1$
\( 2^{2} \)
$0.954750506$
$3.161759683$
4.563832806
\( -\frac{1}{15} \)
\( \bigl[a\) , \( a\) , \( 0\) , \( -1\) , \( 3 a - 1\bigr] \)
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}-{x}+3a-1$
14400.7-d2
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
$1$
\( 2^{2} \)
$0.954750506$
$3.161759683$
4.563832806
\( -\frac{1}{15} \)
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 2 a - 2\) , \( -3 a + 1\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(2a-2\right){x}-3a+1$
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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.