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-a8
225.1-a
$8$
$16$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
225.1
\( 3^{2} \cdot 5^{2} \)
\( 3^{8} \cdot 5^{2} \)
$0.91566$
$(3), (5)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$0.689178076$
$0.558925428$
0.582366377
\( \frac{1114544804970241}{405} \)
\( \bigl[1\) , \( 1\) , \( 1\) , \( -2160\) , \( -39540\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-2160{x}-39540$
2025.1-a8
2025.1-a
$8$
$16$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
2025.1
\( 3^{4} \cdot 5^{2} \)
\( 3^{20} \cdot 5^{2} \)
$1.58597$
$(3), (5)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$16$
\( 2^{2} \)
$1$
$0.186308476$
2.253375518
\( \frac{1114544804970241}{405} \)
\( \bigl[1\) , \( -1\) , \( 0\) , \( -19440\) , \( 1048135\bigr] \)
${y}^2+{x}{y}={x}^{3}-{x}^{2}-19440{x}+1048135$
5625.1-b8
5625.1-b
$8$
$16$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
5625.1
\( 3^{2} \cdot 5^{4} \)
\( 3^{8} \cdot 5^{14} \)
$2.04747$
$(3), (5)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$4$
\( 2^{4} \)
$1$
$0.111785085$
1.352025311
\( \frac{1114544804970241}{405} \)
\( \bigl[1\) , \( 0\) , \( 1\) , \( -54001\) , \( -4834477\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-54001{x}-4834477$
14400.1-d8
14400.1-d
$8$
$16$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
14400.1
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \)
\( 2^{18} \cdot 3^{8} \cdot 5^{2} \)
$2.58987$
$(a), (3), (5)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \)
$15.27600809$
$0.197609980$
4.563832806
\( \frac{1114544804970241}{405} \)
\( \bigl[a\) , \( a\) , \( 0\) , \( -10800 a - 4321\) , \( -661377 a + 241559\bigr] \)
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(-10800a-4321\right){x}-661377a+241559$
14400.7-d8
14400.7-d
$8$
$16$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
14400.7
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \)
\( 2^{18} \cdot 3^{8} \cdot 5^{2} \)
$2.58987$
$(-a+1), (3), (5)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \)
$15.27600809$
$0.197609980$
4.563832806
\( \frac{1114544804970241}{405} \)
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 10802 a - 15122\) , \( 657057 a - 441419\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(10802a-15122\right){x}+657057a-441419$
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Pari/GP
SageMath
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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.