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-a5
225.1-a
$8$
$16$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
225.1
\( 3^{2} \cdot 5^{2} \)
\( 3^{4} \cdot 5^{4} \)
$0.91566$
$(3), (5)$
$1$
$\Z/2\Z\oplus\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2Cs
$1$
\( 2^{2} \)
$1.378356153$
$4.471403425$
0.582366377
\( \frac{13997521}{225} \)
\( \bigl[1\) , \( 1\) , \( 1\) , \( -5\) , \( 2\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-5{x}+2$
2025.1-a5
2025.1-a
$8$
$16$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
2025.1
\( 3^{4} \cdot 5^{2} \)
\( 3^{16} \cdot 5^{4} \)
$1.58597$
$(3), (5)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2Cs
$4$
\( 2^{3} \)
$1$
$1.490467808$
2.253375518
\( \frac{13997521}{225} \)
\( \bigl[1\) , \( -1\) , \( 0\) , \( -45\) , \( -104\bigr] \)
${y}^2+{x}{y}={x}^{3}-{x}^{2}-45{x}-104$
5625.1-b5
5625.1-b
$8$
$16$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
5625.1
\( 3^{2} \cdot 5^{4} \)
\( 3^{4} \cdot 5^{16} \)
$2.04747$
$(3), (5)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2Cs
$4$
\( 2^{3} \)
$1$
$0.894280685$
1.352025311
\( \frac{13997521}{225} \)
\( \bigl[1\) , \( 0\) , \( 1\) , \( -126\) , \( 523\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-126{x}+523$
14400.1-d5
14400.1-d
$8$
$16$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
14400.1
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \)
\( 2^{18} \cdot 3^{4} \cdot 5^{4} \)
$2.58987$
$(a), (3), (5)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2^{4} \)
$1.909501012$
$1.580879841$
4.563832806
\( \frac{13997521}{225} \)
\( \bigl[a\) , \( a\) , \( 0\) , \( -25 a - 11\) , \( 62 a - 3\bigr] \)
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(-25a-11\right){x}+62a-3$
14400.7-d5
14400.7-d
$8$
$16$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
14400.7
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \)
\( 2^{18} \cdot 3^{4} \cdot 5^{4} \)
$2.58987$
$(-a+1), (3), (5)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2^{4} \)
$1.909501012$
$1.580879841$
4.563832806
\( \frac{13997521}{225} \)
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 27 a - 37\) , \( -72 a + 8\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(27a-37\right){x}-72a+8$
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Pari/GP
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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.