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
450.1-a6
450.1-a
$8$
$12$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
450.1
\( 2 \cdot 3^{2} \cdot 5^{2} \)
\( 2^{12} \cdot 3^{4} \cdot 5^{12} \)
$1.16409$
$(a), (3), (5)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2Cs , 3B.1.2
$1$
\( 2^{3} \cdot 3 \)
$1$
$1.248395236$
0.662061553
\( \frac{4102915888729}{9000000} \)
\( \bigl[1\) , \( 0\) , \( 1\) , \( -334\) , \( -2368\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-334{x}-2368$
3600.1-g6
3600.1-g
$8$
$12$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
3600.1
\( 2^{4} \cdot 3^{2} \cdot 5^{2} \)
\( 2^{24} \cdot 3^{4} \cdot 5^{12} \)
$1.95776$
$(a), (3), (5)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2Cs , 3B
$1$
\( 2^{4} \cdot 3 \)
$1$
$2.683744567$
2.846540973
\( \frac{4102915888729}{9000000} \)
\( \bigl[a\) , \( -1\) , \( 0\) , \( -1334\) , \( 18942\bigr] \)
${y}^2+a{x}{y}={x}^{3}-{x}^{2}-1334{x}+18942$
4050.1-a6
4050.1-a
$8$
$12$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
4050.1
\( 2 \cdot 3^{4} \cdot 5^{2} \)
\( 2^{12} \cdot 3^{16} \cdot 5^{12} \)
$2.01626$
$(a), (3), (5)$
0
$\Z/2\Z\oplus\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2Cs , 3B.1.1
$1$
\( 2^{5} \cdot 3^{2} \)
$1$
$1.789163044$
1.265129321
\( \frac{4102915888729}{9000000} \)
\( \bigl[1\) , \( -1\) , \( 1\) , \( -3002\) , \( 63929\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-3002{x}+63929$
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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.