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
300.1-g6
300.1-g
$8$
$12$
\(\Q(\sqrt{33}) \)
$2$
$[2, 0]$
300.1
\( 2^{2} \cdot 3 \cdot 5^{2} \)
\( 2^{12} \cdot 3^{4} \cdot 5^{12} \)
$2.13637$
$(-a-2), (-a+3), (-2a+7), (5)$
0
$\Z/2\Z\oplus\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2Cs , 3B.1.1
$1$
\( 2^{5} \cdot 3^{3} \)
$1$
$5.367489134$
5.606159561
\( \frac{4102915888729}{9000000} \)
\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( 122736 a - 413897\) , \( -39525706 a + 133291793\bigr] \)
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(122736a-413897\right){x}-39525706a+133291793$
300.1-h6
300.1-h
$8$
$12$
\(\Q(\sqrt{33}) \)
$2$
$[2, 0]$
300.1
\( 2^{2} \cdot 3 \cdot 5^{2} \)
\( 2^{12} \cdot 3^{4} \cdot 5^{12} \)
$2.13637$
$(-a-2), (-a+3), (-2a+7), (5)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2Cs , 3B.1.2
$1$
\( 2^{5} \cdot 3 \)
$1$
$1.248395236$
1.303906299
\( \frac{4102915888729}{9000000} \)
\( \bigl[1\) , \( 0\) , \( 1\) , \( -334\) , \( -2368\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-334{x}-2368$
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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.