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-b1
300.1-b
$2$
$2$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
300.1
\( 2^{2} \cdot 3 \cdot 5^{2} \)
\( 2^{4} \cdot 3^{4} \cdot 5^{2} \)
$1.28828$
$(a+1), (a), (5)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2 \cdot 3 \)
$0.084851841$
$22.67813171$
1.666476432
\( -\frac{21248}{45} a - \frac{35536}{45} \)
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -9 a + 16\) , \( -142 a + 246\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-9a+16\right){x}-142a+246$
300.1-c1
300.1-c
$2$
$2$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
300.1
\( 2^{2} \cdot 3 \cdot 5^{2} \)
\( 2^{4} \cdot 3^{4} \cdot 5^{2} \)
$1.28828$
$(a+1), (a), (5)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$1$
$5.874289784$
1.695761394
\( -\frac{21248}{45} a - \frac{35536}{45} \)
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -9 a + 13\) , \( 133 a - 232\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-9a+13\right){x}+133a-232$
3600.1-e1
3600.1-e
$2$
$2$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
3600.1
\( 2^{4} \cdot 3^{2} \cdot 5^{2} \)
\( 2^{4} \cdot 3^{10} \cdot 5^{2} \)
$2.39775$
$(a+1), (a), (5)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$1$
$8.341753900$
2.408056929
\( -\frac{21248}{45} a - \frac{35536}{45} \)
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -349 a + 601\) , \( 36040 a - 62425\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-349a+601\right){x}+36040a-62425$
3600.1-n1
3600.1-n
$2$
$2$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
3600.1
\( 2^{4} \cdot 3^{2} \cdot 5^{2} \)
\( 2^{4} \cdot 3^{10} \cdot 5^{2} \)
$2.39775$
$(a+1), (a), (5)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$1$
$5.323337634$
1.536715208
\( -\frac{21248}{45} a - \frac{35536}{45} \)
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -349 a + 601\) , \( -36041 a + 62423\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-349a+601\right){x}-36041a+62423$
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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.