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
300.3-i1 300.3-i $2$
$5$
\(\Q(\sqrt{21}) \) $2$
$[2, 0]$
300.3
\( 2^{2} \cdot 3 \cdot 5^{2} \)
\( - 2^{10} \cdot 3^{5} \cdot 5^{2} \)
$1.70423$
$(-a+2), (-a), (2)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ $5$
5B.4.1 $1$
\( 5 \)
$0.102239097$
$10.30074545$
2.298137527
\( \frac{167449}{216} a + \frac{1792795}{864} \)
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -5 a + 7\) , \( -9 a + 21\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-5a+7\right){x}-9a+21$
300.3-l1 300.3-l $2$
$5$
\(\Q(\sqrt{21}) \) $2$
$[2, 0]$
300.3
\( 2^{2} \cdot 3 \cdot 5^{2} \)
\( - 2^{10} \cdot 3^{5} \cdot 5^{2} \)
$1.70423$
$(-a+2), (-a), (2)$
0
$\Z/5\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ $5$
5B.1.1 $1$
\( 5^{2} \)
$1$
$10.44113981$
2.278443501
\( \frac{167449}{216} a + \frac{1792795}{864} \)
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( -2 a - 3\) , \( -a - 2\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-2a-3\right){x}-a-2$
900.2-e1 900.2-e $2$
$5$
\(\Q(\sqrt{21}) \) $2$
$[2, 0]$
900.2
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \)
\( - 2^{10} \cdot 3^{11} \cdot 5^{2} \)
$2.24289$
$(-a+2), (-a), (2)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ $5$
5B.4.1 $1$
\( 2^{2} \)
$0.246495566$
$7.706521872$
3.316254618
\( \frac{167449}{216} a + \frac{1792795}{864} \)
\( \bigl[a\) , \( -1\) , \( 0\) , \( -42 a + 117\) , \( -273 a + 762\bigr] \) ${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-42a+117\right){x}-273a+762$
900.2-w1 900.2-w $2$
$5$
\(\Q(\sqrt{21}) \) $2$
$[2, 0]$
900.2
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \)
\( - 2^{10} \cdot 3^{11} \cdot 5^{2} \)
$2.24289$
$(-a+2), (-a), (2)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ $5$
5B.4.1 $1$
\( 2 \)
$0.900165376$
$4.651969904$
3.655186534
\( \frac{167449}{216} a + \frac{1792795}{864} \)
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -5 a + 2\) , \( -a - 4\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-5a+2\right){x}-a-4$
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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.
