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
336.1-a4 336.1-a $4$
$6$
\(\Q(\sqrt{21}) \) $2$
$[2, 0]$
336.1
\( 2^{4} \cdot 3 \cdot 7 \)
\( 2^{16} \cdot 3^{4} \cdot 7^{6} \)
$1.75321$
$(-a+2), (a+3), (2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$2, 3$
2B , 3B.1.2 $1$
\( 2^{3} \cdot 3^{2} \)
$1$
$0.533054337$
2.093795872
\( \frac{2640279346000}{3087} \)
\( \bigl[0\) , \( 1\) , \( 0\) , \( -1828\) , \( -30700\bigr] \) ${y}^2={x}^{3}+{x}^{2}-1828{x}-30700$
336.1-d4 336.1-d $4$
$6$
\(\Q(\sqrt{21}) \) $2$
$[2, 0]$
336.1
\( 2^{4} \cdot 3 \cdot 7 \)
\( 2^{16} \cdot 3^{4} \cdot 7^{6} \)
$1.75321$
$(-a+2), (a+3), (2)$
$1$
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$2, 3$
2B , 3B.1.1 $1$
\( 2^{2} \cdot 3^{2} \)
$0.998952810$
$5.711517702$
2.490100344
\( \frac{2640279346000}{3087} \)
\( \bigl[0\) , \( a\) , \( 0\) , \( 9142 a - 25595\) , \( -727659 a + 2031306\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(9142a-25595\right){x}-727659a+2031306$
1008.1-b4 1008.1-b $4$
$6$
\(\Q(\sqrt{21}) \) $2$
$[2, 0]$
1008.1
\( 2^{4} \cdot 3^{2} \cdot 7 \)
\( 2^{16} \cdot 3^{10} \cdot 7^{6} \)
$2.30735$
$(-a+2), (a+3), (2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2, 3$
2B , 3B $1$
\( 2^{3} \)
$4.009596522$
$1.007397519$
3.525753077
\( \frac{2640279346000}{3087} \)
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 5486 a - 16453\) , \( 362915 a - 996647\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(5486a-16453\right){x}+362915a-996647$
1008.1-c4 1008.1-c $4$
$6$
\(\Q(\sqrt{21}) \) $2$
$[2, 0]$
1008.1
\( 2^{4} \cdot 3^{2} \cdot 7 \)
\( 2^{16} \cdot 3^{10} \cdot 7^{6} \)
$2.30735$
$(-a+2), (a+3), (2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2, 3$
2B , 3B $1$
\( 2^{3} \)
$4.009596522$
$1.007397519$
3.525753077
\( \frac{2640279346000}{3087} \)
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -5484 a - 10968\) , \( -368400 a - 644700\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-5484a-10968\right){x}-368400a-644700$
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Pari/GP
SageMath
Magma
Oscar
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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.
