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-a1 336.1-a $4$
$6$
\(\Q(\sqrt{21}) \) $2$
$[2, 0]$
336.1
\( 2^{4} \cdot 3 \cdot 7 \)
\( 2^{8} \cdot 3^{2} \cdot 7^{12} \)
$1.75321$
$(-a+2), (a+3), (2)$
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
\( -\frac{10061824000}{352947} \)
\( \bigl[0\) , \( 1\) , \( 0\) , \( -113\) , \( -516\bigr] \) ${y}^2={x}^{3}+{x}^{2}-113{x}-516$
336.1-d1 336.1-d $4$
$6$
\(\Q(\sqrt{21}) \) $2$
$[2, 0]$
336.1
\( 2^{4} \cdot 3 \cdot 7 \)
\( 2^{8} \cdot 3^{2} \cdot 7^{12} \)
$1.75321$
$(-a+2), (a+3), (2)$
$1$
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$2, 3$
2B , 3B.1.1 $1$
\( 2^{3} \cdot 3^{2} \)
$0.499476405$
$5.711517702$
2.490100344
\( -\frac{10061824000}{352947} \)
\( \bigl[0\) , \( a\) , \( 0\) , \( 567 a - 1585\) , \( -11818 a + 32988\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(567a-1585\right){x}-11818a+32988$
1008.1-b1 1008.1-b $4$
$6$
\(\Q(\sqrt{21}) \) $2$
$[2, 0]$
1008.1
\( 2^{4} \cdot 3^{2} \cdot 7 \)
\( 2^{8} \cdot 3^{8} \cdot 7^{12} \)
$2.30735$
$(-a+2), (a+3), (2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2, 3$
2B , 3B $1$
\( 2^{2} \)
$8.019193045$
$1.007397519$
3.525753077
\( -\frac{10061824000}{352947} \)
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 341 a - 1018\) , \( 5852 a - 16010\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(341a-1018\right){x}+5852a-16010$
1008.1-c1 1008.1-c $4$
$6$
\(\Q(\sqrt{21}) \) $2$
$[2, 0]$
1008.1
\( 2^{4} \cdot 3^{2} \cdot 7 \)
\( 2^{8} \cdot 3^{8} \cdot 7^{12} \)
$2.30735$
$(-a+2), (a+3), (2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2, 3$
2B , 3B $1$
\( 2^{2} \)
$8.019193045$
$1.007397519$
3.525753077
\( -\frac{10061824000}{352947} \)
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -339 a - 678\) , \( -6192 a - 10836\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-339a-678\right){x}-6192a-10836$
Download
displayed columns for
to
Text
Pari/GP
SageMath
Magma
Oscar
CSV
*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.
