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
64.1-a1 64.1-a $4$
$4$
3.3.169.1 $3$
$[3, 0]$
64.1
\( 2^{6} \)
\( - 2^{24} \)
$2.32334$
$(2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$2$
2B $1$
\( 1 \)
$1$
$82.94864304$
1.595166212
\( 115659804096 a^{2} + 190965142512 a + 43627210848 \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( -155 a^{2} - 255 a - 59\) , \( 2546 a^{2} + 4202 a + 960\bigr] \) ${y}^2={x}^{3}+\left(-155a^{2}-255a-59\right){x}+2546a^{2}+4202a+960$
64.1-a2 64.1-a $4$
$4$
3.3.169.1 $3$
$[3, 0]$
64.1
\( 2^{6} \)
\( - 2^{24} \)
$2.32334$
$(2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$2$
2B $1$
\( 1 \)
$1$
$82.94864304$
1.595166212
\( -422284750704 a^{2} + 537944554800 a + 1541801071152 \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( -5 a^{2} - 15 a - 14\) , \( 54 a^{2} + 100 a + 36\bigr] \) ${y}^2={x}^{3}+\left(-5a^{2}-15a-14\right){x}+54a^{2}+100a+36$
64.1-a3 64.1-a $4$
$4$
3.3.169.1 $3$
$[3, 0]$
64.1
\( 2^{6} \)
\( 2^{12} \)
$2.32334$
$(2)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
✓
$2$
2Cs $1$
\( 1 \)
$1$
$331.7945721$
1.595166212
\( 1168128 \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( -10 a^{2} - 15 a - 4\) , \( 40 a^{2} + 65 a + 15\bigr] \) ${y}^2={x}^{3}+\left(-10a^{2}-15a-4\right){x}+40a^{2}+65a+15$
64.1-a4 64.1-a $4$
$4$
3.3.169.1 $3$
$[3, 0]$
64.1
\( 2^{6} \)
\( - 2^{24} \)
$2.32334$
$(2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$2$
2B $1$
\( 1 \)
$1$
$82.94864304$
1.595166212
\( 306624946608 a^{2} - 728909697312 a - 222643270080 \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( -20 a^{2} + 1\) , \( 40 a^{2} - 12 a - 6\bigr] \) ${y}^2={x}^{3}+\left(-20a^{2}+1\right){x}+40a^{2}-12a-6$
64.1-b1 64.1-b $2$
$3$
3.3.169.1 $3$
$[3, 0]$
64.1
\( 2^{6} \)
\( - 2^{24} \)
$2.32334$
$(2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
✓
$3$
3B.1.2 $9$
\( 1 \)
$1$
$0.447583986$
0.309865836
\( -368484688 \)
\( \bigl[0\) , \( -a^{2} + 2 a + 4\) , \( 0\) , \( -a^{2} - 200 a - 278\) , \( -329 a^{2} - 1965 a - 2085\bigr] \) ${y}^2={x}^{3}+\left(-a^{2}+2a+4\right){x}^{2}+\left(-a^{2}-200a-278\right){x}-329a^{2}-1965a-2085$
64.1-b2 64.1-b $2$
$3$
3.3.169.1 $3$
$[3, 0]$
64.1
\( 2^{6} \)
\( - 2^{24} \)
$2.32334$
$(2)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
✓
$3$
3B.1.1 $1$
\( 3 \)
$1$
$12.08476763$
0.309865836
\( -208 \)
\( \bigl[0\) , \( -a^{2} + 2 a + 4\) , \( 0\) , \( -a^{2} + 2\) , \( -a^{2} - 5 a - 5\bigr] \) ${y}^2={x}^{3}+\left(-a^{2}+2a+4\right){x}^{2}+\left(-a^{2}+2\right){x}-a^{2}-5a-5$
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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.
