| 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 |
$4$ |
$21$ |
6.6.1397493.1 |
$6$ |
$[6, 0]$ |
64.1 |
\( 2^{6} \) |
\( 2^{42} \) |
$149.39235$ |
$(2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3, 7$ |
3B.1.1, 7B.6.3 |
$1$ |
\( 7 \) |
$0.047238327$ |
$13029.94564$ |
2.42979 |
\( -\frac{189613868625}{128} \) |
\( \bigl[a^{5} - 2 a^{4} - 6 a^{3} + 9 a^{2} + 9 a - 6\) , \( a^{3} - a^{2} - 4 a\) , \( a\) , \( -a^{5} - 117 a^{4} - 237 a^{3} - 126 a^{2} - 2 a + 4\) , \( 2525 a^{5} + 3324 a^{4} - 2271 a^{3} - 1226 a^{2} + 1885 a - 313\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-6a^{3}+9a^{2}+9a-6\right){x}{y}+a{y}={x}^{3}+\left(a^{3}-a^{2}-4a\right){x}^{2}+\left(-a^{5}-117a^{4}-237a^{3}-126a^{2}-2a+4\right){x}+2525a^{5}+3324a^{4}-2271a^{3}-1226a^{2}+1885a-313$ |
| 64.1-a2 |
64.1-a |
$4$ |
$21$ |
6.6.1397493.1 |
$6$ |
$[6, 0]$ |
64.1 |
\( 2^{6} \) |
\( 2^{18} \) |
$149.39235$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3, 7$ |
3B.1.2, 7B.6.1 |
$1$ |
\( 3 \) |
$0.992004875$ |
$160.8635265$ |
2.42979 |
\( -\frac{140625}{8} \) |
\( \bigl[a^{5} - 3 a^{4} - 3 a^{3} + 9 a^{2} + 5 a - 3\) , \( -a^{4} + 4 a^{3} - 8 a + 2\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 5 a + 1\) , \( -a^{5} + 2 a^{4} + 10 a^{3} - 12 a^{2} - 24 a + 3\) , \( a^{5} + a^{4} - 5 a^{3} - 10 a^{2} - 7 a - 4\bigr] \) |
${y}^2+\left(a^{5}-3a^{4}-3a^{3}+9a^{2}+5a-3\right){x}{y}+\left(a^{4}-2a^{3}-3a^{2}+5a+1\right){y}={x}^{3}+\left(-a^{4}+4a^{3}-8a+2\right){x}^{2}+\left(-a^{5}+2a^{4}+10a^{3}-12a^{2}-24a+3\right){x}+a^{5}+a^{4}-5a^{3}-10a^{2}-7a-4$ |
| 64.1-a3 |
64.1-a |
$4$ |
$21$ |
6.6.1397493.1 |
$6$ |
$[6, 0]$ |
64.1 |
\( 2^{6} \) |
\( 2^{126} \) |
$149.39235$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3, 7$ |
3B.1.2, 7B.6.3 |
$1$ |
\( 3 \cdot 7 \) |
$0.141714982$ |
$160.8635265$ |
2.42979 |
\( -\frac{1159088625}{2097152} \) |
\( \bigl[a^{3} - a^{2} - 3 a\) , \( a^{5} - 3 a^{4} - 4 a^{3} + 11 a^{2} + 6 a - 5\) , \( a^{5} - 3 a^{4} - 2 a^{3} + 8 a^{2} + a - 2\) , \( -85 a^{5} + 97 a^{4} + 338 a^{3} - 237 a^{2} - 347 a + 77\) , \( 2530 a^{5} - 1383 a^{4} - 9879 a^{3} + 1347 a^{2} + 6782 a - 1319\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a\right){x}{y}+\left(a^{5}-3a^{4}-2a^{3}+8a^{2}+a-2\right){y}={x}^{3}+\left(a^{5}-3a^{4}-4a^{3}+11a^{2}+6a-5\right){x}^{2}+\left(-85a^{5}+97a^{4}+338a^{3}-237a^{2}-347a+77\right){x}+2530a^{5}-1383a^{4}-9879a^{3}+1347a^{2}+6782a-1319$ |
| 64.1-a4 |
64.1-a |
$4$ |
$21$ |
6.6.1397493.1 |
$6$ |
$[6, 0]$ |
64.1 |
\( 2^{6} \) |
\( 2^{6} \) |
$149.39235$ |
$(2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3, 7$ |
3B.1.1, 7B.6.1 |
$1$ |
\( 1 \) |
$0.330668291$ |
$13029.94564$ |
2.42979 |
\( \frac{3375}{2} \) |
\( \bigl[a^{5} - 3 a^{4} - 3 a^{3} + 10 a^{2} + 4 a - 4\) , \( -a^{5} + 2 a^{4} + 5 a^{3} - 5 a^{2} - 10 a - 1\) , \( a^{2} - a - 2\) , \( 12 a^{5} - 30 a^{4} - 52 a^{3} + 94 a^{2} + 87 a - 23\) , \( -23 a^{5} + 55 a^{4} + 102 a^{3} - 168 a^{2} - 169 a + 38\bigr] \) |
${y}^2+\left(a^{5}-3a^{4}-3a^{3}+10a^{2}+4a-4\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(-a^{5}+2a^{4}+5a^{3}-5a^{2}-10a-1\right){x}^{2}+\left(12a^{5}-30a^{4}-52a^{3}+94a^{2}+87a-23\right){x}-23a^{5}+55a^{4}+102a^{3}-168a^{2}-169a+38$ |
| 64.1-b1 |
64.1-b |
$1$ |
$1$ |
6.6.1397493.1 |
$6$ |
$[6, 0]$ |
64.1 |
\( 2^{6} \) |
\( 2^{42} \) |
$149.39235$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7Nn |
$1$ |
\( 7 \) |
$0.059228742$ |
$1399.516486$ |
2.94500 |
\( \frac{348831}{8} a^{5} - \frac{1046493}{8} a^{4} - \frac{4926215}{32} a^{3} + \frac{7019201}{16} a^{2} + \frac{3530891}{16} a - \frac{30188951}{128} \) |
\( \bigl[a^{5} - 2 a^{4} - 6 a^{3} + 8 a^{2} + 10 a - 4\) , \( -a^{5} + 4 a^{4} + a^{3} - 13 a^{2} + a + 5\) , \( a^{3} - 2 a^{2} - a + 2\) , \( 6 a^{5} - 17 a^{4} - 21 a^{3} + 56 a^{2} + 28 a - 25\) , \( -5 a^{4} + 17 a^{3} - a^{2} - 32 a + 19\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-6a^{3}+8a^{2}+10a-4\right){x}{y}+\left(a^{3}-2a^{2}-a+2\right){y}={x}^{3}+\left(-a^{5}+4a^{4}+a^{3}-13a^{2}+a+5\right){x}^{2}+\left(6a^{5}-17a^{4}-21a^{3}+56a^{2}+28a-25\right){x}-5a^{4}+17a^{3}-a^{2}-32a+19$ |
| 64.1-c1 |
64.1-c |
$1$ |
$1$ |
6.6.1397493.1 |
$6$ |
$[6, 0]$ |
64.1 |
\( 2^{6} \) |
\( 2^{42} \) |
$149.39235$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7Nn |
$1$ |
\( 7 \) |
$0.059228742$ |
$1399.516486$ |
2.94500 |
\( \frac{348831}{8} a^{5} - \frac{1046493}{8} a^{4} - \frac{4926215}{32} a^{3} + \frac{7019201}{16} a^{2} + \frac{3530891}{16} a - \frac{30188951}{128} \) |
\( \bigl[a^{2} - a - 1\) , \( a^{5} - 4 a^{4} + a^{3} + 9 a^{2} - 6 a - 1\) , \( a^{5} - 2 a^{4} - 5 a^{3} + 6 a^{2} + 8 a - 1\) , \( 3 a^{5} - 11 a^{4} + 23 a^{2} - 10 a + 2\) , \( -a^{5} + 9 a^{4} - 10 a^{3} - 23 a^{2} + 14 a - 2\bigr] \) |
${y}^2+\left(a^{2}-a-1\right){x}{y}+\left(a^{5}-2a^{4}-5a^{3}+6a^{2}+8a-1\right){y}={x}^{3}+\left(a^{5}-4a^{4}+a^{3}+9a^{2}-6a-1\right){x}^{2}+\left(3a^{5}-11a^{4}+23a^{2}-10a+2\right){x}-a^{5}+9a^{4}-10a^{3}-23a^{2}+14a-2$ |
| 64.1-d1 |
64.1-d |
$4$ |
$21$ |
6.6.1397493.1 |
$6$ |
$[6, 0]$ |
64.1 |
\( 2^{6} \) |
\( 2^{42} \) |
$149.39235$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3, 7$ |
3B.1.2, 7B.1.3 |
$49$ |
\( 7 \) |
$8.578636127$ |
$0.141300615$ |
2.11024 |
\( -\frac{189613868625}{128} \) |
\( \bigl[1\) , \( -a^{5} + 3 a^{4} + 4 a^{3} - 11 a^{2} - 6 a + 4\) , \( a^{5} - 3 a^{4} - 2 a^{3} + 7 a^{2} + 2 a\) , \( -a^{5} + 3 a^{4} + 2 a^{3} - 7 a^{2} - 2 a - 117\) , \( 39 a^{5} - 117 a^{4} - 157 a^{3} + 431 a^{2} + 236 a - 672\bigr] \) |
${y}^2+{x}{y}+\left(a^{5}-3a^{4}-2a^{3}+7a^{2}+2a\right){y}={x}^{3}+\left(-a^{5}+3a^{4}+4a^{3}-11a^{2}-6a+4\right){x}^{2}+\left(-a^{5}+3a^{4}+2a^{3}-7a^{2}-2a-117\right){x}+39a^{5}-117a^{4}-157a^{3}+431a^{2}+236a-672$ |
| 64.1-d2 |
64.1-d |
$4$ |
$21$ |
6.6.1397493.1 |
$6$ |
$[6, 0]$ |
64.1 |
\( 2^{6} \) |
\( 2^{18} \) |
$149.39235$ |
$(2)$ |
$1$ |
$\Z/21\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3, 7$ |
3B.1.1, 7B.1.1 |
$1$ |
\( 3 \) |
$0.408506482$ |
$149614.8855$ |
2.11024 |
\( -\frac{140625}{8} \) |
\( \bigl[a^{5} - 3 a^{4} - 2 a^{3} + 7 a^{2} + 2 a - 1\) , \( a^{5} - 3 a^{4} - 4 a^{3} + 11 a^{2} + 6 a - 6\) , \( a^{3} - 2 a^{2} - 2 a + 3\) , \( -1\) , \( -4 a^{5} + 12 a^{4} + 14 a^{3} - 40 a^{2} - 20 a + 21\bigr] \) |
${y}^2+\left(a^{5}-3a^{4}-2a^{3}+7a^{2}+2a-1\right){x}{y}+\left(a^{3}-2a^{2}-2a+3\right){y}={x}^{3}+\left(a^{5}-3a^{4}-4a^{3}+11a^{2}+6a-6\right){x}^{2}-{x}-4a^{5}+12a^{4}+14a^{3}-40a^{2}-20a+21$ |
| 64.1-d3 |
64.1-d |
$4$ |
$21$ |
6.6.1397493.1 |
$6$ |
$[6, 0]$ |
64.1 |
\( 2^{6} \) |
\( 2^{126} \) |
$149.39235$ |
$(2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3, 7$ |
3B.1.1, 7B.1.3 |
$49$ |
\( 3 \cdot 7 \) |
$2.859545375$ |
$1.271705543$ |
2.11024 |
\( -\frac{1159088625}{2097152} \) |
\( \bigl[a^{5} - 3 a^{4} - 2 a^{3} + 7 a^{2} + 2 a - 1\) , \( a^{5} - 3 a^{4} - 4 a^{3} + 11 a^{2} + 6 a - 6\) , \( a^{3} - 2 a^{2} - 2 a + 3\) , \( 40 a^{5} - 120 a^{4} - 130 a^{3} + 380 a^{2} + 180 a - 201\) , \( 346 a^{5} - 1038 a^{4} - 1162 a^{3} + 3362 a^{2} + 1632 a - 1777\bigr] \) |
${y}^2+\left(a^{5}-3a^{4}-2a^{3}+7a^{2}+2a-1\right){x}{y}+\left(a^{3}-2a^{2}-2a+3\right){y}={x}^{3}+\left(a^{5}-3a^{4}-4a^{3}+11a^{2}+6a-6\right){x}^{2}+\left(40a^{5}-120a^{4}-130a^{3}+380a^{2}+180a-201\right){x}+346a^{5}-1038a^{4}-1162a^{3}+3362a^{2}+1632a-1777$ |
| 64.1-d4 |
64.1-d |
$4$ |
$21$ |
6.6.1397493.1 |
$6$ |
$[6, 0]$ |
64.1 |
\( 2^{6} \) |
\( 2^{6} \) |
$149.39235$ |
$(2)$ |
$1$ |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3, 7$ |
3B.1.2, 7B.1.1 |
$1$ |
\( 1 \) |
$1.225519446$ |
$16623.87616$ |
2.11024 |
\( \frac{3375}{2} \) |
\( \bigl[1\) , \( -a^{5} + 3 a^{4} + 4 a^{3} - 11 a^{2} - 6 a + 4\) , \( a^{5} - 3 a^{4} - 2 a^{3} + 7 a^{2} + 2 a\) , \( -a^{5} + 3 a^{4} + 2 a^{3} - 7 a^{2} - 2 a + 3\) , \( -a^{5} + 3 a^{4} + 3 a^{3} - 9 a^{2} - 4 a + 2\bigr] \) |
${y}^2+{x}{y}+\left(a^{5}-3a^{4}-2a^{3}+7a^{2}+2a\right){y}={x}^{3}+\left(-a^{5}+3a^{4}+4a^{3}-11a^{2}-6a+4\right){x}^{2}+\left(-a^{5}+3a^{4}+2a^{3}-7a^{2}-2a+3\right){x}-a^{5}+3a^{4}+3a^{3}-9a^{2}-4a+2$ |
*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.
