| 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 |
| 5929.2-b3 |
5929.2-b |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
5929.2 |
\( 7^{2} \cdot 11^{2} \) |
\( 7^{4} \cdot 11^{18} \) |
$1.35814$ |
$(-3a+1), (3a-2), (11)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.1[2] |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$0.200443024$ |
0.925806674 |
\( \frac{9463555063808}{115539436859} \) |
\( \bigl[0\) , \( a - 1\) , \( 1\) , \( -441 a\) , \( -15815\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a-1\right){x}^{2}-441a{x}-15815$ |
| 5929.1-b3 |
5929.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
5929.1 |
\( 7^{2} \cdot 11^{2} \) |
\( 7^{4} \cdot 11^{18} \) |
$1.56825$ |
$(7), (11)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \cdot 3^{2} \) |
$0.356556453$ |
$0.200443024$ |
2.572893145 |
\( \frac{9463555063808}{115539436859} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( 441\) , \( -15815\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}+441{x}-15815$ |
| 847.2-b3 |
847.2-b |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
847.2 |
\( 7 \cdot 11^{2} \) |
\( 7^{4} \cdot 11^{18} \) |
$1.27544$ |
$(-2a+1), (-2a+3), (2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$0.200443024$ |
0.606082737 |
\( \frac{9463555063808}{115539436859} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( 441\) , \( -15815\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}+441{x}-15815$ |
| 5929.2-b3 |
5929.2-b |
$3$ |
$9$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5929.2 |
\( 7^{2} \cdot 11^{2} \) |
\( 7^{4} \cdot 11^{18} \) |
$2.21783$ |
$(a+3), (a-3), (7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.2 |
$4$ |
\( 2 \) |
$1$ |
$0.200443024$ |
1.133876976 |
\( \frac{9463555063808}{115539436859} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( 441\) , \( -15815\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}+441{x}-15815$ |
| 539.1-b3 |
539.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
539.1 |
\( 7^{2} \cdot 11 \) |
\( 7^{4} \cdot 11^{18} \) |
$1.42801$ |
$(-2a+1), (7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cn, 3B.1.2 |
$4$ |
\( 2^{2} \) |
$1$ |
$0.200443024$ |
1.933947068 |
\( \frac{9463555063808}{115539436859} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( 441\) , \( -15815\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}+441{x}-15815$ |
| 5929.5-b3 |
5929.5-b |
$3$ |
$9$ |
\(\Q(\sqrt{-19}) \) |
$2$ |
$[0, 1]$ |
5929.5 |
\( 7^{2} \cdot 11^{2} \) |
\( 7^{4} \cdot 11^{18} \) |
$3.41791$ |
$(-a-1), (a-2), (a+2), (a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2^{2} \) |
$6.244421456$ |
$0.200443024$ |
4.594373911 |
\( \frac{9463555063808}{115539436859} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( 441\) , \( -15815\bigr] \) |
${y}^2+{y}={x}^3+{x}^2+441{x}-15815$ |
| 847.2-d3 |
847.2-d |
$3$ |
$9$ |
\(\Q(\sqrt{-35}) \) |
$2$ |
$[0, 1]$ |
847.2 |
\( 7 \cdot 11^{2} \) |
\( 7^{4} \cdot 11^{18} \) |
$2.85196$ |
$(7,a+3), (a+1), (a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$0.200443024$ |
0.271048440 |
\( \frac{9463555063808}{115539436859} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( 441\) , \( -15815\bigr] \) |
${y}^2+{y}={x}^3+{x}^2+441{x}-15815$ |
| 5929.2-a3 |
5929.2-a |
$3$ |
$9$ |
\(\Q(\sqrt{-43}) \) |
$2$ |
$[0, 1]$ |
5929.2 |
\( 7^{2} \cdot 11^{2} \) |
\( 7^{4} \cdot 11^{18} \) |
$5.14184$ |
$(-a), (a-1), (7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.2 |
$4$ |
\( 2 \) |
$1$ |
$0.200443024$ |
0.489076395 |
\( \frac{9463555063808}{115539436859} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( 441\) , \( -15815\bigr] \) |
${y}^2+{y}={x}^3+{x}^2+441{x}-15815$ |
| 539.2-g3 |
539.2-g |
$3$ |
$9$ |
\(\Q(\sqrt{-55}) \) |
$2$ |
$[0, 1]$ |
539.2 |
\( 7^{2} \cdot 11 \) |
\( 7^{4} \cdot 11^{18} \) |
$3.19313$ |
$(7,a), (7,a+6), (11,a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2^{3} \) |
$3.077885547$ |
$0.200443024$ |
2.662024496 |
\( \frac{9463555063808}{115539436859} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( 441\) , \( -15815\bigr] \) |
${y}^2+{y}={x}^3+{x}^2+441{x}-15815$ |
| 847.1-e3 |
847.1-e |
$3$ |
$9$ |
\(\Q(\sqrt{-14}) \) |
$2$ |
$[0, 1]$ |
847.1 |
\( 7 \cdot 11^{2} \) |
\( 7^{4} \cdot 11^{18} \) |
$3.60748$ |
$(7,a), (11)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs.1.1 |
|
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$0.200443024$ |
8.707328091 |
\( \frac{9463555063808}{115539436859} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( 441\) , \( -15815\bigr] \) |
${y}^2+{y}={x}^3+{x}^2+441{x}-15815$ |
| 5929.1-a3 |
5929.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{-67}) \) |
$2$ |
$[0, 1]$ |
5929.1 |
\( 7^{2} \cdot 11^{2} \) |
\( 7^{4} \cdot 11^{18} \) |
$6.41832$ |
$(7), (11)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1.576237265$ |
$0.200443024$ |
2.779122138 |
\( \frac{9463555063808}{115539436859} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( 441\) , \( -15815\bigr] \) |
${y}^2+{y}={x}^3+{x}^2+441{x}-15815$ |
| 847.2-h3 |
847.2-h |
$3$ |
$9$ |
\(\Q(\sqrt{-21}) \) |
$2$ |
$[0, 1]$ |
847.2 |
\( 7 \cdot 11^{2} \) |
\( 7^{4} \cdot 11^{18} \) |
$4.41824$ |
$(7,a), (11,a+1), (11,a+10)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs.1.1 |
$25$ |
\( 2^{2} \) |
$1$ |
$0.200443024$ |
4.374025396 |
\( \frac{9463555063808}{115539436859} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( 441\) , \( -15815\bigr] \) |
${y}^2+{y}={x}^3+{x}^2+441{x}-15815$ |
| 539.1-b3 |
539.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{-22}) \) |
$2$ |
$[0, 1]$ |
539.1 |
\( 7^{2} \cdot 11 \) |
\( 7^{4} \cdot 11^{18} \) |
$4.03903$ |
$(11,a), (7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs.1.1 |
$4$ |
\( 2^{2} \) |
$1$ |
$0.200443024$ |
0.683753543 |
\( \frac{9463555063808}{115539436859} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( 441\) , \( -15815\bigr] \) |
${y}^2+{y}={x}^3+{x}^2+441{x}-15815$ |
| 847.1-d3 |
847.1-d |
$3$ |
$9$ |
\(\Q(\sqrt{-91}) \) |
$2$ |
$[0, 1]$ |
847.1 |
\( 7 \cdot 11^{2} \) |
\( 7^{4} \cdot 11^{18} \) |
$4.59865$ |
$(7,a+3), (11)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs.1.1 |
|
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$0.200443024$ |
6.042966591 |
\( \frac{9463555063808}{115539436859} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( 441\) , \( -15815\bigr] \) |
${y}^2+{y}={x}^3+{x}^2+441{x}-15815$ |
| 847.1-c3 |
847.1-c |
$3$ |
$9$ |
\(\Q(\sqrt{-119}) \) |
$2$ |
$[0, 1]$ |
847.1 |
\( 7 \cdot 11^{2} \) |
\( 7^{4} \cdot 11^{18} \) |
$5.25875$ |
$(7,a+3), (11)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs.1.1 |
|
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$0.400886049$ |
9.681390930 |
\( \frac{9463555063808}{115539436859} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( 441\) , \( -15815\bigr] \) |
${y}^2+{y}={x}^3+{x}^2+441{x}-15815$ |
| 77.1-d3 |
77.1-d |
$3$ |
$9$ |
\(\Q(\sqrt{-231}) \) |
$2$ |
$[0, 1]$ |
77.1 |
\( 7 \cdot 11 \) |
\( 7^{4} \cdot 11^{18} \) |
$4.02316$ |
$(7,a+3), (11,a+5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs.1.1 |
$9$ |
\( 2^{3} \) |
$1$ |
$0.200443024$ |
1.899098321 |
\( \frac{9463555063808}{115539436859} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( 441\) , \( -15815\bigr] \) |
${y}^2+{y}={x}^3+{x}^2+441{x}-15815$ |
| 77.1-d3 |
77.1-d |
$3$ |
$9$ |
\(\Q(\sqrt{-77}) \) |
$2$ |
$[0, 1]$ |
77.1 |
\( 7 \cdot 11 \) |
\( 7^{4} \cdot 11^{18} \) |
$4.64554$ |
$(7,a), (11,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2^{3} \) |
$1$ |
$0.200443024$ |
0.182740821 |
\( \frac{9463555063808}{115539436859} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( 441\) , \( -15815\bigr] \) |
${y}^2+{y}={x}^3+{x}^2+441{x}-15815$ |
| 77.1-j3 |
77.1-j |
$3$ |
$9$ |
\(\Q(\sqrt{-154}) \) |
$2$ |
$[0, 1]$ |
77.1 |
\( 7 \cdot 11 \) |
\( 7^{4} \cdot 11^{18} \) |
$6.56979$ |
$(7,a), (11,a)$ |
$0 \le r \le 2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs.1.1 |
$16$ |
\( 2^{3} \) |
$1$ |
$0.400886049$ |
2.067476381 |
\( \frac{9463555063808}{115539436859} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( 441\) , \( -15815\bigr] \) |
${y}^2+{y}={x}^3+{x}^2+441{x}-15815$ |
| 847.1-c3 |
847.1-c |
$3$ |
$9$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
847.1 |
\( 7 \cdot 11^{2} \) |
\( 7^{4} \cdot 11^{18} \) |
$2.20912$ |
$(a+3), (11)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$0.266569154$ |
2.094125706 |
\( \frac{9463555063808}{115539436859} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( 441\) , \( -15815\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}+441{x}-15815$ |
| 539.1-f3 |
539.1-f |
$3$ |
$9$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
539.1 |
\( 7^{2} \cdot 11 \) |
\( 7^{4} \cdot 11^{18} \) |
$2.47339$ |
$(-4a-9), (7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2^{2} \) |
$6.706046397$ |
$0.266569154$ |
2.489484723 |
\( \frac{9463555063808}{115539436859} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( 441\) , \( -15815\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}+441{x}-15815$ |
| 77.1-e3 |
77.1-e |
$3$ |
$9$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
77.1 |
\( 7 \cdot 11 \) |
\( 7^{4} \cdot 11^{18} \) |
$2.32277$ |
$(a+3), (a-6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2^{3} \) |
$3.428115269$ |
$0.266569154$ |
1.666249113 |
\( \frac{9463555063808}{115539436859} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( 441\) , \( -15815\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}+441{x}-15815$ |
*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.
