| 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 |
| 576.1-a1 |
576.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{22} \) |
$2.35745$ |
$(2), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$0.627096544$ |
0.232897809 |
\( -\frac{3764768000}{177147} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 408 a - 1304\) , \( 7244 a - 23131\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(408a-1304\right){x}+7244a-23131$ |
| 576.1-b1 |
576.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{14} \) |
$2.35745$ |
$(2), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$0.873973834$ |
$5.547524399$ |
3.601294554 |
\( -\frac{23359588864}{2187} a - \frac{51217829632}{2187} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -49 a - 105\) , \( 271 a + 585\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-49a-105\right){x}+271a+585$ |
| 576.1-c1 |
576.1-c |
$1$ |
$1$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{2} \) |
$2.35745$ |
$(2), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$0.128532560$ |
$15.43036157$ |
1.473161143 |
\( -\frac{63488}{3} a - \frac{143360}{3} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( a - 2\) , \( a - 3\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(a-2\right){x}+a-3$ |
| 576.1-d1 |
576.1-d |
$1$ |
$1$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{2} \) |
$2.35745$ |
$(2), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$0.157669676$ |
$28.36031148$ |
3.321392230 |
\( \frac{3584}{3} a - \frac{11008}{3} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 2\) , \( 1\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+2{x}+1$ |
| 576.1-e1 |
576.1-e |
$1$ |
$1$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{14} \) |
$2.35745$ |
$(2), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$0.873973834$ |
$5.547524399$ |
3.601294554 |
\( \frac{23359588864}{2187} a - \frac{74577418496}{2187} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 49 a - 154\) , \( -271 a + 856\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(49a-154\right){x}-271a+856$ |
| 576.1-f1 |
576.1-f |
$1$ |
$1$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{10} \) |
$2.35745$ |
$(2), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$0.363251668$ |
$12.43212376$ |
3.354392936 |
\( \frac{210944}{243} a - \frac{483328}{243} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 9 a - 25\) , \( -33 a + 107\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(9a-25\right){x}-33a+107$ |
| 576.1-g1 |
576.1-g |
$2$ |
$2$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{2} \) |
$2.35745$ |
$(2), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$15.07153731$ |
1.399357109 |
\( -\frac{500}{3} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 8 a - 24\) , \( -64 a + 204\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(8a-24\right){x}-64a+204$ |
| 576.1-g2 |
576.1-g |
$2$ |
$2$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{22} \cdot 3^{4} \) |
$2.35745$ |
$(2), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$15.07153731$ |
1.399357109 |
\( \frac{3906250}{9} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -208 a - 456\) , \( 2464 a + 5404\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-208a-456\right){x}+2464a+5404$ |
| 576.1-h1 |
576.1-h |
$1$ |
$1$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{2} \) |
$2.35745$ |
$(2), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$0.590459315$ |
$6.562507725$ |
2.878198873 |
\( 39936 a - \frac{378112}{3} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 4 a + 12\) , \( 1\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(4a+12\right){x}+1$ |
| 576.1-i1 |
576.1-i |
$6$ |
$8$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{22} \cdot 3^{16} \) |
$2.35745$ |
$(2), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.162639934$ |
0.431793631 |
\( \frac{207646}{6561} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 16\) , \( -180\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+16{x}-180$ |
| 576.1-i2 |
576.1-i |
$6$ |
$8$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{2} \) |
$2.35745$ |
$(2), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$18.60223895$ |
0.431793631 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+{x}$ |
| 576.1-i3 |
576.1-i |
$6$ |
$8$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{4} \) |
$2.35745$ |
$(2), (3)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$18.60223895$ |
0.431793631 |
\( \frac{35152}{9} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -4\) , \( 4\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-4{x}+4$ |
| 576.1-i4 |
576.1-i |
$6$ |
$8$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{8} \) |
$2.35745$ |
$(2), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$4.650559737$ |
0.431793631 |
\( \frac{1556068}{81} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -24\) , \( -36\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-24{x}-36$ |
| 576.1-i5 |
576.1-i |
$6$ |
$8$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{2} \) |
$2.35745$ |
$(2), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$18.60223895$ |
0.431793631 |
\( \frac{28756228}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -64\) , \( 220\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-64{x}+220$ |
| 576.1-i6 |
576.1-i |
$6$ |
$8$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{22} \cdot 3^{4} \) |
$2.35745$ |
$(2), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$1.162639934$ |
0.431793631 |
\( \frac{3065617154}{9} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -384\) , \( -2772\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-384{x}-2772$ |
| 576.1-j1 |
576.1-j |
$1$ |
$1$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{10} \) |
$2.35745$ |
$(2), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$0.363251668$ |
$12.43212376$ |
3.354392936 |
\( -\frac{210944}{243} a - \frac{272384}{243} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -9 a - 16\) , \( 33 a + 74\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-9a-16\right){x}+33a+74$ |
| 576.1-k1 |
576.1-k |
$1$ |
$1$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{2} \) |
$2.35745$ |
$(2), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$0.128532560$ |
$15.43036157$ |
1.473161143 |
\( \frac{63488}{3} a - \frac{206848}{3} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -a - 1\) , \( -a - 2\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-a-1\right){x}-a-2$ |
| 576.1-l1 |
576.1-l |
$1$ |
$1$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{2} \) |
$2.35745$ |
$(2), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$0.157669676$ |
$28.36031148$ |
3.321392230 |
\( -\frac{3584}{3} a - \frac{7424}{3} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 2\) , \( 1\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+2{x}+1$ |
| 576.1-m1 |
576.1-m |
$1$ |
$1$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{2} \) |
$2.35745$ |
$(2), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$0.590459315$ |
$6.562507725$ |
2.878198873 |
\( -39936 a - \frac{258304}{3} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -4 a + 16\) , \( 1\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-4a+16\right){x}+1$ |
*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.
