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 |
900.1-a1 |
900.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{2} \cdot 3^{2} \cdot 5^{3} \) |
$2.63571$ |
$(-a-1), (-a+2), (2), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$10.78783701$ |
4.006502083 |
\( -\frac{137842}{75} a - \frac{206763}{50} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( 1\) , \( -a - 1\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+{x}-a-1$ |
900.1-b1 |
900.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{2} \cdot 3^{2} \cdot 5^{16} \) |
$2.63571$ |
$(-a-1), (-a+2), (2), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$3.095871229$ |
2.299555419 |
\( \frac{11238253632427}{36621093750} a + \frac{25530816266197}{36621093750} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 120 a + 264\) , \( 306 a + 672\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(120a+264\right){x}+306a+672$ |
900.1-b2 |
900.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{4} \cdot 5^{8} \) |
$2.63571$ |
$(-a-1), (-a+2), (2), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$12.38348491$ |
2.299555419 |
\( -\frac{1107339117}{312500} a + \frac{9206219698}{703125} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -30 a - 66\) , \( 0\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-30a-66\right){x}$ |
900.1-c1 |
900.1-c |
$1$ |
$1$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{6} \cdot 3^{10} \cdot 5^{7} \) |
$2.63571$ |
$(-a-1), (-a+2), (2), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \cdot 5 \) |
$0.439425551$ |
$1.646296837$ |
2.686732615 |
\( \frac{15960776744491}{30375000} a - \frac{184981029506767}{30375000} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 85 a - 410\) , \( -1349 a + 3252\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(85a-410\right){x}-1349a+3252$ |
900.1-d1 |
900.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{16} \cdot 5^{16} \) |
$2.63571$ |
$(-a-1), (-a+2), (2), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{8} \cdot 3 \) |
$1$ |
$0.299157433$ |
2.666502761 |
\( \frac{294954351463474339}{2135742187500} a - \frac{706247196983156426}{1601806640625} \) |
\( \bigl[a + 1\) , \( -1\) , \( a\) , \( 475 a + 955\) , \( 301889 a + 661630\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-{x}^{2}+\left(475a+955\right){x}+301889a+661630$ |
900.1-d2 |
900.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{4} \cdot 5^{4} \) |
$2.63571$ |
$(-a-1), (-a+2), (2), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$0.299157433$ |
2.666502761 |
\( -\frac{85554943975757333790673471}{1500} a + \frac{204855906506388702659500514}{1125} \) |
\( \bigl[a + 1\) , \( -1\) , \( a\) , \( -4925 a - 12165\) , \( -202871 a - 463938\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-4925a-12165\right){x}-202871a-463938$ |
900.1-d3 |
900.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{8} \cdot 5^{8} \) |
$2.63571$ |
$(-a-1), (-a+2), (2), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \cdot 3 \) |
$1$ |
$1.196629735$ |
2.666502761 |
\( -\frac{694674202653933229}{6750000} a + \frac{6653414650282085119}{20250000} \) |
\( \bigl[a + 1\) , \( -1\) , \( a\) , \( -2225 a - 4965\) , \( 89989 a + 197022\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-2225a-4965\right){x}+89989a+197022$ |
900.1-d4 |
900.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{16} \cdot 3^{4} \cdot 5^{4} \) |
$2.63571$ |
$(-a-1), (-a+2), (2), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$4.786518942$ |
2.666502761 |
\( \frac{23045201367769}{96000} a + \frac{18975015785927}{36000} \) |
\( \bigl[a\) , \( 0\) , \( 1\) , \( 717 a - 2305\) , \( 17536 a - 55973\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(717a-2305\right){x}+17536a-55973$ |
900.1-e1 |
900.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{2} \cdot 3^{2} \cdot 5^{24} \) |
$2.63571$ |
$(-a-1), (-a+2), (2), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 11 \) |
$1$ |
$1.230411063$ |
2.513297583 |
\( -\frac{65416907943123070004}{7152557373046875} a + \frac{466100650602549625037}{14305114746093750} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -198 a - 673\) , \( 2558 a + 3982\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-198a-673\right){x}+2558a+3982$ |
900.1-e2 |
900.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{4} \cdot 5^{12} \) |
$2.63571$ |
$(-a-1), (-a+2), (2), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 11 \) |
$1$ |
$1.230411063$ |
2.513297583 |
\( -\frac{73236291142251116}{146484375} a + \frac{2805797225284693813}{1757812500} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -48 a - 343\) , \( -490 a - 2714\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-48a-343\right){x}-490a-2714$ |
900.1-f1 |
900.1-f |
$4$ |
$10$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{8} \cdot 5^{20} \) |
$2.63571$ |
$(-a-1), (-a+2), (2), (3)$ |
$2$ |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 2^{4} \cdot 5^{2} \) |
$0.926027028$ |
$1.872219187$ |
5.151116097 |
\( -\frac{19904714311301}{3164062500} \) |
\( \bigl[a\) , \( 1\) , \( 1\) , \( 2823 a - 9031\) , \( -149493 a + 477287\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(2823a-9031\right){x}-149493a+477287$ |
900.1-f2 |
900.1-f |
$4$ |
$10$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{20} \cdot 3^{40} \cdot 5^{4} \) |
$2.63571$ |
$(-a-1), (-a+2), (2), (3)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$1$ |
\( 2^{4} \) |
$23.15067570$ |
$0.074888767$ |
5.151116097 |
\( -\frac{36267977929301}{89261680665600} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 1\) , \( -3449 a - 7583\) , \( -11821257 a - 25922356\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-3449a-7583\right){x}-11821257a-25922356$ |
900.1-f3 |
900.1-f |
$4$ |
$10$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{40} \cdot 3^{20} \cdot 5^{2} \) |
$2.63571$ |
$(-a-1), (-a+2), (2), (3)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$1$ |
\( 2^{2} \) |
$23.15067570$ |
$0.299555070$ |
5.151116097 |
\( \frac{21685195471991381}{309586821120} \) |
\( \bigl[a\) , \( 1\) , \( 1\) , \( 29048 a - 92951\) , \( 4397257 a - 14040061\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(29048a-92951\right){x}+4397257a-14040061$ |
900.1-f4 |
900.1-f |
$4$ |
$10$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{4} \cdot 5^{10} \) |
$2.63571$ |
$(-a-1), (-a+2), (2), (3)$ |
$2$ |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 2^{2} \cdot 5^{2} \) |
$0.926027028$ |
$7.488876750$ |
5.151116097 |
\( \frac{22095784790981}{450000} \) |
\( \bigl[a\) , \( 1\) , \( 1\) , \( 2923 a - 9351\) , \( -139293 a + 444719\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(2923a-9351\right){x}-139293a+444719$ |
900.1-g1 |
900.1-g |
$4$ |
$4$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{16} \cdot 5^{16} \) |
$2.63571$ |
$(-a-1), (-a+2), (2), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{8} \cdot 3 \) |
$1$ |
$0.299157433$ |
2.666502761 |
\( -\frac{294954351463474339}{2135742187500} a - \frac{1940125733542202687}{6407226562500} \) |
\( \bigl[a\) , \( -a\) , \( a + 1\) , \( -477 a + 1431\) , \( -301890 a + 963519\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-477a+1431\right){x}-301890a+963519$ |
900.1-g2 |
900.1-g |
$4$ |
$4$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{16} \cdot 3^{4} \cdot 5^{4} \) |
$2.63571$ |
$(-a-1), (-a+2), (2), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$4.786518942$ |
2.666502761 |
\( -\frac{23045201367769}{96000} a + \frac{220935730390723}{288000} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -718 a - 1588\) , \( -17536 a - 38437\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-718a-1588\right){x}-17536a-38437$ |
900.1-g3 |
900.1-g |
$4$ |
$4$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{8} \cdot 5^{8} \) |
$2.63571$ |
$(-a-1), (-a+2), (2), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \cdot 3 \) |
$1$ |
$1.196629735$ |
2.666502761 |
\( \frac{694674202653933229}{6750000} a + \frac{571174005290035679}{2531250} \) |
\( \bigl[a\) , \( -a\) , \( a + 1\) , \( 2223 a - 7189\) , \( -89990 a + 287011\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(2223a-7189\right){x}-89990a+287011$ |
900.1-g4 |
900.1-g |
$4$ |
$4$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{4} \cdot 5^{4} \) |
$2.63571$ |
$(-a-1), (-a+2), (2), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$0.299157433$ |
2.666502761 |
\( \frac{85554943975757333790673471}{1500} a + \frac{562758794098282809265981643}{4500} \) |
\( \bigl[a\) , \( -a\) , \( a + 1\) , \( 4923 a - 17089\) , \( 202870 a - 666809\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(4923a-17089\right){x}+202870a-666809$ |
900.1-h1 |
900.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{2} \cdot 3^{2} \cdot 5^{16} \) |
$2.63571$ |
$(-a-1), (-a+2), (2), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$3.095871229$ |
2.299555419 |
\( -\frac{11238253632427}{36621093750} a + \frac{18384534949312}{18310546875} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -120 a + 384\) , \( -306 a + 978\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-120a+384\right){x}-306a+978$ |
900.1-h2 |
900.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{4} \cdot 5^{8} \) |
$2.63571$ |
$(-a-1), (-a+2), (2), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$12.38348491$ |
2.299555419 |
\( \frac{1107339117}{312500} a + \frac{26858826739}{2812500} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 30 a - 96\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(30a-96\right){x}$ |
900.1-i1 |
900.1-i |
$2$ |
$2$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( - 2^{2} \cdot 3^{2} \cdot 5^{8} \) |
$2.63571$ |
$(-a-1), (-a+2), (2), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.841320914$ |
$11.23266571$ |
3.509744614 |
\( -\frac{5621182120957}{93750} a + \frac{17946181535359}{93750} \) |
\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( 30 a - 93\) , \( -108 a + 348\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(30a-93\right){x}-108a+348$ |
900.1-i2 |
900.1-i |
$2$ |
$2$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{4} \cdot 5^{4} \) |
$2.63571$ |
$(-a-1), (-a+2), (2), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.420660457$ |
$22.46533143$ |
3.509744614 |
\( -\frac{13266137}{4500} a + \frac{13792936}{1125} \) |
\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -3\) , \( 0\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}-3{x}$ |
900.1-j1 |
900.1-j |
$1$ |
$1$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{2} \cdot 3^{2} \cdot 5^{3} \) |
$2.63571$ |
$(-a-1), (-a+2), (2), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$10.78783701$ |
4.006502083 |
\( \frac{137842}{75} a - \frac{895973}{150} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -a + 2\) , \( -1\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-a+2\right){x}-1$ |
900.1-k1 |
900.1-k |
$2$ |
$2$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{4} \cdot 5^{4} \) |
$2.63571$ |
$(-a-1), (-a+2), (2), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.420660457$ |
$22.46533143$ |
3.509744614 |
\( \frac{13266137}{4500} a + \frac{41905607}{4500} \) |
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -a - 3\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a-3\right){x}$ |
900.1-k2 |
900.1-k |
$2$ |
$2$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( - 2^{2} \cdot 3^{2} \cdot 5^{8} \) |
$2.63571$ |
$(-a-1), (-a+2), (2), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.841320914$ |
$11.23266571$ |
3.509744614 |
\( \frac{5621182120957}{93750} a + \frac{2054166569067}{15625} \) |
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -31 a - 63\) , \( 108 a + 240\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-31a-63\right){x}+108a+240$ |
900.1-l1 |
900.1-l |
$4$ |
$10$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{2} \cdot 3^{2} \cdot 5^{20} \) |
$2.63571$ |
$(-a-1), (-a+2), (2), (3)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$4$ |
\( 2^{2} \cdot 5^{2} \) |
$1$ |
$2.798086155$ |
2.078366219 |
\( \frac{101259856781}{58593750} \) |
\( \bigl[a\) , \( a\) , \( 1\) , \( 487 a - 1549\) , \( -255 a + 814\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(487a-1549\right){x}-255a+814$ |
900.1-l2 |
900.1-l |
$4$ |
$10$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{4} \cdot 5^{10} \) |
$2.63571$ |
$(-a-1), (-a+2), (2), (3)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 2^{2} \cdot 5^{2} \) |
$1$ |
$11.19234462$ |
2.078366219 |
\( \frac{33417362861}{112500} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -331 a - 728\) , \( 4527 a + 9928\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-331a-728\right){x}+4527a+9928$ |
900.1-l3 |
900.1-l |
$4$ |
$10$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{20} \cdot 3^{20} \cdot 5^{2} \) |
$2.63571$ |
$(-a-1), (-a+2), (2), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$25$ |
\( 2^{2} \) |
$1$ |
$0.447693784$ |
2.078366219 |
\( \frac{1926109896270461}{302330880} \) |
\( \bigl[a\) , \( a\) , \( 1\) , \( 12962 a - 41469\) , \( 1316055 a - 4202154\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(12962a-41469\right){x}+1316055a-4202154$ |
900.1-l4 |
900.1-l |
$4$ |
$10$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{10} \cdot 3^{10} \cdot 5^{4} \) |
$2.63571$ |
$(-a-1), (-a+2), (2), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$100$ |
\( 2^{2} \) |
$1$ |
$0.111923446$ |
2.078366219 |
\( \frac{7888454487007174781}{194400} \) |
\( \bigl[a\) , \( a\) , \( 1\) , \( 207362 a - 663549\) , \( 84441495 a - 269612586\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(207362a-663549\right){x}+84441495a-269612586$ |
900.1-m1 |
900.1-m |
$8$ |
$12$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{24} \cdot 3^{2} \cdot 5^{6} \) |
$2.63571$ |
$(-a-1), (-a+2), (2), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$1.248395236$ |
0.695463527 |
\( -\frac{273359449}{1536000} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -14\) , \( -64\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-14{x}-64$ |
900.1-m2 |
900.1-m |
$8$ |
$12$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{6} \cdot 5^{2} \) |
$2.63571$ |
$(-a-1), (-a+2), (2), (3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$11.23555713$ |
0.695463527 |
\( \frac{357911}{2160} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 1\) , \( 2\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}+2$ |
900.1-m3 |
900.1-m |
$8$ |
$12$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{6} \cdot 3^{2} \cdot 5^{24} \) |
$2.63571$ |
$(-a-1), (-a+2), (2), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$1.248395236$ |
0.695463527 |
\( \frac{10316097499609}{5859375000} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -454\) , \( -544\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-454{x}-544$ |
900.1-m4 |
900.1-m |
$8$ |
$12$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{2} \cdot 3^{24} \cdot 5^{2} \) |
$2.63571$ |
$(-a-1), (-a+2), (2), (3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$2.808889283$ |
0.695463527 |
\( \frac{35578826569}{5314410} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -69\) , \( -194\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-69{x}-194$ |
900.1-m5 |
900.1-m |
$8$ |
$12$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{12} \cdot 5^{4} \) |
$2.63571$ |
$(-a-1), (-a+2), (2), (3)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$11.23555713$ |
0.695463527 |
\( \frac{702595369}{72900} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -19\) , \( 26\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-19{x}+26$ |
900.1-m6 |
900.1-m |
$8$ |
$12$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{12} \cdot 3^{4} \cdot 5^{12} \) |
$2.63571$ |
$(-a-1), (-a+2), (2), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B.1.2 |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$1.248395236$ |
0.695463527 |
\( \frac{4102915888729}{9000000} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -334\) , \( -2368\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-334{x}-2368$ |
900.1-m7 |
900.1-m |
$8$ |
$12$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{2} \cdot 3^{6} \cdot 5^{8} \) |
$2.63571$ |
$(-a-1), (-a+2), (2), (3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$11.23555713$ |
0.695463527 |
\( \frac{2656166199049}{33750} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -289\) , \( 1862\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-289{x}+1862$ |
900.1-m8 |
900.1-m |
$8$ |
$12$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{6} \cdot 3^{8} \cdot 5^{6} \) |
$2.63571$ |
$(-a-1), (-a+2), (2), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$4$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$0.312098809$ |
0.695463527 |
\( \frac{16778985534208729}{81000} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -5334\) , \( -150368\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-5334{x}-150368$ |
900.1-n1 |
900.1-n |
$2$ |
$2$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{2} \cdot 3^{2} \cdot 5^{24} \) |
$2.63571$ |
$(-a-1), (-a+2), (2), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 11 \) |
$1$ |
$1.230411063$ |
2.513297583 |
\( \frac{65416907943123070004}{7152557373046875} a + \frac{335266834716303485029}{14305114746093750} \) |
\( \bigl[a\) , \( 0\) , \( 1\) , \( 197 a - 870\) , \( -2558 a + 6540\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(197a-870\right){x}-2558a+6540$ |
900.1-n2 |
900.1-n |
$2$ |
$2$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{4} \cdot 5^{12} \) |
$2.63571$ |
$(-a-1), (-a+2), (2), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 11 \) |
$1$ |
$1.230411063$ |
2.513297583 |
\( \frac{73236291142251116}{146484375} a + \frac{1926961731577680421}{1757812500} \) |
\( \bigl[a\) , \( 0\) , \( 1\) , \( 47 a - 390\) , \( 490 a - 3204\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(47a-390\right){x}+490a-3204$ |
900.1-o1 |
900.1-o |
$1$ |
$1$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{6} \cdot 3^{10} \cdot 5^{7} \) |
$2.63571$ |
$(-a-1), (-a+2), (2), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \cdot 5 \) |
$0.439425551$ |
$1.646296837$ |
2.686732615 |
\( -\frac{15960776744491}{30375000} a - \frac{14085021063523}{2531250} \) |
\( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( -81 a - 332\) , \( 935 a + 1320\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-81a-332\right){x}+935a+1320$ |
*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.