| 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 |
| 16250.5-a1 |
16250.5-a |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16250.5 |
\( 2 \cdot 5^{4} \cdot 13 \) |
\( 2^{4} \cdot 5^{19} \cdot 13^{3} \) |
$2.01782$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$1.474091777$ |
$0.192856619$ |
2.274306853 |
\( -\frac{1411302663595036}{34328125} a - \frac{1774751413484333}{137312500} \) |
\( \bigl[1\) , \( 1\) , \( i + 1\) , \( -4038 i - 5513\) , \( 174937 i + 124500\bigr] \) |
${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+{x}^{2}+\left(-4038i-5513\right){x}+174937i+124500$ |
| 16250.5-a2 |
16250.5-a |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16250.5 |
\( 2 \cdot 5^{4} \cdot 13 \) |
\( 2^{12} \cdot 5^{17} \cdot 13 \) |
$2.01782$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$0.491363925$ |
$0.578569857$ |
2.274306853 |
\( -\frac{171697}{6500} a + \frac{2279159}{104000} \) |
\( \bigl[1\) , \( 1\) , \( i + 1\) , \( -38 i - 13\) , \( 437 i + 500\bigr] \) |
${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+{x}^{2}+\left(-38i-13\right){x}+437i+500$ |
| 16250.5-a3 |
16250.5-a |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16250.5 |
\( 2 \cdot 5^{4} \cdot 13 \) |
\( 2 \cdot 5^{37} \cdot 13^{3} \) |
$2.01782$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$5.896367111$ |
$0.048214154$ |
2.274306853 |
\( \frac{94290382838862669189021}{261902809143066406250} a + \frac{23228384730714798359947}{261902809143066406250} \) |
\( \bigl[1\) , \( 1\) , \( i + 1\) , \( 11837 i + 3612\) , \( 1029062 i + 473125\bigr] \) |
${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+{x}^{2}+\left(11837i+3612\right){x}+1029062i+473125$ |
| 16250.5-a4 |
16250.5-a |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16250.5 |
\( 2 \cdot 5^{4} \cdot 13 \) |
\( 2^{3} \cdot 5^{26} \cdot 13^{4} \) |
$2.01782$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$1.965455703$ |
$0.144642464$ |
2.274306853 |
\( -\frac{20122730162024161}{27891601562500} a + \frac{104798752060117927}{27891601562500} \) |
\( \bigl[i\) , \( -1\) , \( i + 1\) , \( 2712 i + 238\) , \( 21312 i + 34250\bigr] \) |
${y}^2+i{x}{y}+\left(i+1\right){y}={x}^{3}-{x}^{2}+\left(2712i+238\right){x}+21312i+34250$ |
| 16250.5-a5 |
16250.5-a |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16250.5 |
\( 2 \cdot 5^{4} \cdot 13 \) |
\( 2^{2} \cdot 5^{26} \cdot 13^{6} \) |
$2.01782$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{6} \) |
$2.948183555$ |
$0.096428309$ |
2.274306853 |
\( -\frac{12415547946147007137}{2356840332031250} a + \frac{5474429230691529908}{1178420166015625} \) |
\( \bigl[i\) , \( -1\) , \( i + 1\) , \( -4288 i - 5512\) , \( -158938 i - 129750\bigr] \) |
${y}^2+i{x}{y}+\left(i+1\right){y}={x}^{3}-{x}^{2}+\left(-4288i-5512\right){x}-158938i-129750$ |
| 16250.5-a6 |
16250.5-a |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16250.5 |
\( 2 \cdot 5^{4} \cdot 13 \) |
\( 2 \cdot 5^{22} \cdot 13^{12} \) |
$2.01782$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$5.896367111$ |
$0.048214154$ |
2.274306853 |
\( \frac{4240925829815707588031}{728065160077531250} a + \frac{3613304062782124177817}{728065160077531250} \) |
\( \bigl[i\) , \( -1\) , \( i + 1\) , \( -24413 i - 14637\) , \( 1730187 i - 122375\bigr] \) |
${y}^2+i{x}{y}+\left(i+1\right){y}={x}^{3}-{x}^{2}+\left(-24413i-14637\right){x}+1730187i-122375$ |
| 16250.5-a7 |
16250.5-a |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16250.5 |
\( 2 \cdot 5^{4} \cdot 13 \) |
\( 2^{6} \cdot 5^{22} \cdot 13^{2} \) |
$2.01782$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{6} \) |
$0.982727851$ |
$0.289284928$ |
2.274306853 |
\( \frac{117057737097}{21125000} a + \frac{49160487287}{2640625} \) |
\( \bigl[i\) , \( -1\) , \( i + 1\) , \( 962 i - 12\) , \( -8438 i - 7500\bigr] \) |
${y}^2+i{x}{y}+\left(i+1\right){y}={x}^{3}-{x}^{2}+\left(962i-12\right){x}-8438i-7500$ |
| 16250.5-a8 |
16250.5-a |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16250.5 |
\( 2 \cdot 5^{4} \cdot 13 \) |
\( 2^{3} \cdot 5^{23} \cdot 13 \) |
$2.01782$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$1.965455703$ |
$0.144642464$ |
2.274306853 |
\( \frac{4023422266102893}{20312500} a + \frac{5856979210600901}{20312500} \) |
\( \bigl[1\) , \( 1\) , \( i + 1\) , \( 15212 i - 263\) , \( 530187 i + 497250\bigr] \) |
${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+{x}^{2}+\left(15212i-263\right){x}+530187i+497250$ |
| 16250.5-b1 |
16250.5-b |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16250.5 |
\( 2 \cdot 5^{4} \cdot 13 \) |
\( 2^{4} \cdot 5^{10} \cdot 13^{2} \) |
$2.01782$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \cdot 3 \) |
$0.058724799$ |
$1.742847925$ |
2.456361493 |
\( -\frac{2456215}{676} a + \frac{821220}{169} \) |
\( \bigl[1\) , \( i\) , \( 0\) , \( -4 i + 20\) , \( 36 i + 16\bigr] \) |
${y}^2+{x}{y}={x}^{3}+i{x}^{2}+\left(-4i+20\right){x}+36i+16$ |
| 16250.5-c1 |
16250.5-c |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16250.5 |
\( 2 \cdot 5^{4} \cdot 13 \) |
\( 2^{7} \cdot 5^{17} \cdot 13 \) |
$2.01782$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$0.677761663$ |
1.355523326 |
\( \frac{1736989}{208} a + \frac{2118627}{208} \) |
\( \bigl[1\) , \( i + 1\) , \( 1\) , \( -145 i + 70\) , \( 12 i - 674\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(i+1\right){x}^{2}+\left(-145i+70\right){x}+12i-674$ |
| 16250.5-d1 |
16250.5-d |
$2$ |
$3$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16250.5 |
\( 2 \cdot 5^{4} \cdot 13 \) |
\( 2^{3} \cdot 5^{11} \cdot 13 \) |
$2.01782$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$0.140596485$ |
$2.113453741$ |
2.377153349 |
\( -\frac{2124209}{6500} a - \frac{5592087}{6500} \) |
\( \bigl[1\) , \( 1\) , \( i + 1\) , \( 2 i - 8\) , \( -8 i + 10\bigr] \) |
${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+{x}^{2}+\left(2i-8\right){x}-8i+10$ |
| 16250.5-d2 |
16250.5-d |
$2$ |
$3$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16250.5 |
\( 2 \cdot 5^{4} \cdot 13 \) |
\( 2 \cdot 5^{17} \cdot 13^{3} \) |
$2.01782$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$0.421789456$ |
$0.704484580$ |
2.377153349 |
\( \frac{1498457535463}{8582031250} a + \frac{5584902421359}{8582031250} \) |
\( \bigl[1\) , \( 1\) , \( i + 1\) , \( -23 i + 67\) , \( 177 i - 195\bigr] \) |
${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+{x}^{2}+\left(-23i+67\right){x}+177i-195$ |
| 16250.5-e1 |
16250.5-e |
$2$ |
$3$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16250.5 |
\( 2 \cdot 5^{4} \cdot 13 \) |
\( 2^{3} \cdot 5^{16} \cdot 13^{9} \) |
$2.01782$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 3^{2} \) |
$1$ |
$0.192247496$ |
1.730227465 |
\( \frac{57371821008205}{42417997492} a - \frac{54181111298935}{42417997492} \) |
\( \bigl[1\) , \( i - 1\) , \( i\) , \( -251 i + 1216\) , \( 22748 i + 2208\bigr] \) |
${y}^2+{x}{y}+i{y}={x}^{3}+\left(i-1\right){x}^{2}+\left(-251i+1216\right){x}+22748i+2208$ |
| 16250.5-e2 |
16250.5-e |
$2$ |
$3$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16250.5 |
\( 2 \cdot 5^{4} \cdot 13 \) |
\( 2 \cdot 5^{16} \cdot 13^{3} \) |
$2.01782$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{3} \) |
$1$ |
$0.576742488$ |
1.730227465 |
\( -\frac{317111135}{4394} a + \frac{950272195}{4394} \) |
\( \bigl[1\) , \( i - 1\) , \( i\) , \( 374 i - 34\) , \( 2123 i + 1583\bigr] \) |
${y}^2+{x}{y}+i{y}={x}^{3}+\left(i-1\right){x}^{2}+\left(374i-34\right){x}+2123i+1583$ |
| 16250.5-f1 |
16250.5-f |
$2$ |
$5$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16250.5 |
\( 2 \cdot 5^{4} \cdot 13 \) |
\( 2^{5} \cdot 5^{17} \cdot 13^{5} \) |
$2.01782$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.1.4 |
$1$ |
\( 2 \) |
$1.826121904$ |
$0.349267308$ |
2.551218730 |
\( \frac{7896854157}{2970344} a + \frac{4573167341}{2970344} \) |
\( \bigl[1\) , \( -i + 1\) , \( i\) , \( -418 i + 133\) , \( -137 i - 3361\bigr] \) |
${y}^2+{x}{y}+i{y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(-418i+133\right){x}-137i-3361$ |
| 16250.5-f2 |
16250.5-f |
$2$ |
$5$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16250.5 |
\( 2 \cdot 5^{4} \cdot 13 \) |
\( 2 \cdot 5^{13} \cdot 13 \) |
$2.01782$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.1.3 |
$1$ |
\( 2 \) |
$0.365224380$ |
$1.746336542$ |
2.551218730 |
\( -\frac{74877}{26} a + \frac{83939}{26} \) |
\( \bigl[i\) , \( i - 1\) , \( 1\) , \( 7 i - 17\) , \( 12 i - 14\bigr] \) |
${y}^2+i{x}{y}+{y}={x}^{3}+\left(i-1\right){x}^{2}+\left(7i-17\right){x}+12i-14$ |
| 16250.5-g1 |
16250.5-g |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16250.5 |
\( 2 \cdot 5^{4} \cdot 13 \) |
\( 2^{2} \cdot 5^{23} \cdot 13^{2} \) |
$2.01782$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.341683782$ |
2.733470263 |
\( -\frac{353750760581}{66015625} a - \frac{156546352109}{132031250} \) |
\( \bigl[i\) , \( i - 1\) , \( i + 1\) , \( -493 i + 171\) , \( -1726 i + 4480\bigr] \) |
${y}^2+i{x}{y}+\left(i+1\right){y}={x}^{3}+\left(i-1\right){x}^{2}+\left(-493i+171\right){x}-1726i+4480$ |
| 16250.5-g2 |
16250.5-g |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16250.5 |
\( 2 \cdot 5^{4} \cdot 13 \) |
\( 2^{4} \cdot 5^{19} \cdot 13 \) |
$2.01782$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.683367565$ |
2.733470263 |
\( \frac{5423261}{8125} a - \frac{19770367}{32500} \) |
\( \bigl[1\) , \( -i + 1\) , \( i + 1\) , \( 7 i - 80\) , \( -25 i - 480\bigr] \) |
${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(7i-80\right){x}-25i-480$ |
| 16250.5-h1 |
16250.5-h |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16250.5 |
\( 2 \cdot 5^{4} \cdot 13 \) |
\( 2^{17} \cdot 5^{11} \cdot 13 \) |
$2.01782$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \cdot 3 \cdot 17 \) |
$0.011864458$ |
$0.939702506$ |
4.548817186 |
\( -\frac{19040273}{33280} a - \frac{28339689}{33280} \) |
\( \bigl[i\) , \( -i - 1\) , \( 0\) , \( 30 i + 33\) , \( 88 i - 145\bigr] \) |
${y}^2+i{x}{y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(30i+33\right){x}+88i-145$ |
| 16250.5-i1 |
16250.5-i |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16250.5 |
\( 2 \cdot 5^{4} \cdot 13 \) |
\( 2^{7} \cdot 5^{5} \cdot 13 \) |
$2.01782$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \cdot 7 \) |
$0.047907620$ |
$3.388808315$ |
4.545792784 |
\( \frac{1736989}{208} a + \frac{2118627}{208} \) |
\( \bigl[1\) , \( -i\) , \( 1\) , \( -6 i + 2\) , \( -i - 8\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-i{x}^{2}+\left(-6i+2\right){x}-i-8$ |
| 16250.5-j1 |
16250.5-j |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16250.5 |
\( 2 \cdot 5^{4} \cdot 13 \) |
\( 2^{4} \cdot 5^{10} \cdot 13^{2} \) |
$2.01782$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{3} \cdot 3 \) |
$0.054785322$ |
$1.742847925$ |
4.583159334 |
\( -\frac{2456215}{676} a + \frac{821220}{169} \) |
\( \bigl[i\) , \( i\) , \( 1\) , \( -19 i - 10\) , \( -34 i + 5\bigr] \) |
${y}^2+i{x}{y}+{y}={x}^{3}+i{x}^{2}+\left(-19i-10\right){x}-34i+5$ |
| 16250.5-k1 |
16250.5-k |
$2$ |
$3$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16250.5 |
\( 2 \cdot 5^{4} \cdot 13 \) |
\( 2^{3} \cdot 5^{4} \cdot 13^{9} \) |
$2.01782$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 3 \) |
$1$ |
$0.961237480$ |
2.883712442 |
\( \frac{57371821008205}{42417997492} a - \frac{54181111298935}{42417997492} \) |
\( \bigl[1\) , \( -i - 1\) , \( i + 1\) , \( -10 i + 48\) , \( 164 i + 4\bigr] \) |
${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(-10i+48\right){x}+164i+4$ |
| 16250.5-k2 |
16250.5-k |
$2$ |
$3$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16250.5 |
\( 2 \cdot 5^{4} \cdot 13 \) |
\( 2 \cdot 5^{4} \cdot 13^{3} \) |
$2.01782$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$2.883712442$ |
2.883712442 |
\( -\frac{317111135}{4394} a + \frac{950272195}{4394} \) |
\( \bigl[1\) , \( -i - 1\) , \( i + 1\) , \( 15 i - 2\) , \( 14 i + 19\bigr] \) |
${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(15i-2\right){x}+14i+19$ |
| 16250.5-l1 |
16250.5-l |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16250.5 |
\( 2 \cdot 5^{4} \cdot 13 \) |
\( 2^{18} \cdot 5^{21} \cdot 13 \) |
$2.01782$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$0.192145277$ |
3.458615002 |
\( \frac{276861163011391}{13000000000} a - \frac{33515586556057}{812500000} \) |
\( \bigl[i\) , \( i + 1\) , \( 0\) , \( 2238 i - 1259\) , \( -50752 i - 1489\bigr] \) |
${y}^2+i{x}{y}={x}^{3}+\left(i+1\right){x}^{2}+\left(2238i-1259\right){x}-50752i-1489$ |
| 16250.5-l2 |
16250.5-l |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16250.5 |
\( 2 \cdot 5^{4} \cdot 13 \) |
\( 2^{6} \cdot 5^{15} \cdot 13^{3} \) |
$2.01782$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.576435833$ |
3.458615002 |
\( -\frac{37525044319}{2197000} a - \frac{7169596274}{274625} \) |
\( \bigl[i\) , \( i + 1\) , \( 0\) , \( 238 i + 116\) , \( 248 i + 1636\bigr] \) |
${y}^2+i{x}{y}={x}^{3}+\left(i+1\right){x}^{2}+\left(238i+116\right){x}+248i+1636$ |
| 16250.5-l3 |
16250.5-l |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16250.5 |
\( 2 \cdot 5^{4} \cdot 13 \) |
\( 2^{3} \cdot 5^{18} \cdot 13^{6} \) |
$2.01782$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$0.288217916$ |
3.458615002 |
\( -\frac{133816114442969}{301675562500} a - \frac{19082395919017}{301675562500} \) |
\( \bigl[i\) , \( i + 1\) , \( 0\) , \( -12 i + 366\) , \( 4498 i + 3386\bigr] \) |
${y}^2+i{x}{y}={x}^{3}+\left(i+1\right){x}^{2}+\left(-12i+366\right){x}+4498i+3386$ |
| 16250.5-l4 |
16250.5-l |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16250.5 |
\( 2 \cdot 5^{4} \cdot 13 \) |
\( 2^{9} \cdot 5^{30} \cdot 13^{2} \) |
$2.01782$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$1$ |
$0.096072638$ |
3.458615002 |
\( \frac{8418015312387897223}{20629882812500000} a + \frac{2783266907131437289}{20629882812500000} \) |
\( \bigl[i\) , \( i + 1\) , \( 0\) , \( 238 i - 3259\) , \( -92752 i - 107489\bigr] \) |
${y}^2+i{x}{y}={x}^{3}+\left(i+1\right){x}^{2}+\left(238i-3259\right){x}-92752i-107489$ |
| 16250.5-l5 |
16250.5-l |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16250.5 |
\( 2 \cdot 5^{4} \cdot 13 \) |
\( 2^{2} \cdot 5^{13} \cdot 13 \) |
$2.01782$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.729307501$ |
3.458615002 |
\( -\frac{31409}{130} a + \frac{101344}{65} \) |
\( \bigl[i\) , \( i + 1\) , \( 0\) , \( -12 i - 9\) , \( -2 i + 11\bigr] \) |
${y}^2+i{x}{y}={x}^{3}+\left(i+1\right){x}^{2}+\left(-12i-9\right){x}-2i+11$ |
| 16250.5-l6 |
16250.5-l |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16250.5 |
\( 2 \cdot 5^{4} \cdot 13 \) |
\( 2 \cdot 5^{14} \cdot 13^{2} \) |
$2.01782$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.864653750$ |
3.458615002 |
\( -\frac{4406742137}{8450} a + \frac{1310300809}{8450} \) |
\( \bigl[i\) , \( i + 1\) , \( 0\) , \( -137 i - 134\) , \( 873 i + 386\bigr] \) |
${y}^2+i{x}{y}={x}^{3}+\left(i+1\right){x}^{2}+\left(-137i-134\right){x}+873i+386$ |
| 16250.5-m1 |
16250.5-m |
$2$ |
$5$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16250.5 |
\( 2 \cdot 5^{4} \cdot 13 \) |
\( 2^{5} \cdot 5^{5} \cdot 13^{5} \) |
$2.01782$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.1.1 |
$1$ |
\( 2 \cdot 5^{2} \) |
$1$ |
$1.746336542$ |
3.492673084 |
\( \frac{7896854157}{2970344} a + \frac{4573167341}{2970344} \) |
\( \bigl[1\) , \( i\) , \( i\) , \( -17 i + 5\) , \( i - 20\bigr] \) |
${y}^2+{x}{y}+i{y}={x}^{3}+i{x}^{2}+\left(-17i+5\right){x}+i-20$ |
| 16250.5-m2 |
16250.5-m |
$2$ |
$5$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16250.5 |
\( 2 \cdot 5^{4} \cdot 13 \) |
\( 2 \cdot 5^{13} \cdot 13 \) |
$2.01782$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$1.746336542$ |
3.492673084 |
\( -\frac{74877}{26} a + \frac{83939}{26} \) |
\( \bigl[i\) , \( -i - 1\) , \( 0\) , \( 15 i + 13\) , \( 3 i - 25\bigr] \) |
${y}^2+i{x}{y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(15i+13\right){x}+3i-25$ |
*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.
