| 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 |
| 3750.1-a1 |
3750.1-a |
$2$ |
$5$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3750.1 |
\( 2 \cdot 3 \cdot 5^{4} \) |
\( 2^{5} \cdot 3^{5} \cdot 5^{16} \) |
$2.42235$ |
$(a+1), (a), (5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.1.4 |
$1$ |
\( 1 \) |
$1$ |
$2.693330677$ |
0.777497595 |
\( -\frac{24119545}{216} a - \frac{13817705}{72} \) |
\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( -667 a - 1137\) , \( 12657 a + 21941\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-667a-1137\right){x}+12657a+21941$ |
| 3750.1-a2 |
3750.1-a |
$2$ |
$5$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3750.1 |
\( 2 \cdot 3 \cdot 5^{4} \) |
\( 2 \cdot 3 \cdot 5^{8} \) |
$2.42235$ |
$(a+1), (a), (5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.1.3 |
$1$ |
\( 1 \) |
$1$ |
$2.693330677$ |
0.777497595 |
\( \frac{2589725}{6} a - \frac{1493275}{2} \) |
\( \bigl[1\) , \( 1\) , \( a + 1\) , \( 137 a - 238\) , \( 1212 a - 2101\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(137a-238\right){x}+1212a-2101$ |
| 3750.1-b1 |
3750.1-b |
$2$ |
$5$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3750.1 |
\( 2 \cdot 3 \cdot 5^{4} \) |
\( 2^{5} \cdot 3^{5} \cdot 5^{4} \) |
$2.42235$ |
$(a+1), (a), (5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.4.1 |
$1$ |
\( 1 \) |
$1$ |
$2.976792409$ |
0.859325949 |
\( -\frac{24119545}{216} a - \frac{13817705}{72} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -28 a - 44\) , \( -94 a - 162\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-28a-44\right){x}-94a-162$ |
| 3750.1-b2 |
3750.1-b |
$2$ |
$5$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3750.1 |
\( 2 \cdot 3 \cdot 5^{4} \) |
\( 2 \cdot 3 \cdot 5^{20} \) |
$2.42235$ |
$(a+1), (a), (5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.4.2 |
$1$ |
\( 1 \) |
$1$ |
$2.976792409$ |
0.859325949 |
\( \frac{2589725}{6} a - \frac{1493275}{2} \) |
\( \bigl[a\) , \( -1\) , \( a + 1\) , \( 3437 a - 5952\) , \( -144688 a + 250607\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(3437a-5952\right){x}-144688a+250607$ |
| 3750.1-c1 |
3750.1-c |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3750.1 |
\( 2 \cdot 3 \cdot 5^{4} \) |
\( 2^{24} \cdot 3^{2} \cdot 5^{18} \) |
$2.42235$ |
$(a+1), (a), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$1.344353050$ |
$1.073497826$ |
3.332835439 |
\( -\frac{273359449}{1536000} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -337\) , \( 7631\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}-337{x}+7631$ |
| 3750.1-c2 |
3750.1-c |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3750.1 |
\( 2 \cdot 3 \cdot 5^{4} \) |
\( 2^{8} \cdot 3^{6} \cdot 5^{14} \) |
$2.42235$ |
$(a+1), (a), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.448117683$ |
$1.073497826$ |
3.332835439 |
\( \frac{357911}{2160} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( 38\) , \( -244\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+38{x}-244$ |
| 3750.1-c3 |
3750.1-c |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3750.1 |
\( 2 \cdot 3 \cdot 5^{4} \) |
\( 2^{6} \cdot 3^{2} \cdot 5^{36} \) |
$2.42235$ |
$(a+1), (a), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$5.377412203$ |
$0.268374456$ |
3.332835439 |
\( \frac{10316097499609}{5859375000} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -11337\) , \( 56631\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}-11337{x}+56631$ |
| 3750.1-c4 |
3750.1-c |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3750.1 |
\( 2 \cdot 3 \cdot 5^{4} \) |
\( 2^{2} \cdot 3^{24} \cdot 5^{14} \) |
$2.42235$ |
$(a+1), (a), (5)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{6} \cdot 3 \) |
$0.448117683$ |
$1.073497826$ |
3.332835439 |
\( \frac{35578826569}{5314410} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -1712\) , \( 22506\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}-1712{x}+22506$ |
| 3750.1-c5 |
3750.1-c |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3750.1 |
\( 2 \cdot 3 \cdot 5^{4} \) |
\( 2^{4} \cdot 3^{12} \cdot 5^{16} \) |
$2.42235$ |
$(a+1), (a), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{5} \cdot 3 \) |
$0.896235367$ |
$1.073497826$ |
3.332835439 |
\( \frac{702595369}{72900} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -462\) , \( -3744\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}-462{x}-3744$ |
| 3750.1-c6 |
3750.1-c |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3750.1 |
\( 2 \cdot 3 \cdot 5^{4} \) |
\( 2^{12} \cdot 3^{4} \cdot 5^{24} \) |
$2.42235$ |
$(a+1), (a), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{5} \) |
$2.688706101$ |
$1.073497826$ |
3.332835439 |
\( \frac{4102915888729}{9000000} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -8337\) , \( 287631\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}-8337{x}+287631$ |
| 3750.1-c7 |
3750.1-c |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3750.1 |
\( 2 \cdot 3 \cdot 5^{4} \) |
\( 2^{2} \cdot 3^{6} \cdot 5^{20} \) |
$2.42235$ |
$(a+1), (a), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1.792470734$ |
$0.268374456$ |
3.332835439 |
\( \frac{2656166199049}{33750} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -7212\) , \( -239994\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}-7212{x}-239994$ |
| 3750.1-c8 |
3750.1-c |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3750.1 |
\( 2 \cdot 3 \cdot 5^{4} \) |
\( 2^{6} \cdot 3^{8} \cdot 5^{18} \) |
$2.42235$ |
$(a+1), (a), (5)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{6} \) |
$1.344353050$ |
$1.073497826$ |
3.332835439 |
\( \frac{16778985534208729}{81000} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -133337\) , \( 18662631\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}-133337{x}+18662631$ |
| 3750.1-d1 |
3750.1-d |
$2$ |
$5$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3750.1 |
\( 2 \cdot 3 \cdot 5^{4} \) |
\( 2 \cdot 3 \cdot 5^{8} \) |
$2.42235$ |
$(a+1), (a), (5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.4.2 |
$1$ |
\( 1 \) |
$1$ |
$14.88396204$ |
4.296629746 |
\( -\frac{2589725}{6} a - \frac{1493275}{2} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( -1478 a + 2564\) , \( -36815 a + 63767\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-1478a+2564\right){x}-36815a+63767$ |
| 3750.1-d2 |
3750.1-d |
$2$ |
$5$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3750.1 |
\( 2 \cdot 3 \cdot 5^{4} \) |
\( 2^{5} \cdot 3^{5} \cdot 5^{16} \) |
$2.42235$ |
$(a+1), (a), (5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.4.1 |
$1$ |
\( 5^{2} \) |
$1$ |
$0.595358481$ |
4.296629746 |
\( \frac{24119545}{216} a - \frac{13817705}{72} \) |
\( \bigl[1\) , \( -a\) , \( a\) , \( 666 a - 1137\) , \( 12657 a - 21942\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(666a-1137\right){x}+12657a-21942$ |
| 3750.1-e1 |
3750.1-e |
$4$ |
$10$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3750.1 |
\( 2 \cdot 3 \cdot 5^{4} \) |
\( 2^{4} \cdot 3^{2} \cdot 5^{6} \) |
$2.42235$ |
$(a+1), (a), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 5$ |
2B, 5B.1.2 |
$1$ |
\( 2^{4} \) |
$1$ |
$3.130278287$ |
3.614534023 |
\( -\frac{24389}{12} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -3\) , \( -3\bigr] \) |
${y}^2+{x}{y}={x}^{3}-3{x}-3$ |
| 3750.1-e2 |
3750.1-e |
$4$ |
$10$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3750.1 |
\( 2 \cdot 3 \cdot 5^{4} \) |
\( 2^{20} \cdot 3^{10} \cdot 5^{6} \) |
$2.42235$ |
$(a+1), (a), (5)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 2^{4} \cdot 5^{2} \) |
$1$ |
$3.130278287$ |
3.614534023 |
\( -\frac{19465109}{248832} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 1568 a - 2716\) , \( -212160 a + 367472\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(1568a-2716\right){x}-212160a+367472$ |
| 3750.1-e3 |
3750.1-e |
$4$ |
$10$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3750.1 |
\( 2 \cdot 3 \cdot 5^{4} \) |
\( 2^{10} \cdot 3^{20} \cdot 5^{6} \) |
$2.42235$ |
$(a+1), (a), (5)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 2^{4} \cdot 5^{2} \) |
$1$ |
$3.130278287$ |
3.614534023 |
\( \frac{502270291349}{1889568} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 46368 a - 80316\) , \( -7076160 a + 12256272\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(46368a-80316\right){x}-7076160a+12256272$ |
| 3750.1-e4 |
3750.1-e |
$4$ |
$10$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3750.1 |
\( 2 \cdot 3 \cdot 5^{4} \) |
\( 2^{2} \cdot 3^{4} \cdot 5^{6} \) |
$2.42235$ |
$(a+1), (a), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 5$ |
2B, 5B.1.2 |
$1$ |
\( 2^{4} \) |
$1$ |
$3.130278287$ |
3.614534023 |
\( \frac{131872229}{18} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -53\) , \( -153\bigr] \) |
${y}^2+{x}{y}={x}^{3}-53{x}-153$ |
| 3750.1-f1 |
3750.1-f |
$4$ |
$10$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3750.1 |
\( 2 \cdot 3 \cdot 5^{4} \) |
\( 2^{4} \cdot 3^{2} \cdot 5^{18} \) |
$2.42235$ |
$(a+1), (a), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 5$ |
2B, 5B.4.2 |
$1$ |
\( 2^{4} \) |
$1$ |
$3.962278619$ |
4.575245255 |
\( -\frac{24389}{12} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -76\) , \( 299\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-76{x}+299$ |
| 3750.1-f2 |
3750.1-f |
$4$ |
$10$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3750.1 |
\( 2 \cdot 3 \cdot 5^{4} \) |
\( 2^{20} \cdot 3^{10} \cdot 5^{18} \) |
$2.42235$ |
$(a+1), (a), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2^{4} \cdot 5^{2} \) |
$1$ |
$0.158491144$ |
4.575245255 |
\( -\frac{19465109}{248832} \) |
\( \bigl[1\) , \( -a\) , \( 1\) , \( 39229 a - 67950\) , \( 26773532 a - 46373129\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(39229a-67950\right){x}+26773532a-46373129$ |
| 3750.1-f3 |
3750.1-f |
$4$ |
$10$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3750.1 |
\( 2 \cdot 3 \cdot 5^{4} \) |
\( 2^{10} \cdot 3^{20} \cdot 5^{18} \) |
$2.42235$ |
$(a+1), (a), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2^{4} \cdot 5^{2} \) |
$1$ |
$0.158491144$ |
4.575245255 |
\( \frac{502270291349}{1889568} \) |
\( \bigl[1\) , \( -a\) , \( 1\) , \( 1159229 a - 2007950\) , \( 892013532 a - 1545013129\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(1159229a-2007950\right){x}+892013532a-1545013129$ |
| 3750.1-f4 |
3750.1-f |
$4$ |
$10$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3750.1 |
\( 2 \cdot 3 \cdot 5^{4} \) |
\( 2^{2} \cdot 3^{4} \cdot 5^{18} \) |
$2.42235$ |
$(a+1), (a), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 5$ |
2B, 5B.4.2 |
$1$ |
\( 2^{4} \) |
$1$ |
$3.962278619$ |
4.575245255 |
\( \frac{131872229}{18} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -1326\) , \( 17799\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-1326{x}+17799$ |
| 3750.1-g1 |
3750.1-g |
$2$ |
$5$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3750.1 |
\( 2 \cdot 3 \cdot 5^{4} \) |
\( 2 \cdot 3 \cdot 5^{20} \) |
$2.42235$ |
$(a+1), (a), (5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.1.2 |
$25$ |
\( 1 \) |
$1$ |
$0.538666135$ |
3.887487979 |
\( -\frac{2589725}{6} a - \frac{1493275}{2} \) |
\( \bigl[1\) , \( a\) , \( 1\) , \( -36979 a + 64050\) , \( 4619093 a - 8000504\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-36979a+64050\right){x}+4619093a-8000504$ |
| 3750.1-g2 |
3750.1-g |
$2$ |
$5$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3750.1 |
\( 2 \cdot 3 \cdot 5^{4} \) |
\( 2^{5} \cdot 3^{5} \cdot 5^{4} \) |
$2.42235$ |
$(a+1), (a), (5)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.1.1 |
$1$ |
\( 5^{2} \) |
$1$ |
$13.46665338$ |
3.887487979 |
\( \frac{24119545}{216} a - \frac{13817705}{72} \) |
\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( 25 a - 45\) , \( -68 a + 116\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(25a-45\right){x}-68a+116$ |
| 3750.1-h1 |
3750.1-h |
$2$ |
$5$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3750.1 |
\( 2 \cdot 3 \cdot 5^{4} \) |
\( 2 \cdot 3 \cdot 5^{20} \) |
$2.42235$ |
$(a+1), (a), (5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.4.2 |
$1$ |
\( 1 \) |
$1$ |
$2.976792409$ |
0.859325949 |
\( -\frac{2589725}{6} a - \frac{1493275}{2} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -36979 a + 64049\) , \( -4619093 a + 8000503\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-36979a+64049\right){x}-4619093a+8000503$ |
| 3750.1-h2 |
3750.1-h |
$2$ |
$5$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3750.1 |
\( 2 \cdot 3 \cdot 5^{4} \) |
\( 2^{5} \cdot 3^{5} \cdot 5^{4} \) |
$2.42235$ |
$(a+1), (a), (5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.4.1 |
$1$ |
\( 1 \) |
$1$ |
$2.976792409$ |
0.859325949 |
\( \frac{24119545}{216} a - \frac{13817705}{72} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( 27 a - 44\) , \( 94 a - 162\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(27a-44\right){x}+94a-162$ |
| 3750.1-i1 |
3750.1-i |
$4$ |
$10$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3750.1 |
\( 2 \cdot 3 \cdot 5^{4} \) |
\( 2^{4} \cdot 3^{2} \cdot 5^{18} \) |
$2.42235$ |
$(a+1), (a), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 5$ |
2B, 5B.1.3 |
$4$ |
\( 2^{3} \) |
$1$ |
$0.626055657$ |
1.445813609 |
\( -\frac{24389}{12} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -75\) , \( -375\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-75{x}-375$ |
| 3750.1-i2 |
3750.1-i |
$4$ |
$10$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3750.1 |
\( 2 \cdot 3 \cdot 5^{4} \) |
\( 2^{20} \cdot 3^{10} \cdot 5^{18} \) |
$2.42235$ |
$(a+1), (a), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 5$ |
2B, 5B.1.4 |
$4$ |
\( 2^{3} \) |
$1$ |
$0.626055657$ |
1.445813609 |
\( -\frac{19465109}{248832} \) |
\( \bigl[a\) , \( a - 1\) , \( a\) , \( 39229 a - 67951\) , \( -26773532 a + 46373128\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(39229a-67951\right){x}-26773532a+46373128$ |
| 3750.1-i3 |
3750.1-i |
$4$ |
$10$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3750.1 |
\( 2 \cdot 3 \cdot 5^{4} \) |
\( 2^{10} \cdot 3^{20} \cdot 5^{18} \) |
$2.42235$ |
$(a+1), (a), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 5$ |
2B, 5B.1.4 |
$4$ |
\( 2^{3} \) |
$1$ |
$0.626055657$ |
1.445813609 |
\( \frac{502270291349}{1889568} \) |
\( \bigl[a\) , \( a - 1\) , \( a\) , \( 1159229 a - 2007951\) , \( -892013532 a + 1545013128\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(1159229a-2007951\right){x}-892013532a+1545013128$ |
| 3750.1-i4 |
3750.1-i |
$4$ |
$10$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3750.1 |
\( 2 \cdot 3 \cdot 5^{4} \) |
\( 2^{2} \cdot 3^{4} \cdot 5^{18} \) |
$2.42235$ |
$(a+1), (a), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 5$ |
2B, 5B.1.3 |
$4$ |
\( 2^{3} \) |
$1$ |
$0.626055657$ |
1.445813609 |
\( \frac{131872229}{18} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -1325\) , \( -19125\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-1325{x}-19125$ |
| 3750.1-j1 |
3750.1-j |
$4$ |
$10$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3750.1 |
\( 2 \cdot 3 \cdot 5^{4} \) |
\( 2^{4} \cdot 3^{2} \cdot 5^{6} \) |
$2.42235$ |
$(a+1), (a), (5)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 5$ |
2B, 5B.4.2 |
$1$ |
\( 2^{3} \) |
$0.071444057$ |
$19.81139309$ |
3.268740832 |
\( -\frac{24389}{12} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -3\) , \( 3\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}-3{x}+3$ |
| 3750.1-j2 |
3750.1-j |
$4$ |
$10$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3750.1 |
\( 2 \cdot 3 \cdot 5^{4} \) |
\( 2^{20} \cdot 3^{10} \cdot 5^{6} \) |
$2.42235$ |
$(a+1), (a), (5)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2^{3} \) |
$1.786101427$ |
$0.792455723$ |
3.268740832 |
\( -\frac{19465109}{248832} \) |
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( 1570 a - 2717\) , \( 213729 a - 370189\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(1570a-2717\right){x}+213729a-370189$ |
| 3750.1-j3 |
3750.1-j |
$4$ |
$10$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3750.1 |
\( 2 \cdot 3 \cdot 5^{4} \) |
\( 2^{10} \cdot 3^{20} \cdot 5^{6} \) |
$2.42235$ |
$(a+1), (a), (5)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2^{3} \) |
$1.786101427$ |
$0.792455723$ |
3.268740832 |
\( \frac{502270291349}{1889568} \) |
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( 46370 a - 80317\) , \( 7122529 a - 12336589\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(46370a-80317\right){x}+7122529a-12336589$ |
| 3750.1-j4 |
3750.1-j |
$4$ |
$10$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3750.1 |
\( 2 \cdot 3 \cdot 5^{4} \) |
\( 2^{2} \cdot 3^{4} \cdot 5^{6} \) |
$2.42235$ |
$(a+1), (a), (5)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 5$ |
2B, 5B.4.2 |
$1$ |
\( 2^{3} \) |
$0.071444057$ |
$19.81139309$ |
3.268740832 |
\( \frac{131872229}{18} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -53\) , \( 153\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}-53{x}+153$ |
| 3750.1-k1 |
3750.1-k |
$2$ |
$5$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3750.1 |
\( 2 \cdot 3 \cdot 5^{4} \) |
\( 2 \cdot 3 \cdot 5^{8} \) |
$2.42235$ |
$(a+1), (a), (5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.1.3 |
$1$ |
\( 1 \) |
$1$ |
$2.693330677$ |
0.777497595 |
\( -\frac{2589725}{6} a - \frac{1493275}{2} \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -1480 a + 2563\) , \( 35336 a - 61204\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-1480a+2563\right){x}+35336a-61204$ |
| 3750.1-k2 |
3750.1-k |
$2$ |
$5$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3750.1 |
\( 2 \cdot 3 \cdot 5^{4} \) |
\( 2^{5} \cdot 3^{5} \cdot 5^{16} \) |
$2.42235$ |
$(a+1), (a), (5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.1.4 |
$1$ |
\( 1 \) |
$1$ |
$2.693330677$ |
0.777497595 |
\( \frac{24119545}{216} a - \frac{13817705}{72} \) |
\( \bigl[a\) , \( a - 1\) , \( 1\) , \( 666 a - 1137\) , \( -12657 a + 21941\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(666a-1137\right){x}-12657a+21941$ |
| 3750.1-l1 |
3750.1-l |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3750.1 |
\( 2 \cdot 3 \cdot 5^{4} \) |
\( 2^{24} \cdot 3^{2} \cdot 5^{18} \) |
$2.42235$ |
$(a+1), (a), (5)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{6} \cdot 3 \) |
$2.765577577$ |
$0.249679047$ |
4.783971269 |
\( -\frac{273359449}{1536000} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -338\) , \( -7969\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-338{x}-7969$ |
| 3750.1-l2 |
3750.1-l |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3750.1 |
\( 2 \cdot 3 \cdot 5^{4} \) |
\( 2^{8} \cdot 3^{6} \cdot 5^{14} \) |
$2.42235$ |
$(a+1), (a), (5)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{6} \) |
$0.921859192$ |
$2.247111426$ |
4.783971269 |
\( \frac{357911}{2160} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 37\) , \( 281\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+37{x}+281$ |
| 3750.1-l3 |
3750.1-l |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3750.1 |
\( 2 \cdot 3 \cdot 5^{4} \) |
\( 2^{6} \cdot 3^{2} \cdot 5^{36} \) |
$2.42235$ |
$(a+1), (a), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \cdot 3 \) |
$2.765577577$ |
$0.249679047$ |
4.783971269 |
\( \frac{10316097499609}{5859375000} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -11338\) , \( -67969\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-11338{x}-67969$ |
| 3750.1-l4 |
3750.1-l |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3750.1 |
\( 2 \cdot 3 \cdot 5^{4} \) |
\( 2^{2} \cdot 3^{24} \cdot 5^{14} \) |
$2.42235$ |
$(a+1), (a), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$3.687436770$ |
$0.561777856$ |
4.783971269 |
\( \frac{35578826569}{5314410} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -1713\) , \( -24219\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-1713{x}-24219$ |
| 3750.1-l5 |
3750.1-l |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3750.1 |
\( 2 \cdot 3 \cdot 5^{4} \) |
\( 2^{4} \cdot 3^{12} \cdot 5^{16} \) |
$2.42235$ |
$(a+1), (a), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{5} \) |
$1.843718385$ |
$2.247111426$ |
4.783971269 |
\( \frac{702595369}{72900} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -463\) , \( 3281\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-463{x}+3281$ |
| 3750.1-l6 |
3750.1-l |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3750.1 |
\( 2 \cdot 3 \cdot 5^{4} \) |
\( 2^{12} \cdot 3^{4} \cdot 5^{24} \) |
$2.42235$ |
$(a+1), (a), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{5} \cdot 3 \) |
$5.531155155$ |
$0.249679047$ |
4.783971269 |
\( \frac{4102915888729}{9000000} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -8338\) , \( -295969\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-8338{x}-295969$ |
| 3750.1-l7 |
3750.1-l |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3750.1 |
\( 2 \cdot 3 \cdot 5^{4} \) |
\( 2^{2} \cdot 3^{6} \cdot 5^{20} \) |
$2.42235$ |
$(a+1), (a), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$0.921859192$ |
$2.247111426$ |
4.783971269 |
\( \frac{2656166199049}{33750} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -7213\) , \( 232781\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-7213{x}+232781$ |
| 3750.1-l8 |
3750.1-l |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3750.1 |
\( 2 \cdot 3 \cdot 5^{4} \) |
\( 2^{6} \cdot 3^{8} \cdot 5^{18} \) |
$2.42235$ |
$(a+1), (a), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \cdot 3 \) |
$11.06231031$ |
$0.062419761$ |
4.783971269 |
\( \frac{16778985534208729}{81000} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -133338\) , \( -18795969\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-133338{x}-18795969$ |
| 3750.1-m1 |
3750.1-m |
$2$ |
$5$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3750.1 |
\( 2 \cdot 3 \cdot 5^{4} \) |
\( 2^{5} \cdot 3^{5} \cdot 5^{4} \) |
$2.42235$ |
$(a+1), (a), (5)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.1.1 |
$1$ |
\( 5^{2} \) |
$1$ |
$13.46665338$ |
3.887487979 |
\( -\frac{24119545}{216} a - \frac{13817705}{72} \) |
\( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( -26 a - 45\) , \( 67 a + 116\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-26a-45\right){x}+67a+116$ |
| 3750.1-m2 |
3750.1-m |
$2$ |
$5$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3750.1 |
\( 2 \cdot 3 \cdot 5^{4} \) |
\( 2 \cdot 3 \cdot 5^{20} \) |
$2.42235$ |
$(a+1), (a), (5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.1.2 |
$25$ |
\( 1 \) |
$1$ |
$0.538666135$ |
3.887487979 |
\( \frac{2589725}{6} a - \frac{1493275}{2} \) |
\( \bigl[1\) , \( 0\) , \( a + 1\) , \( 3437 a - 5951\) , \( 144687 a - 250609\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(3437a-5951\right){x}+144687a-250609$ |
| 3750.1-n1 |
3750.1-n |
$2$ |
$5$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3750.1 |
\( 2 \cdot 3 \cdot 5^{4} \) |
\( 2^{5} \cdot 3^{5} \cdot 5^{16} \) |
$2.42235$ |
$(a+1), (a), (5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.4.1 |
$1$ |
\( 5^{2} \) |
$1$ |
$0.595358481$ |
4.296629746 |
\( -\frac{24119545}{216} a - \frac{13817705}{72} \) |
\( \bigl[1\) , \( a\) , \( a\) , \( -667 a - 1137\) , \( -12657 a - 21942\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-667a-1137\right){x}-12657a-21942$ |
| 3750.1-n2 |
3750.1-n |
$2$ |
$5$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3750.1 |
\( 2 \cdot 3 \cdot 5^{4} \) |
\( 2 \cdot 3 \cdot 5^{8} \) |
$2.42235$ |
$(a+1), (a), (5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.4.2 |
$1$ |
\( 1 \) |
$1$ |
$14.88396204$ |
4.296629746 |
\( \frac{2589725}{6} a - \frac{1493275}{2} \) |
\( \bigl[a\) , \( 1\) , \( 1\) , \( 137 a - 237\) , \( -1075 a + 1862\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(137a-237\right){x}-1075a+1862$ |
*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.
