| 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 |
| 36288.4-a1 |
36288.4-a |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
36288.4 |
\( 2^{6} \cdot 3^{4} \cdot 7 \) |
\( 2^{8} \cdot 3^{6} \cdot 7^{4} \) |
$3.26308$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.257561760$ |
$2.574730348$ |
4.010366825 |
\( -\frac{55296}{49} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -6\) , \( 9\bigr] \) |
${y}^2={x}^{3}-6{x}+9$ |
| 36288.4-a2 |
36288.4-a |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
36288.4 |
\( 2^{6} \cdot 3^{4} \cdot 7 \) |
\( 2^{16} \cdot 3^{6} \cdot 7^{2} \) |
$3.26308$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.515123520$ |
$1.287365174$ |
4.010366825 |
\( \frac{21882096}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -111\) , \( 450\bigr] \) |
${y}^2={x}^{3}-111{x}+450$ |
| 36288.4-b1 |
36288.4-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
36288.4 |
\( 2^{6} \cdot 3^{4} \cdot 7 \) |
\( 2^{20} \cdot 3^{14} \cdot 7^{8} \) |
$3.26308$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1.149717591$ |
$0.328726139$ |
4.571159483 |
\( \frac{11696828}{7203} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 429\) , \( -866\bigr] \) |
${y}^2={x}^{3}+429{x}-866$ |
| 36288.4-b2 |
36288.4-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
36288.4 |
\( 2^{6} \cdot 3^{4} \cdot 7 \) |
\( 2^{16} \cdot 3^{16} \cdot 7^{4} \) |
$3.26308$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$0.574858795$ |
$0.657452278$ |
4.571159483 |
\( \frac{810448}{441} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -111\) , \( -110\bigr] \) |
${y}^2={x}^{3}-111{x}-110$ |
| 36288.4-b3 |
36288.4-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
36288.4 |
\( 2^{6} \cdot 3^{4} \cdot 7 \) |
\( 2^{8} \cdot 3^{14} \cdot 7^{2} \) |
$3.26308$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1.149717591$ |
$1.314904556$ |
4.571159483 |
\( \frac{2725888}{21} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -66\) , \( 205\bigr] \) |
${y}^2={x}^{3}-66{x}+205$ |
| 36288.4-b4 |
36288.4-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
36288.4 |
\( 2^{6} \cdot 3^{4} \cdot 7 \) |
\( 2^{20} \cdot 3^{20} \cdot 7^{2} \) |
$3.26308$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1.149717591$ |
$0.328726139$ |
4.571159483 |
\( \frac{381775972}{567} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -1371\) , \( -19514\bigr] \) |
${y}^2={x}^{3}-1371{x}-19514$ |
| 36288.4-c1 |
36288.4-c |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
36288.4 |
\( 2^{6} \cdot 3^{4} \cdot 7 \) |
\( 2^{8} \cdot 3^{18} \cdot 7^{4} \) |
$3.26308$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.026806232$ |
$0.858243449$ |
5.329297391 |
\( -\frac{55296}{49} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -54\) , \( -243\bigr] \) |
${y}^2={x}^{3}-54{x}-243$ |
| 36288.4-c2 |
36288.4-c |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
36288.4 |
\( 2^{6} \cdot 3^{4} \cdot 7 \) |
\( 2^{16} \cdot 3^{18} \cdot 7^{2} \) |
$3.26308$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$0.513403116$ |
$0.429121724$ |
5.329297391 |
\( \frac{21882096}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -999\) , \( -12150\bigr] \) |
${y}^2={x}^{3}-999{x}-12150$ |
| 36288.4-d1 |
36288.4-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
36288.4 |
\( 2^{6} \cdot 3^{4} \cdot 7 \) |
\( 2^{14} \cdot 3^{12} \cdot 7 \) |
$3.26308$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.647061100$ |
$1.338765239$ |
5.238665667 |
\( \frac{516132}{7} a - \frac{52056}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 27 a + 36\) , \( 81 a - 189\bigr] \) |
${y}^2={x}^{3}+\left(27a+36\right){x}+81a-189$ |
| 36288.4-d2 |
36288.4-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
36288.4 |
\( 2^{6} \cdot 3^{4} \cdot 7 \) |
\( 2^{16} \cdot 3^{12} \cdot 7^{2} \) |
$3.26308$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1.294122201$ |
$1.338765239$ |
5.238665667 |
\( \frac{432}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 9\) , \( -54\bigr] \) |
${y}^2={x}^{3}+9{x}-54$ |
| 36288.4-d3 |
36288.4-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
36288.4 |
\( 2^{6} \cdot 3^{4} \cdot 7 \) |
\( 2^{22} \cdot 3^{12} \cdot 7^{8} \) |
$3.26308$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$5.176488807$ |
$0.334691309$ |
5.238665667 |
\( \frac{11090466}{2401} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -531\) , \( 3726\bigr] \) |
${y}^2={x}^{3}-531{x}+3726$ |
| 36288.4-d4 |
36288.4-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
36288.4 |
\( 2^{6} \cdot 3^{4} \cdot 7 \) |
\( 2^{20} \cdot 3^{12} \cdot 7^{4} \) |
$3.26308$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$2.588244403$ |
$0.669382619$ |
5.238665667 |
\( \frac{740772}{49} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -171\) , \( -810\bigr] \) |
${y}^2={x}^{3}-171{x}-810$ |
| 36288.4-d5 |
36288.4-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
36288.4 |
\( 2^{6} \cdot 3^{4} \cdot 7 \) |
\( 2^{14} \cdot 3^{12} \cdot 7 \) |
$3.26308$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.647061100$ |
$1.338765239$ |
5.238665667 |
\( -\frac{516132}{7} a + \frac{464076}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -27 a + 63\) , \( -81 a - 108\bigr] \) |
${y}^2={x}^{3}+\left(-27a+63\right){x}-81a-108$ |
| 36288.4-d6 |
36288.4-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
36288.4 |
\( 2^{6} \cdot 3^{4} \cdot 7 \) |
\( 2^{22} \cdot 3^{12} \cdot 7^{2} \) |
$3.26308$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$5.176488807$ |
$0.334691309$ |
5.238665667 |
\( \frac{1443468546}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -2691\) , \( -53730\bigr] \) |
${y}^2={x}^{3}-2691{x}-53730$ |
| 36288.4-e1 |
36288.4-e |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
36288.4 |
\( 2^{6} \cdot 3^{4} \cdot 7 \) |
\( 2^{16} \cdot 3^{6} \cdot 7^{4} \) |
$3.26308$ |
$(a), (-a+1), (-2a+1), (3)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$0.043261494$ |
$1.669786470$ |
6.989617430 |
\( \frac{11664}{49} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 9\) , \( 26\bigr] \) |
${y}^2={x}^{3}+9{x}+26$ |
| 36288.4-e2 |
36288.4-e |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
36288.4 |
\( 2^{6} \cdot 3^{4} \cdot 7 \) |
\( 2^{8} \cdot 3^{6} \cdot 7^{2} \) |
$3.26308$ |
$(a), (-a+1), (-2a+1), (3)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.173045979$ |
$3.339572940$ |
6.989617430 |
\( \frac{55296}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -6\) , \( 5\bigr] \) |
${y}^2={x}^{3}-6{x}+5$ |
| 36288.4-f1 |
36288.4-f |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
36288.4 |
\( 2^{6} \cdot 3^{4} \cdot 7 \) |
\( 2^{20} \cdot 3^{12} \cdot 7^{2} \) |
$3.26308$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.065956547$ |
1.611574819 |
\( -\frac{4}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -3\) , \( 110\bigr] \) |
${y}^2={x}^{3}-3{x}+110$ |
| 36288.4-f2 |
36288.4-f |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
36288.4 |
\( 2^{6} \cdot 3^{4} \cdot 7 \) |
\( 2^{19} \cdot 3^{12} \cdot 7 \) |
$3.26308$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.065956547$ |
1.611574819 |
\( \frac{59930}{7} a + \frac{286932}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 36 a - 87\) , \( -172 a + 266\bigr] \) |
${y}^2={x}^{3}+\left(36a-87\right){x}-172a+266$ |
| 36288.4-f3 |
36288.4-f |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
36288.4 |
\( 2^{6} \cdot 3^{4} \cdot 7 \) |
\( 2^{19} \cdot 3^{12} \cdot 7 \) |
$3.26308$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.065956547$ |
1.611574819 |
\( -\frac{59930}{7} a + \frac{346862}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -36 a - 51\) , \( 172 a + 94\bigr] \) |
${y}^2={x}^{3}+\left(-36a-51\right){x}+172a+94$ |
| 36288.4-f4 |
36288.4-f |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
36288.4 |
\( 2^{6} \cdot 3^{4} \cdot 7 \) |
\( 2^{22} \cdot 3^{12} \cdot 7^{4} \) |
$3.26308$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.532978273$ |
1.611574819 |
\( \frac{3543122}{49} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -363\) , \( 2630\bigr] \) |
${y}^2={x}^{3}-363{x}+2630$ |
| 36288.4-g1 |
36288.4-g |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
36288.4 |
\( 2^{6} \cdot 3^{4} \cdot 7 \) |
\( 2^{8} \cdot 3^{18} \cdot 7^{8} \) |
$3.26308$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$1$ |
$0.463617288$ |
2.803693826 |
\( -\frac{2725888}{64827} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -66\) , \( -1339\bigr] \) |
${y}^2={x}^{3}-66{x}-1339$ |
| 36288.4-g2 |
36288.4-g |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
36288.4 |
\( 2^{6} \cdot 3^{4} \cdot 7 \) |
\( 2^{20} \cdot 3^{36} \cdot 7^{2} \) |
$3.26308$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{5} \) |
$1$ |
$0.115904322$ |
2.803693826 |
\( \frac{6522128932}{3720087} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -3531\) , \( 9686\bigr] \) |
${y}^2={x}^{3}-3531{x}+9686$ |
| 36288.4-g3 |
36288.4-g |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
36288.4 |
\( 2^{6} \cdot 3^{4} \cdot 7 \) |
\( 2^{16} \cdot 3^{24} \cdot 7^{4} \) |
$3.26308$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{8} \) |
$1$ |
$0.231808644$ |
2.803693826 |
\( \frac{6940769488}{35721} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -2271\) , \( -41470\bigr] \) |
${y}^2={x}^{3}-2271{x}-41470$ |
| 36288.4-g4 |
36288.4-g |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
36288.4 |
\( 2^{6} \cdot 3^{4} \cdot 7 \) |
\( 2^{20} \cdot 3^{18} \cdot 7^{2} \) |
$3.26308$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{5} \) |
$1$ |
$0.115904322$ |
2.803693826 |
\( \frac{7080974546692}{189} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -36291\) , \( -2661010\bigr] \) |
${y}^2={x}^{3}-36291{x}-2661010$ |
| 36288.4-h1 |
36288.4-h |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
36288.4 |
\( 2^{6} \cdot 3^{4} \cdot 7 \) |
\( 2^{16} \cdot 3^{18} \cdot 7^{4} \) |
$3.26308$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.556595490$ |
3.365973137 |
\( \frac{11664}{49} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 81\) , \( -702\bigr] \) |
${y}^2={x}^{3}+81{x}-702$ |
| 36288.4-h2 |
36288.4-h |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
36288.4 |
\( 2^{6} \cdot 3^{4} \cdot 7 \) |
\( 2^{8} \cdot 3^{18} \cdot 7^{2} \) |
$3.26308$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.113190980$ |
3.365973137 |
\( \frac{55296}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -54\) , \( -135\bigr] \) |
${y}^2={x}^{3}-54{x}-135$ |
*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.
