| 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 |
| 294.1-a1 |
294.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
294.1 |
\( 2 \cdot 3 \cdot 7^{2} \) |
\( 2^{16} \cdot 3^{16} \cdot 7^{2} \) |
$4.05337$ |
$(2,a), (3,a), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$2.740367332$ |
2.001281338 |
\( -\frac{7189057}{16128} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -36\) , \( -176\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-36{x}-176$ |
| 294.1-a2 |
294.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
294.1 |
\( 2 \cdot 3 \cdot 7^{2} \) |
\( 2^{2} \cdot 3^{44} \cdot 7^{4} \) |
$4.05337$ |
$(2,a), (3,a), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{3} \) |
$1$ |
$0.342545916$ |
2.001281338 |
\( \frac{6359387729183}{4218578658} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 3474\) , \( -31010\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2+3474{x}-31010$ |
| 294.1-a3 |
294.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
294.1 |
\( 2 \cdot 3 \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{28} \cdot 7^{8} \) |
$4.05337$ |
$(2,a), (3,a), (7)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{4} \) |
$1$ |
$0.685091833$ |
2.001281338 |
\( \frac{124475734657}{63011844} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -936\) , \( -3668\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-936{x}-3668$ |
| 294.1-a4 |
294.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
294.1 |
\( 2 \cdot 3 \cdot 7^{2} \) |
\( 2^{2} \cdot 3^{20} \cdot 7^{16} \) |
$4.05337$ |
$(2,a), (3,a), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{5} \) |
$1$ |
$0.342545916$ |
2.001281338 |
\( \frac{84448510979617}{933897762} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -8226\) , \( 286474\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-8226{x}+286474$ |
| 294.1-a5 |
294.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
294.1 |
\( 2 \cdot 3 \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{20} \cdot 7^{4} \) |
$4.05337$ |
$(2,a), (3,a), (7)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{3} \) |
$1$ |
$1.370183666$ |
2.001281338 |
\( \frac{65597103937}{63504} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -756\) , \( -7808\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-756{x}-7808$ |
| 294.1-a6 |
294.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
294.1 |
\( 2 \cdot 3 \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{16} \cdot 7^{2} \) |
$4.05337$ |
$(2,a), (3,a), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{2} \) |
$1$ |
$0.685091833$ |
2.001281338 |
\( \frac{268498407453697}{252} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -12096\) , \( -509036\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-12096{x}-509036$ |
| 294.1-b1 |
294.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
294.1 |
\( 2 \cdot 3 \cdot 7^{2} \) |
\( 2^{16} \cdot 3^{4} \cdot 5^{12} \cdot 7^{2} \) |
$4.05337$ |
$(2,a), (3,a), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.697547317$ |
$2.740367332$ |
1.395988428 |
\( -\frac{7189057}{16128} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -101\) , \( 848\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-101{x}+848$ |
| 294.1-b2 |
294.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
294.1 |
\( 2 \cdot 3 \cdot 7^{2} \) |
\( 2^{2} \cdot 3^{32} \cdot 5^{12} \cdot 7^{4} \) |
$4.05337$ |
$(2,a), (3,a), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$0.348773658$ |
$0.342545916$ |
1.395988428 |
\( \frac{6359387729183}{4218578658} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 9649\) , \( 140348\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+9649{x}+140348$ |
| 294.1-b3 |
294.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
294.1 |
\( 2 \cdot 3 \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{16} \cdot 5^{12} \cdot 7^{8} \) |
$4.05337$ |
$(2,a), (3,a), (7)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{7} \) |
$0.174386829$ |
$0.685091833$ |
1.395988428 |
\( \frac{124475734657}{63011844} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2601\) , \( 17848\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-2601{x}+17848$ |
| 294.1-b4 |
294.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
294.1 |
\( 2 \cdot 3 \cdot 7^{2} \) |
\( 2^{2} \cdot 3^{8} \cdot 5^{12} \cdot 7^{16} \) |
$4.05337$ |
$(2,a), (3,a), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$0.348773658$ |
$0.342545916$ |
1.395988428 |
\( \frac{84448510979617}{933897762} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -22851\) , \( -1318652\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-22851{x}-1318652$ |
| 294.1-b5 |
294.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
294.1 |
\( 2 \cdot 3 \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{8} \cdot 5^{12} \cdot 7^{4} \) |
$4.05337$ |
$(2,a), (3,a), (7)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{5} \) |
$0.348773658$ |
$1.370183666$ |
1.395988428 |
\( \frac{65597103937}{63504} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2101\) , \( 36848\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-2101{x}+36848$ |
| 294.1-b6 |
294.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
294.1 |
\( 2 \cdot 3 \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{4} \cdot 5^{12} \cdot 7^{2} \) |
$4.05337$ |
$(2,a), (3,a), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$0.697547317$ |
$0.685091833$ |
1.395988428 |
\( \frac{268498407453697}{252} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -33601\) , \( 2367848\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-33601{x}+2367848$ |
| 294.1-c1 |
294.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
294.1 |
\( 2 \cdot 3 \cdot 7^{2} \) |
\( 2^{16} \cdot 3^{4} \cdot 7^{2} \) |
$4.05337$ |
$(2,a), (3,a), (7)$ |
$1$ |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$13.72682190$ |
$2.740367332$ |
6.867808126 |
\( -\frac{7189057}{16128} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -4\) , \( 5\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-4{x}+5$ |
| 294.1-c2 |
294.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
294.1 |
\( 2 \cdot 3 \cdot 7^{2} \) |
\( 2^{2} \cdot 3^{32} \cdot 7^{4} \) |
$4.05337$ |
$(2,a), (3,a), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$6.863410950$ |
$0.342545916$ |
6.867808126 |
\( \frac{6359387729183}{4218578658} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 386\) , \( 1277\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2+386{x}+1277$ |
| 294.1-c3 |
294.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
294.1 |
\( 2 \cdot 3 \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{16} \cdot 7^{8} \) |
$4.05337$ |
$(2,a), (3,a), (7)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{5} \) |
$3.431705475$ |
$0.685091833$ |
6.867808126 |
\( \frac{124475734657}{63011844} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -104\) , \( 101\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-104{x}+101$ |
| 294.1-c4 |
294.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
294.1 |
\( 2 \cdot 3 \cdot 7^{2} \) |
\( 2^{2} \cdot 3^{8} \cdot 7^{16} \) |
$4.05337$ |
$(2,a), (3,a), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{5} \) |
$1.715852737$ |
$0.342545916$ |
6.867808126 |
\( \frac{84448510979617}{933897762} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -914\) , \( -10915\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-914{x}-10915$ |
| 294.1-c5 |
294.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
294.1 |
\( 2 \cdot 3 \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{8} \cdot 7^{4} \) |
$4.05337$ |
$(2,a), (3,a), (7)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{5} \) |
$6.863410950$ |
$1.370183666$ |
6.867808126 |
\( \frac{65597103937}{63504} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -84\) , \( 261\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-84{x}+261$ |
| 294.1-c6 |
294.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
294.1 |
\( 2 \cdot 3 \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{4} \cdot 7^{2} \) |
$4.05337$ |
$(2,a), (3,a), (7)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$13.72682190$ |
$0.685091833$ |
6.867808126 |
\( \frac{268498407453697}{252} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -1344\) , \( 18405\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-1344{x}+18405$ |
| 294.1-d1 |
294.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
294.1 |
\( 2 \cdot 3 \cdot 7^{2} \) |
\( 2^{28} \cdot 3^{4} \cdot 7^{2} \) |
$4.05337$ |
$(2,a), (3,a), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$2.740367332$ |
8.005125353 |
\( -\frac{7189057}{16128} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 13\) , \( 87\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+{x}^2+13{x}+87$ |
| 294.1-d2 |
294.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
294.1 |
\( 2 \cdot 3 \cdot 7^{2} \) |
\( 2^{14} \cdot 3^{32} \cdot 7^{4} \) |
$4.05337$ |
$(2,a), (3,a), (7)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{7} \) |
$1$ |
$0.342545916$ |
8.005125353 |
\( \frac{6359387729183}{4218578658} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 1573\) , \( 5583\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+{x}^2+1573{x}+5583$ |
| 294.1-d3 |
294.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
294.1 |
\( 2 \cdot 3 \cdot 7^{2} \) |
\( 2^{16} \cdot 3^{16} \cdot 7^{8} \) |
$4.05337$ |
$(2,a), (3,a), (7)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{8} \) |
$1$ |
$0.685091833$ |
8.005125353 |
\( \frac{124475734657}{63011844} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -387\) , \( 2055\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+{x}^2-387{x}+2055$ |
| 294.1-d4 |
294.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
294.1 |
\( 2 \cdot 3 \cdot 7^{2} \) |
\( 2^{14} \cdot 3^{8} \cdot 7^{16} \) |
$4.05337$ |
$(2,a), (3,a), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{7} \) |
$1$ |
$0.342545916$ |
8.005125353 |
\( \frac{84448510979617}{933897762} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -3627\) , \( -76353\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+{x}^2-3627{x}-76353$ |
| 294.1-d5 |
294.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
294.1 |
\( 2 \cdot 3 \cdot 7^{2} \) |
\( 2^{20} \cdot 3^{8} \cdot 7^{4} \) |
$4.05337$ |
$(2,a), (3,a), (7)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{7} \) |
$1$ |
$1.370183666$ |
8.005125353 |
\( \frac{65597103937}{63504} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -307\) , \( 3095\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+{x}^2-307{x}+3095$ |
| 294.1-d6 |
294.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
294.1 |
\( 2 \cdot 3 \cdot 7^{2} \) |
\( 2^{16} \cdot 3^{4} \cdot 7^{2} \) |
$4.05337$ |
$(2,a), (3,a), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{4} \) |
$1$ |
$0.685091833$ |
8.005125353 |
\( \frac{268498407453697}{252} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -5347\) , \( 163367\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+{x}^2-5347{x}+163367$ |
*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.
