| 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 |
| 17.1-a1 |
17.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{51}) \) |
$2$ |
$[2, 0]$ |
17.1 |
\( 17 \) |
\( 3^{12} \cdot 17^{8} \) |
$2.59159$ |
$(17,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$16$ |
\( 2 \) |
$1$ |
$7.539083304$ |
4.222731281 |
\( -\frac{35937}{83521} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -6\) , \( 377\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-6{x}+377$ |
| 17.1-a2 |
17.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{51}) \) |
$2$ |
$[2, 0]$ |
17.1 |
\( 17 \) |
\( 3^{12} \cdot 17^{2} \) |
$2.59159$ |
$(17,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$30.15633321$ |
4.222731281 |
\( \frac{35937}{17} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -6\) , \( -1\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-6{x}-1$ |
| 17.1-a3 |
17.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{51}) \) |
$2$ |
$[2, 0]$ |
17.1 |
\( 17 \) |
\( 3^{12} \cdot 17^{4} \) |
$2.59159$ |
$(17,a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$16$ |
\( 2 \) |
$1$ |
$30.15633321$ |
4.222731281 |
\( \frac{20346417}{289} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -51\) , \( 152\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-51{x}+152$ |
| 17.1-a4 |
17.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{51}) \) |
$2$ |
$[2, 0]$ |
17.1 |
\( 17 \) |
\( 3^{12} \cdot 17^{2} \) |
$2.59159$ |
$(17,a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$16$ |
\( 2 \) |
$1$ |
$30.15633321$ |
4.222731281 |
\( \frac{82483294977}{17} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -816\) , \( 9179\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-816{x}+9179$ |
| 17.1-b1 |
17.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{51}) \) |
$2$ |
$[2, 0]$ |
17.1 |
\( 17 \) |
\( 3^{12} \cdot 17^{8} \) |
$2.59159$ |
$(17,a)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$11.00049651$ |
$2.393455763$ |
3.686825688 |
\( -\frac{35937}{83521} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 48\) , \( -325\bigr] \) |
${y}^2+w{x}{y}={x}^3+48{x}-325$ |
| 17.1-b2 |
17.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{51}) \) |
$2$ |
$[2, 0]$ |
17.1 |
\( 17 \) |
\( 3^{12} \cdot 17^{2} \) |
$2.59159$ |
$(17,a)$ |
$2$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$2.750124128$ |
$38.29529222$ |
3.686825688 |
\( \frac{35937}{17} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 48\) , \( 53\bigr] \) |
${y}^2+w{x}{y}={x}^3+48{x}+53$ |
| 17.1-b3 |
17.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{51}) \) |
$2$ |
$[2, 0]$ |
17.1 |
\( 17 \) |
\( 3^{12} \cdot 17^{4} \) |
$2.59159$ |
$(17,a)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$11.00049651$ |
$9.573823055$ |
3.686825688 |
\( \frac{20346417}{289} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 3\) , \( -280\bigr] \) |
${y}^2+w{x}{y}={x}^3+3{x}-280$ |
| 17.1-b4 |
17.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{51}) \) |
$2$ |
$[2, 0]$ |
17.1 |
\( 17 \) |
\( 3^{12} \cdot 17^{2} \) |
$2.59159$ |
$(17,a)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$11.00049651$ |
$2.393455763$ |
3.686825688 |
\( \frac{82483294977}{17} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -762\) , \( -12367\bigr] \) |
${y}^2+w{x}{y}={x}^3-762{x}-12367$ |
| 17.1-c1 |
17.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{51}) \) |
$2$ |
$[2, 0]$ |
17.1 |
\( 17 \) |
\( 17^{8} \) |
$2.59159$ |
$(17,a)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$2.036297434$ |
$7.539083304$ |
1.074842109 |
\( -\frac{35937}{83521} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 28\) , \( 75\bigr] \) |
${y}^2+w{x}{y}+w{y}={x}^3+28{x}+75$ |
| 17.1-c2 |
17.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{51}) \) |
$2$ |
$[2, 0]$ |
17.1 |
\( 17 \) |
\( 17^{2} \) |
$2.59159$ |
$(17,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.509074358$ |
$30.15633321$ |
1.074842109 |
\( \frac{35937}{17} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 28\) , \( 61\bigr] \) |
${y}^2+w{x}{y}+w{y}={x}^3+28{x}+61$ |
| 17.1-c3 |
17.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{51}) \) |
$2$ |
$[2, 0]$ |
17.1 |
\( 17 \) |
\( 17^{4} \) |
$2.59159$ |
$(17,a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1.018148717$ |
$30.15633321$ |
1.074842109 |
\( \frac{20346417}{289} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 23\) , \( 45\bigr] \) |
${y}^2+w{x}{y}+w{y}={x}^3+23{x}+45$ |
| 17.1-c4 |
17.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{51}) \) |
$2$ |
$[2, 0]$ |
17.1 |
\( 17 \) |
\( 17^{2} \) |
$2.59159$ |
$(17,a)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$2.036297434$ |
$30.15633321$ |
1.074842109 |
\( \frac{82483294977}{17} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -62\) , \( 11\bigr] \) |
${y}^2+w{x}{y}+w{y}={x}^3-62{x}+11$ |
| 17.1-d1 |
17.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{51}) \) |
$2$ |
$[2, 0]$ |
17.1 |
\( 17 \) |
\( 17^{8} \) |
$2.59159$ |
$(17,a)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$13.65757227$ |
$2.393455763$ |
2.288673435 |
\( -\frac{35937}{83521} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -1\) , \( -14\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-{x}-14$ |
| 17.1-d2 |
17.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{51}) \) |
$2$ |
$[2, 0]$ |
17.1 |
\( 17 \) |
\( 17^{2} \) |
$2.59159$ |
$(17,a)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$3.414393067$ |
$38.29529222$ |
2.288673435 |
\( \frac{35937}{17} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -1\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-{x}$ |
| 17.1-d3 |
17.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{51}) \) |
$2$ |
$[2, 0]$ |
17.1 |
\( 17 \) |
\( 17^{4} \) |
$2.59159$ |
$(17,a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$6.828786135$ |
$9.573823055$ |
2.288673435 |
\( \frac{20346417}{289} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -6\) , \( -4\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-6{x}-4$ |
| 17.1-d4 |
17.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{51}) \) |
$2$ |
$[2, 0]$ |
17.1 |
\( 17 \) |
\( 17^{2} \) |
$2.59159$ |
$(17,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$13.65757227$ |
$2.393455763$ |
2.288673435 |
\( \frac{82483294977}{17} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -91\) , \( -310\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-91{x}-310$ |
*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.
