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 |
32.1-a1 |
32.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$1.34418$ |
$(2,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.949741086$ |
$13.75037163$ |
2.064855508 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+{x}$ |
32.1-a2 |
32.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{24} \) |
$1.34418$ |
$(2,a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1.899482172$ |
$27.50074327$ |
2.064855508 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -4\) , \( 0\bigr] \) |
${y}^2={x}^{3}-4{x}$ |
32.1-b1 |
32.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$1.34418$ |
$(2,a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$27.50074327$ |
1.087062326 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -1\) , \( 0\bigr] \) |
${y}^2={x}^{3}-{x}$ |
32.1-b2 |
32.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{24} \) |
$1.34418$ |
$(2,a)$ |
0 |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$4$ |
\( 2 \) |
$1$ |
$13.75037163$ |
1.087062326 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 4\) , \( 0\bigr] \) |
${y}^2={x}^{3}+4{x}$ |
256.1-b1 |
256.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{12} \) |
$2.26063$ |
$(2,a)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1.838697222$ |
$13.75037163$ |
3.997556959 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -6 a + 19\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-6a+19\right){x}$ |
256.1-b2 |
256.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{24} \) |
$2.26063$ |
$(2,a)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1.838697222$ |
$27.50074327$ |
3.997556959 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 24 a - 76\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(24a-76\right){x}$ |
256.1-e1 |
256.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{24} \) |
$2.26063$ |
$(2,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$4$ |
\( 1 \) |
$1$ |
$13.75037163$ |
2.174124652 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -24 a + 76\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-24a+76\right){x}$ |
256.1-e2 |
256.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{12} \) |
$2.26063$ |
$(2,a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$4$ |
\( 2 \) |
$1$ |
$27.50074327$ |
2.174124652 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 6 a - 19\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(6a-19\right){x}$ |
288.2-a1 |
288.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
288.2 |
\( 2^{5} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{6} \) |
$2.32818$ |
$(2,a), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$15.87756153$ |
2.510462906 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 4 a - 13\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(4a-13\right){x}$ |
288.2-a2 |
288.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
288.2 |
\( 2^{5} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{6} \) |
$2.32818$ |
$(2,a), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$1$ |
$7.938780765$ |
2.510462906 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -16 a + 52\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-16a+52\right){x}$ |
288.2-f1 |
288.2-f |
$2$ |
$2$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
288.2 |
\( 2^{5} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{6} \) |
$2.32818$ |
$(2,a), (3,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$0.492517393$ |
$7.938780765$ |
2.472893293 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -4 a + 13\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-4a+13\right){x}$ |
288.2-f2 |
288.2-f |
$2$ |
$2$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
288.2 |
\( 2^{5} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{6} \) |
$2.32818$ |
$(2,a), (3,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$0.246258696$ |
$15.87756153$ |
2.472893293 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 16 a - 52\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(16a-52\right){x}$ |
288.3-a1 |
288.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
288.3 |
\( 2^{5} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{6} \) |
$2.32818$ |
$(2,a), (3,a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$15.87756153$ |
2.510462906 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -4 a - 13\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-4a-13\right){x}$ |
288.3-a2 |
288.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
288.3 |
\( 2^{5} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{6} \) |
$2.32818$ |
$(2,a), (3,a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$1$ |
$7.938780765$ |
2.510462906 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 16 a + 52\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(16a+52\right){x}$ |
288.3-f1 |
288.3-f |
$2$ |
$2$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
288.3 |
\( 2^{5} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{6} \) |
$2.32818$ |
$(2,a), (3,a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$0.492517393$ |
$7.938780765$ |
2.472893293 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 4 a + 13\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(4a+13\right){x}$ |
288.3-f2 |
288.3-f |
$2$ |
$2$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
288.3 |
\( 2^{5} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{6} \) |
$2.32818$ |
$(2,a), (3,a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$0.246258696$ |
$15.87756153$ |
2.472893293 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -16 a - 52\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-16a-52\right){x}$ |
*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.