| 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 |
| 9.1-a3 |
9.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{3} \) |
$0.53615$ |
$(a)$ |
0 |
$\Z/6\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \) |
$1$ |
$29.55147182$ |
0.473931950 |
\( 1728 \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( 0\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}$ |
| 9.1-a4 |
9.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{3} \) |
$0.53615$ |
$(a)$ |
0 |
$\Z/6\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \) |
$1$ |
$29.55147182$ |
0.473931950 |
\( 1728 \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( -7 a + 13\) , \( 6 a - 10\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-7a+13\right){x}+6a-10$ |
| 64.1-a1 |
64.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
64.1 |
\( 2^{6} \) |
\( 2^{12} \) |
$0.87554$ |
$(a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$27.50074327$ |
0.992347595 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -1\) , \( 0\bigr] \) |
${y}^2={x}^{3}-{x}$ |
| 64.1-a2 |
64.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
64.1 |
\( 2^{6} \) |
\( 2^{12} \) |
$0.87554$ |
$(a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$13.75037163$ |
0.992347595 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -4 a + 7\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-4a+7\right){x}$ |
| 121.2-a1 |
121.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
121.2 |
\( 11^{2} \) |
\( - 11^{9} \) |
$1.02666$ |
$(-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$6.438947969$ |
0.929382085 |
\( 1728 \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( -8 a + 10\) , \( 5 a - 12\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-8a+10\right){x}+5a-12$ |
| 121.2-a2 |
121.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
121.2 |
\( 11^{2} \) |
\( - 11^{9} \) |
$1.02666$ |
$(-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$6.438947969$ |
0.929382085 |
\( 1728 \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( 15 a + 27\) , \( 13 a + 23\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(15a+27\right){x}+13a+23$ |
| 121.3-a1 |
121.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
121.3 |
\( 11^{2} \) |
\( - 11^{9} \) |
$1.02666$ |
$(2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$6.438947969$ |
0.929382085 |
\( 1728 \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( -16 a + 26\) , \( 13 a - 24\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-16a+26\right){x}+13a-24$ |
| 121.3-a2 |
121.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
121.3 |
\( 11^{2} \) |
\( - 11^{9} \) |
$1.02666$ |
$(2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$6.438947969$ |
0.929382085 |
\( 1728 \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( 209 a - 361\) , \( -181 a + 314\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(209a-361\right){x}-181a+314$ |
| 144.1-b3 |
144.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( - 2^{12} \cdot 3^{9} \) |
$1.07231$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3$ |
3Cs |
$1$ |
\( 2 \) |
$1$ |
$8.530775105$ |
1.231311325 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -6 a - 9\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-6a-9\right){x}$ |
| 144.1-b4 |
144.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( - 2^{12} \cdot 3^{9} \) |
$1.07231$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3$ |
3Cs |
$1$ |
\( 2 \) |
$1$ |
$8.530775105$ |
1.231311325 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 6 a - 9\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(6a-9\right){x}$ |
| 169.2-b1 |
169.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
169.2 |
\( 13^{2} \) |
\( 13^{3} \) |
$1.11609$ |
$(a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.328668069$ |
$14.48300210$ |
1.374122605 |
\( 1728 \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( -22 a + 38\) , \( 19 a - 33\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-22a+38\right){x}+19a-33$ |
| 169.2-b2 |
169.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
169.2 |
\( 13^{2} \) |
\( 13^{3} \) |
$1.11609$ |
$(a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.164334034$ |
$28.96600420$ |
1.374122605 |
\( 1728 \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( a - 1\) , \( -a + 2\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(a-1\right){x}-a+2$ |
| 169.3-b1 |
169.3-b |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
169.3 |
\( 13^{2} \) |
\( 13^{3} \) |
$1.11609$ |
$(a+4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.164334034$ |
$28.96600420$ |
1.374122605 |
\( 1728 \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( 8 a - 14\) , \( -7 a + 12\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(8a-14\right){x}-7a+12$ |
| 169.3-b2 |
169.3-b |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
169.3 |
\( 13^{2} \) |
\( 13^{3} \) |
$1.11609$ |
$(a+4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.328668069$ |
$14.48300210$ |
1.374122605 |
\( 1728 \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( -a + 3\) , \( a - 1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-a+3\right){x}+a-1$ |
| 256.1-f1 |
256.1-f |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{12} \) |
$1.23820$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.444312937$ |
$13.75037163$ |
1.763651500 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+{x}$ |
| 256.1-f2 |
256.1-f |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{12} \) |
$1.23820$ |
$(a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.888625874$ |
$27.50074327$ |
1.763651500 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 4 a - 7\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(4a-7\right){x}$ |
| 576.1-c1 |
576.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{6} \) |
$1.51647$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$0.501182392$ |
$7.938780765$ |
2.297148049 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 3\) , \( 0\bigr] \) |
${y}^2={x}^{3}+3{x}$ |
| 576.1-c2 |
576.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{6} \) |
$1.51647$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.250591196$ |
$15.87756153$ |
2.297148049 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 12 a - 21\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(12a-21\right){x}$ |
| 1024.1-h1 |
1024.1-h |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{18} \) |
$1.75107$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$9.722981027$ |
1.403391428 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -2 a + 4\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-2a+4\right){x}$ |
| 1024.1-h2 |
1024.1-h |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{18} \) |
$1.75107$ |
$(a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$19.44596205$ |
1.403391428 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 30 a - 52\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(30a-52\right){x}$ |
| 1024.1-m1 |
1024.1-m |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{18} \) |
$1.75107$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$9.722981027$ |
1.403391428 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 2 a + 4\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(2a+4\right){x}$ |
| 1024.1-m2 |
1024.1-m |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{18} \) |
$1.75107$ |
$(a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$19.44596205$ |
1.403391428 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 2 a - 4\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(2a-4\right){x}$ |
| 1089.2-d3 |
1089.2-d |
$6$ |
$18$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1089.2 |
\( 3^{2} \cdot 11^{2} \) |
\( - 3^{9} \cdot 11^{6} \) |
$1.77822$ |
$(a), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3$ |
3Cs |
$1$ |
\( 2^{2} \) |
$0.799820881$ |
$5.144250944$ |
2.375495747 |
\( 1728 \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( 388 a - 672\) , \( -336 a + 582\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(388a-672\right){x}-336a+582$ |
| 1089.2-d4 |
1089.2-d |
$6$ |
$18$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1089.2 |
\( 3^{2} \cdot 11^{2} \) |
\( - 3^{9} \cdot 11^{6} \) |
$1.77822$ |
$(a), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3$ |
3Cs |
$1$ |
\( 2^{3} \) |
$0.399910440$ |
$5.144250944$ |
2.375495747 |
\( 1728 \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( -29 a + 49\) , \( 24 a - 43\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-29a+49\right){x}+24a-43$ |
| 1089.2-g1 |
1089.2-g |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1089.2 |
\( 3^{2} \cdot 11^{2} \) |
\( - 3^{6} \cdot 11^{3} \) |
$1.77822$ |
$(a), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$0.329680234$ |
$12.32964666$ |
2.346836933 |
\( 1728 \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( -8 a - 12\) , \( -6 a - 12\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-8a-12\right){x}-6a-12$ |
| 1089.2-g2 |
1089.2-g |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1089.2 |
\( 3^{2} \cdot 11^{2} \) |
\( - 3^{6} \cdot 11^{3} \) |
$1.77822$ |
$(a), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$0.164840117$ |
$12.32964666$ |
2.346836933 |
\( 1728 \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( a + 1\) , \( 2\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(a+1\right){x}+2$ |
| 1089.3-d3 |
1089.3-d |
$6$ |
$18$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1089.3 |
\( 3^{2} \cdot 11^{2} \) |
\( - 3^{9} \cdot 11^{6} \) |
$1.77822$ |
$(a), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3$ |
3Cs |
$1$ |
\( 2^{2} \) |
$0.799820881$ |
$5.144250944$ |
2.375495747 |
\( 1728 \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( -11 a + 13\) , \( 6 a - 16\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-11a+13\right){x}+6a-16$ |
| 1089.3-d4 |
1089.3-d |
$6$ |
$18$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1089.3 |
\( 3^{2} \cdot 11^{2} \) |
\( - 3^{9} \cdot 11^{6} \) |
$1.77822$ |
$(a), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3$ |
3Cs |
$1$ |
\( 2^{3} \) |
$0.399910440$ |
$5.144250944$ |
2.375495747 |
\( 1728 \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( 118 a - 204\) , \( -102 a + 177\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(118a-204\right){x}-102a+177$ |
| 1089.3-g1 |
1089.3-g |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1089.3 |
\( 3^{2} \cdot 11^{2} \) |
\( - 3^{6} \cdot 11^{3} \) |
$1.77822$ |
$(a), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$0.329680234$ |
$12.32964666$ |
2.346836933 |
\( 1728 \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( 7 a - 11\) , \( -6 a + 11\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(7a-11\right){x}-6a+11$ |
| 1089.3-g2 |
1089.3-g |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1089.3 |
\( 3^{2} \cdot 11^{2} \) |
\( - 3^{6} \cdot 11^{3} \) |
$1.77822$ |
$(a), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$0.164840117$ |
$12.32964666$ |
2.346836933 |
\( 1728 \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( -104 a + 180\) , \( 90 a - 156\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-104a+180\right){x}+90a-156$ |
| 1369.2-a1 |
1369.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1369.2 |
\( 37^{2} \) |
\( 37^{9} \) |
$1.88291$ |
$(2a+7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$2.260953916$ |
$3.666258935$ |
2.392898194 |
\( 1728 \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( 618 a - 1072\) , \( -536 a + 927\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(618a-1072\right){x}-536a+927$ |
| 1369.2-a2 |
1369.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1369.2 |
\( 37^{2} \) |
\( 37^{9} \) |
$1.88291$ |
$(2a+7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$4.521907833$ |
$1.833129467$ |
2.392898194 |
\( 1728 \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( -39 a + 89\) , \( 44 a - 58\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-39a+89\right){x}+44a-58$ |
| 1369.3-a1 |
1369.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1369.3 |
\( 37^{2} \) |
\( 37^{9} \) |
$1.88291$ |
$(-2a+7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$4.521907833$ |
$1.833129467$ |
2.392898194 |
\( 1728 \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( 38 a + 88\) , \( 44 a + 57\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(38a+88\right){x}+44a+57$ |
| 1369.3-a2 |
1369.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1369.3 |
\( 37^{2} \) |
\( 37^{9} \) |
$1.88291$ |
$(-2a+7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$2.260953916$ |
$3.666258935$ |
2.392898194 |
\( 1728 \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( 79 a - 147\) , \( -74 a + 119\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(79a-147\right){x}-74a+119$ |
| 1521.2-a1 |
1521.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1521.2 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{6} \cdot 13^{9} \) |
$1.93313$ |
$(a), (a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$4.638272776$ |
1.338954018 |
\( 1728 \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( -131 a - 227\) , \( -114 a - 196\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-131a-227\right){x}-114a-196$ |
| 1521.2-a2 |
1521.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1521.2 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{6} \cdot 13^{9} \) |
$1.93313$ |
$(a), (a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$1$ |
$2.319136388$ |
1.338954018 |
\( 1728 \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( -2 a + 36\) , \( 18 a - 3\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-2a+36\right){x}+18a-3$ |
| 1521.2-b3 |
1521.2-b |
$6$ |
$18$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1521.2 |
\( 3^{2} \cdot 13^{2} \) |
\( - 3^{9} \cdot 13^{6} \) |
$1.93313$ |
$(a), (a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3$ |
3Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$4.732022625$ |
1.366017268 |
\( 1728 \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( 46 a - 78\) , \( -39 a + 69\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(46a-78\right){x}-39a+69$ |
| 1521.2-b4 |
1521.2-b |
$6$ |
$18$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1521.2 |
\( 3^{2} \cdot 13^{2} \) |
\( - 3^{9} \cdot 13^{6} \) |
$1.93313$ |
$(a), (a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3$ |
3Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$4.732022625$ |
1.366017268 |
\( 1728 \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( -641 a + 1111\) , \( 555 a - 961\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-641a+1111\right){x}+555a-961$ |
| 1521.3-a1 |
1521.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1521.3 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{6} \cdot 13^{9} \) |
$1.93313$ |
$(a), (a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$4.638272776$ |
1.338954018 |
\( 1728 \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( 130 a - 228\) , \( -114 a + 195\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(130a-228\right){x}-114a+195$ |
| 1521.3-a2 |
1521.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1521.3 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{6} \cdot 13^{9} \) |
$1.93313$ |
$(a), (a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$1$ |
$2.319136388$ |
1.338954018 |
\( 1728 \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( a + 37\) , \( 18 a + 2\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(a+37\right){x}+18a+2$ |
| 1521.3-b3 |
1521.3-b |
$6$ |
$18$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1521.3 |
\( 3^{2} \cdot 13^{2} \) |
\( - 3^{9} \cdot 13^{6} \) |
$1.93313$ |
$(a), (a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3$ |
3Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$4.732022625$ |
1.366017268 |
\( 1728 \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( 10 a - 6\) , \( -3 a + 15\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(10a-6\right){x}-3a+15$ |
| 1521.3-b4 |
1521.3-b |
$6$ |
$18$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1521.3 |
\( 3^{2} \cdot 13^{2} \) |
\( - 3^{9} \cdot 13^{6} \) |
$1.93313$ |
$(a), (a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3$ |
3Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$4.732022625$ |
1.366017268 |
\( 1728 \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( -101 a + 175\) , \( 87 a - 151\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-101a+175\right){x}+87a-151$ |
| 1936.2-e1 |
1936.2-e |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1936.2 |
\( 2^{4} \cdot 11^{2} \) |
\( - 2^{12} \cdot 11^{3} \) |
$2.05331$ |
$(a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$10.67778723$ |
1.541205832 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 2 a - 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(2a-1\right){x}$ |
| 1936.2-e2 |
1936.2-e |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1936.2 |
\( 2^{4} \cdot 11^{2} \) |
\( - 2^{12} \cdot 11^{3} \) |
$2.05331$ |
$(a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$10.67778723$ |
1.541205832 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -18 a + 31\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-18a+31\right){x}$ |
| 1936.3-e1 |
1936.3-e |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1936.3 |
\( 2^{4} \cdot 11^{2} \) |
\( - 2^{12} \cdot 11^{3} \) |
$2.05331$ |
$(a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$10.67778723$ |
1.541205832 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 10 a - 17\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(10a-17\right){x}$ |
| 1936.3-e2 |
1936.3-e |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1936.3 |
\( 2^{4} \cdot 11^{2} \) |
\( - 2^{12} \cdot 11^{3} \) |
$2.05331$ |
$(a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$10.67778723$ |
1.541205832 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -2 a - 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-2a-1\right){x}$ |
| 2304.1-c1 |
2304.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{6} \) |
$2.14462$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$7.938780765$ |
2.291728606 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -12 a + 21\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-12a+21\right){x}$ |
| 2304.1-c2 |
2304.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{6} \) |
$2.14462$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$15.87756153$ |
2.291728606 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -3\) , \( 0\bigr] \) |
${y}^2={x}^{3}-3{x}$ |
| 2304.1-g3 |
2304.1-g |
$6$ |
$18$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( - 2^{12} \cdot 3^{3} \) |
$2.14462$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3$ |
3Cs |
$1$ |
\( 2 \) |
$1$ |
$14.77573591$ |
2.132693776 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -2 a - 3\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-2a-3\right){x}$ |
| 2304.1-g4 |
2304.1-g |
$6$ |
$18$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( - 2^{12} \cdot 3^{3} \) |
$2.14462$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3$ |
3Cs |
$1$ |
\( 2 \) |
$1$ |
$14.77573591$ |
2.132693776 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 2 a - 3\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(2a-3\right){x}$ |
*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.
