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-a1 |
9.1-a |
$4$ |
$14$ |
\(\Q(\sqrt{-35}) \) |
$2$ |
$[0, 1]$ |
9.1 |
\( 3^{2} \) |
\( 3^{18} \) |
$0.91566$ |
$(3,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-7$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5, 7$ |
5Nn.1.1.1, 7B.6.2 |
$1$ |
\( 2 \) |
$1$ |
$7.552855534$ |
1.276665598 |
\( -3375 \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( 2 a + 3\) , \( -a - 10\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^3-{x}^2+\left(2a+3\right){x}-a-10$ |
9.1-a2 |
9.1-a |
$4$ |
$14$ |
\(\Q(\sqrt{-35}) \) |
$2$ |
$[0, 1]$ |
9.1 |
\( 3^{2} \) |
\( 3^{6} \) |
$0.91566$ |
$(3,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-7$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5, 7$ |
5Nn.1.1.1, 7B.6.2 |
$1$ |
\( 2 \) |
$1$ |
$7.552855534$ |
1.276665598 |
\( -3375 \) |
\( \bigl[a\) , \( -a\) , \( 0\) , \( a\) , \( 0\bigr] \) |
${y}^2+a{x}{y}={x}^3-a{x}^2+a{x}$ |
9.1-a3 |
9.1-a |
$4$ |
$14$ |
\(\Q(\sqrt{-35}) \) |
$2$ |
$[0, 1]$ |
9.1 |
\( 3^{2} \) |
\( 3^{6} \) |
$0.91566$ |
$(3,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-28$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5, 7$ |
5Nn.1.1.1, 7B.6.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$3.776427767$ |
1.276665598 |
\( 16581375 \) |
\( \bigl[a\) , \( -a\) , \( 0\) , \( -4 a\) , \( 12 a - 27\bigr] \) |
${y}^2+a{x}{y}={x}^3-a{x}^2-4a{x}+12a-27$ |
9.1-a4 |
9.1-a |
$4$ |
$14$ |
\(\Q(\sqrt{-35}) \) |
$2$ |
$[0, 1]$ |
9.1 |
\( 3^{2} \) |
\( 3^{18} \) |
$0.91566$ |
$(3,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-28$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5, 7$ |
5Nn.1.1.1, 7B.6.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$3.776427767$ |
1.276665598 |
\( 16581375 \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( 42 a + 48\) , \( -18 a - 667\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^3-{x}^2+\left(42a+48\right){x}-18a-667$ |
9.3-a1 |
9.3-a |
$4$ |
$14$ |
\(\Q(\sqrt{-35}) \) |
$2$ |
$[0, 1]$ |
9.3 |
\( 3^{2} \) |
\( 3^{6} \) |
$0.91566$ |
$(3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-7$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5, 7$ |
5Nn.1.1.1, 7B.6.2 |
$1$ |
\( 2 \) |
$1$ |
$7.552855534$ |
1.276665598 |
\( -3375 \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -a + 1\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3-{x}^2+\left(-a+1\right){x}$ |
9.3-a2 |
9.3-a |
$4$ |
$14$ |
\(\Q(\sqrt{-35}) \) |
$2$ |
$[0, 1]$ |
9.3 |
\( 3^{2} \) |
\( 3^{18} \) |
$0.91566$ |
$(3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-7$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5, 7$ |
5Nn.1.1.1, 7B.6.2 |
$1$ |
\( 2 \) |
$1$ |
$7.552855534$ |
1.276665598 |
\( -3375 \) |
\( \bigl[a\) , \( -a\) , \( 1\) , \( -2 a\) , \( -a + 2\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^3-a{x}^2-2a{x}-a+2$ |
9.3-a3 |
9.3-a |
$4$ |
$14$ |
\(\Q(\sqrt{-35}) \) |
$2$ |
$[0, 1]$ |
9.3 |
\( 3^{2} \) |
\( 3^{18} \) |
$0.91566$ |
$(3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-28$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5, 7$ |
5Nn.1.1.1, 7B.6.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$3.776427767$ |
1.276665598 |
\( 16581375 \) |
\( \bigl[a\) , \( -a\) , \( 1\) , \( -47 a\) , \( -145 a + 326\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^3-a{x}^2-47a{x}-145a+326$ |
9.3-a4 |
9.3-a |
$4$ |
$14$ |
\(\Q(\sqrt{-35}) \) |
$2$ |
$[0, 1]$ |
9.3 |
\( 3^{2} \) |
\( 3^{6} \) |
$0.91566$ |
$(3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-28$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5, 7$ |
5Nn.1.1.1, 7B.6.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$3.776427767$ |
1.276665598 |
\( 16581375 \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 4 a - 4\) , \( -12 a - 15\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3-{x}^2+\left(4a-4\right){x}-12a-15$ |
27.2-a1 |
27.2-a |
$4$ |
$6$ |
\(\Q(\sqrt{-35}) \) |
$2$ |
$[0, 1]$ |
27.2 |
\( 3^{3} \) |
\( 3^{22} \) |
$1.20507$ |
$(3,a), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.726183581$ |
1.167113118 |
\( \frac{423756935}{531441} a + \frac{2520558145}{531441} \) |
\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -6 a - 5\) , \( 14 a - 39\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+\left(-a-1\right){x}^2+\left(-6a-5\right){x}+14a-39$ |
27.2-a2 |
27.2-a |
$4$ |
$6$ |
\(\Q(\sqrt{-35}) \) |
$2$ |
$[0, 1]$ |
27.2 |
\( 3^{3} \) |
\( 3^{34} \) |
$1.20507$ |
$(3,a), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.726183581$ |
1.167113118 |
\( -\frac{423756935}{531441} a + \frac{327146120}{59049} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 61 a - 77\) , \( 235 a + 303\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^3-{x}^2+\left(61a-77\right){x}+235a+303$ |
27.2-a3 |
27.2-a |
$4$ |
$6$ |
\(\Q(\sqrt{-35}) \) |
$2$ |
$[0, 1]$ |
27.2 |
\( 3^{3} \) |
\( 3^{26} \) |
$1.20507$ |
$(3,a), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.452367163$ |
1.167113118 |
\( \frac{1314665}{729} a + \frac{707095}{81} \) |
\( \bigl[a\) , \( a\) , \( 1\) , \( 16 a\) , \( 18 a + 47\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^3+a{x}^2+16a{x}+18a+47$ |
27.2-a4 |
27.2-a |
$4$ |
$6$ |
\(\Q(\sqrt{-35}) \) |
$2$ |
$[0, 1]$ |
27.2 |
\( 3^{3} \) |
\( 3^{14} \) |
$1.20507$ |
$(3,a), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.452367163$ |
1.167113118 |
\( -\frac{1314665}{729} a + \frac{7678520}{729} \) |
\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -a - 5\) , \( -3\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+\left(-a-1\right){x}^2+\left(-a-5\right){x}-3$ |
27.2-b1 |
27.2-b |
$4$ |
$6$ |
\(\Q(\sqrt{-35}) \) |
$2$ |
$[0, 1]$ |
27.2 |
\( 3^{3} \) |
\( 3^{34} \) |
$1.20507$ |
$(3,a), (3,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{4} \) |
$0.376040148$ |
$1.726183581$ |
1.755525560 |
\( \frac{423756935}{531441} a + \frac{2520558145}{531441} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( 50 a + 70\) , \( 22 a - 1196\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^3+\left(a-1\right){x}^2+\left(50a+70\right){x}+22a-1196$ |
27.2-b2 |
27.2-b |
$4$ |
$6$ |
\(\Q(\sqrt{-35}) \) |
$2$ |
$[0, 1]$ |
27.2 |
\( 3^{3} \) |
\( 3^{22} \) |
$1.20507$ |
$(3,a), (3,a+2)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{4} \cdot 3 \) |
$1.128120444$ |
$1.726183581$ |
1.755525560 |
\( -\frac{423756935}{531441} a + \frac{327146120}{59049} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( -10 a - 5\) , \( 12 a + 20\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^3+\left(a-1\right){x}^2+\left(-10a-5\right){x}+12a+20$ |
27.2-b3 |
27.2-b |
$4$ |
$6$ |
\(\Q(\sqrt{-35}) \) |
$2$ |
$[0, 1]$ |
27.2 |
\( 3^{3} \) |
\( 3^{14} \) |
$1.20507$ |
$(3,a), (3,a+2)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$2.256240889$ |
$3.452367163$ |
1.755525560 |
\( \frac{1314665}{729} a + \frac{707095}{81} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( -5 a - 5\) , \( 20\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^3+\left(a-1\right){x}^2+\left(-5a-5\right){x}+20$ |
27.2-b4 |
27.2-b |
$4$ |
$6$ |
\(\Q(\sqrt{-35}) \) |
$2$ |
$[0, 1]$ |
27.2 |
\( 3^{3} \) |
\( 3^{26} \) |
$1.20507$ |
$(3,a), (3,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$0.752080296$ |
$3.452367163$ |
1.755525560 |
\( -\frac{1314665}{729} a + \frac{7678520}{729} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( 10 a + 25\) , \( -8 a + 46\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^3+\left(a-1\right){x}^2+\left(10a+25\right){x}-8a+46$ |
27.3-a1 |
27.3-a |
$4$ |
$6$ |
\(\Q(\sqrt{-35}) \) |
$2$ |
$[0, 1]$ |
27.3 |
\( 3^{3} \) |
\( 3^{34} \) |
$1.20507$ |
$(3,a), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.726183581$ |
1.167113118 |
\( \frac{423756935}{531441} a + \frac{2520558145}{531441} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( -62 a - 15\) , \( -236 a + 539\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^3-{x}^2+\left(-62a-15\right){x}-236a+539$ |
27.3-a2 |
27.3-a |
$4$ |
$6$ |
\(\Q(\sqrt{-35}) \) |
$2$ |
$[0, 1]$ |
27.3 |
\( 3^{3} \) |
\( 3^{22} \) |
$1.20507$ |
$(3,a), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.726183581$ |
1.167113118 |
\( -\frac{423756935}{531441} a + \frac{327146120}{59049} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( 8 a - 11\) , \( -7 a - 36\bigr] \) |
${y}^2+{x}{y}={x}^3+\left(a+1\right){x}^2+\left(8a-11\right){x}-7a-36$ |
27.3-a3 |
27.3-a |
$4$ |
$6$ |
\(\Q(\sqrt{-35}) \) |
$2$ |
$[0, 1]$ |
27.3 |
\( 3^{3} \) |
\( 3^{14} \) |
$1.20507$ |
$(3,a), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.452367163$ |
1.167113118 |
\( \frac{1314665}{729} a + \frac{707095}{81} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( 3 a - 6\) , \( 2 a - 9\bigr] \) |
${y}^2+{x}{y}={x}^3+\left(a+1\right){x}^2+\left(3a-6\right){x}+2a-9$ |
27.3-a4 |
27.3-a |
$4$ |
$6$ |
\(\Q(\sqrt{-35}) \) |
$2$ |
$[0, 1]$ |
27.3 |
\( 3^{3} \) |
\( 3^{26} \) |
$1.20507$ |
$(3,a), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.452367163$ |
1.167113118 |
\( -\frac{1314665}{729} a + \frac{7678520}{729} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( -17 a - 15\) , \( 52 a - 28\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^3-{x}^2+\left(-17a-15\right){x}+52a-28$ |
27.3-b1 |
27.3-b |
$4$ |
$6$ |
\(\Q(\sqrt{-35}) \) |
$2$ |
$[0, 1]$ |
27.3 |
\( 3^{3} \) |
\( 3^{22} \) |
$1.20507$ |
$(3,a), (3,a+2)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{4} \cdot 3 \) |
$1.128120444$ |
$1.726183581$ |
1.755525560 |
\( \frac{423756935}{531441} a + \frac{2520558145}{531441} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( 6 a - 5\) , \( -12 a - 33\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+\left(a+1\right){x}^2+\left(6a-5\right){x}-12a-33$ |
27.3-b2 |
27.3-b |
$4$ |
$6$ |
\(\Q(\sqrt{-35}) \) |
$2$ |
$[0, 1]$ |
27.3 |
\( 3^{3} \) |
\( 3^{34} \) |
$1.20507$ |
$(3,a), (3,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{4} \) |
$0.376040148$ |
$1.726183581$ |
1.755525560 |
\( -\frac{423756935}{531441} a + \frac{327146120}{59049} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( -54 a + 130\) , \( 53 a - 699\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+\left(a+1\right){x}^2+\left(-54a+130\right){x}+53a-699$ |
27.3-b3 |
27.3-b |
$4$ |
$6$ |
\(\Q(\sqrt{-35}) \) |
$2$ |
$[0, 1]$ |
27.3 |
\( 3^{3} \) |
\( 3^{26} \) |
$1.20507$ |
$(3,a), (3,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$0.752080296$ |
$3.452367163$ |
1.755525560 |
\( \frac{1314665}{729} a + \frac{707095}{81} \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( -20 a + 16\) , \( 44 a - 107\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^3-{x}^2+\left(-20a+16\right){x}+44a-107$ |
27.3-b4 |
27.3-b |
$4$ |
$6$ |
\(\Q(\sqrt{-35}) \) |
$2$ |
$[0, 1]$ |
27.3 |
\( 3^{3} \) |
\( 3^{14} \) |
$1.20507$ |
$(3,a), (3,a+2)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \cdot 3 \) |
$2.256240889$ |
$3.452367163$ |
1.755525560 |
\( -\frac{1314665}{729} a + \frac{7678520}{729} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( a\) , \( 0\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+\left(a+1\right){x}^2+a{x}$ |
28.1-a1 |
28.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-35}) \) |
$2$ |
$[0, 1]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{36} \cdot 7^{2} \) |
$1.21608$ |
$(7,a+3), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$0.208472088$ |
$0.875417135$ |
1.110532924 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -171\) , \( -874\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-171{x}-874$ |
28.1-a2 |
28.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-35}) \) |
$2$ |
$[0, 1]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{4} \cdot 7^{2} \) |
$1.21608$ |
$(7,a+3), (2)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{2} \) |
$1.876248795$ |
$7.878754216$ |
1.110532924 |
\( -\frac{15625}{28} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}$ |
28.1-a3 |
28.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-35}) \) |
$2$ |
$[0, 1]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{12} \cdot 7^{6} \) |
$1.21608$ |
$(7,a+3), (2)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$0.625416265$ |
$2.626251405$ |
1.110532924 |
\( \frac{9938375}{21952} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 4\) , \( -6\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+4{x}-6$ |
28.1-a4 |
28.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-35}) \) |
$2$ |
$[0, 1]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{6} \cdot 7^{12} \) |
$1.21608$ |
$(7,a+3), (2)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1.250832530$ |
$1.313125702$ |
1.110532924 |
\( \frac{4956477625}{941192} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -36\) , \( -70\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-36{x}-70$ |
28.1-a5 |
28.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-35}) \) |
$2$ |
$[0, 1]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{2} \cdot 7^{4} \) |
$1.21608$ |
$(7,a+3), (2)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{2} \) |
$3.752497591$ |
$3.939377108$ |
1.110532924 |
\( \frac{128787625}{98} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -11\) , \( 12\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-11{x}+12$ |
28.1-a6 |
28.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-35}) \) |
$2$ |
$[0, 1]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{18} \cdot 7^{4} \) |
$1.21608$ |
$(7,a+3), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$0.416944176$ |
$0.437708567$ |
1.110532924 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2731\) , \( -55146\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-2731{x}-55146$ |
28.1-b1 |
28.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{-35}) \) |
$2$ |
$[0, 1]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{36} \cdot 3^{12} \cdot 7^{2} \) |
$1.21608$ |
$(7,a+3), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$0.875417135$ |
2.663505059 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[a\) , \( -1\) , \( a + 1\) , \( 169 a + 1372\) , \( 6819 a - 16217\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^3-{x}^2+\left(169a+1372\right){x}+6819a-16217$ |
28.1-b2 |
28.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{-35}) \) |
$2$ |
$[0, 1]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{4} \cdot 3^{12} \cdot 7^{2} \) |
$1.21608$ |
$(7,a+3), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$7.878754216$ |
2.663505059 |
\( -\frac{15625}{28} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( -a + 12\) , \( 2 a - 1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^3+\left(-a-1\right){x}^2+\left(-a+12\right){x}+2a-1$ |
28.1-b3 |
28.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{-35}) \) |
$2$ |
$[0, 1]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{12} \cdot 3^{12} \cdot 7^{6} \) |
$1.21608$ |
$(7,a+3), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$2.626251405$ |
2.663505059 |
\( \frac{9938375}{21952} \) |
\( \bigl[a\) , \( -1\) , \( a + 1\) , \( -6 a - 28\) , \( 50 a - 61\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^3-{x}^2+\left(-6a-28\right){x}+50a-61$ |
28.1-b4 |
28.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{-35}) \) |
$2$ |
$[0, 1]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{6} \cdot 3^{12} \cdot 7^{12} \) |
$1.21608$ |
$(7,a+3), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$4$ |
\( 2 \cdot 3 \) |
$1$ |
$1.313125702$ |
2.663505059 |
\( \frac{4956477625}{941192} \) |
\( \bigl[a\) , \( -1\) , \( a + 1\) , \( 34 a + 292\) , \( 522 a - 1469\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^3-{x}^2+\left(34a+292\right){x}+522a-1469$ |
28.1-b5 |
28.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{-35}) \) |
$2$ |
$[0, 1]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{2} \cdot 3^{12} \cdot 7^{4} \) |
$1.21608$ |
$(7,a+3), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$4$ |
\( 2 \) |
$1$ |
$3.939377108$ |
2.663505059 |
\( \frac{128787625}{98} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( -11 a + 102\) , \( 108 a + 17\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^3+\left(-a-1\right){x}^2+\left(-11a+102\right){x}+108a+17$ |
28.1-b6 |
28.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{-35}) \) |
$2$ |
$[0, 1]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{18} \cdot 3^{12} \cdot 7^{4} \) |
$1.21608$ |
$(7,a+3), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$4$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$0.437708567$ |
2.663505059 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[a\) , \( -1\) , \( a + 1\) , \( 2729 a + 21852\) , \( 438435 a - 959321\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^3-{x}^2+\left(2729a+21852\right){x}+438435a-959321$ |
35.1-a1 |
35.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{-35}) \) |
$2$ |
$[0, 1]$ |
35.1 |
\( 5 \cdot 7 \) |
\( 3^{12} \cdot 5^{18} \cdot 7^{2} \) |
$1.28585$ |
$(5,a+2), (7,a+3)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cn, 3Cs |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$0.034009387$ |
$0.774975202$ |
1.283054450 |
\( -\frac{250523582464}{13671875} \) |
\( \bigl[0\) , \( a - 1\) , \( 1\) , \( 131 a + 1048\) , \( 5198 a - 11046\bigr] \) |
${y}^2+{y}={x}^3+\left(a-1\right){x}^2+\left(131a+1048\right){x}+5198a-11046$ |
35.1-a2 |
35.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{-35}) \) |
$2$ |
$[0, 1]$ |
35.1 |
\( 5 \cdot 7 \) |
\( 3^{12} \cdot 5^{2} \cdot 7^{2} \) |
$1.28585$ |
$(5,a+2), (7,a+3)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cn, 3Cs |
$1$ |
\( 2^{2} \) |
$0.034009387$ |
$6.974776820$ |
1.283054450 |
\( -\frac{262144}{35} \) |
\( \bigl[0\) , \( -a\) , \( 1\) , \( -a + 9\) , \( 2 a + 2\bigr] \) |
${y}^2+{y}={x}^3-a{x}^2+\left(-a+9\right){x}+2a+2$ |
35.1-a3 |
35.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{-35}) \) |
$2$ |
$[0, 1]$ |
35.1 |
\( 5 \cdot 7 \) |
\( 3^{12} \cdot 5^{6} \cdot 7^{6} \) |
$1.28585$ |
$(5,a+2), (7,a+3)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cn, 3Cs |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.034009387$ |
$2.324925606$ |
1.283054450 |
\( \frac{71991296}{42875} \) |
\( \bigl[0\) , \( a - 1\) , \( 1\) , \( -9 a - 72\) , \( -10 a + 21\bigr] \) |
${y}^2+{y}={x}^3+\left(a-1\right){x}^2+\left(-9a-72\right){x}-10a+21$ |
35.1-b1 |
35.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{-35}) \) |
$2$ |
$[0, 1]$ |
35.1 |
\( 5 \cdot 7 \) |
\( 5^{18} \cdot 7^{2} \) |
$1.28585$ |
$(5,a+2), (7,a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cn, 3Cs.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$0.774975202$ |
1.047957743 |
\( -\frac{250523582464}{13671875} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -131\) , \( -650\bigr] \) |
${y}^2+{y}={x}^3+{x}^2-131{x}-650$ |
35.1-b2 |
35.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{-35}) \) |
$2$ |
$[0, 1]$ |
35.1 |
\( 5 \cdot 7 \) |
\( 5^{2} \cdot 7^{2} \) |
$1.28585$ |
$(5,a+2), (7,a+3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cn, 3Cs.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$6.974776820$ |
1.047957743 |
\( -\frac{262144}{35} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -1\) , \( 0\bigr] \) |
${y}^2+{y}={x}^3+{x}^2-{x}$ |
35.1-b3 |
35.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{-35}) \) |
$2$ |
$[0, 1]$ |
35.1 |
\( 5 \cdot 7 \) |
\( 5^{6} \cdot 7^{6} \) |
$1.28585$ |
$(5,a+2), (7,a+3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cn, 3Cs.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$2.324925606$ |
1.047957743 |
\( \frac{71991296}{42875} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( 9\) , \( 1\bigr] \) |
${y}^2+{y}={x}^3+{x}^2+9{x}+1$ |
45.1-a1 |
45.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-35}) \) |
$2$ |
$[0, 1]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{18} \cdot 5^{6} \) |
$1.36923$ |
$(3,a), (5,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cn, 3Nn |
$1$ |
\( 2 \cdot 3 \) |
$0.101186768$ |
$3.515460658$ |
1.443056014 |
\( -\frac{110592}{125} \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 9 a - 9\) , \( -27 a - 34\bigr] \) |
${y}^2+{y}={x}^3+\left(9a-9\right){x}-27a-34$ |
45.1-b1 |
45.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{-35}) \) |
$2$ |
$[0, 1]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{6} \cdot 5^{6} \) |
$1.36923$ |
$(3,a), (5,a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cn, 3Nn |
$1$ |
\( 2 \) |
$1$ |
$3.515460658$ |
2.376885226 |
\( -\frac{110592}{125} \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -a\) , \( -a + 2\bigr] \) |
${y}^2+{y}={x}^3-a{x}-a+2$ |
45.2-a1 |
45.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-35}) \) |
$2$ |
$[0, 1]$ |
45.2 |
\( 3^{2} \cdot 5 \) |
\( 3^{32} \cdot 5^{2} \) |
$1.36923$ |
$(3,a), (3,a+2), (5,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$0.558925428$ |
0.377902562 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -110\) , \( -880\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-110{x}-880$ |
45.2-a2 |
45.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-35}) \) |
$2$ |
$[0, 1]$ |
45.2 |
\( 3^{2} \cdot 5 \) |
\( 3^{2} \cdot 5^{2} \) |
$1.36923$ |
$(3,a), (3,a+2), (5,a+2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$8.942806850$ |
0.377902562 |
\( -\frac{1}{15} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2$ |
45.2-a3 |
45.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-35}) \) |
$2$ |
$[0, 1]$ |
45.2 |
\( 3^{2} \cdot 5 \) |
\( 3^{4} \cdot 5^{16} \) |
$1.36923$ |
$(3,a), (3,a+2), (5,a+2)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$1.117850856$ |
0.377902562 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 35\) , \( -28\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2+35{x}-28$ |
45.2-a4 |
45.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-35}) \) |
$2$ |
$[0, 1]$ |
45.2 |
\( 3^{2} \cdot 5 \) |
\( 3^{8} \cdot 5^{8} \) |
$1.36923$ |
$(3,a), (3,a+2), (5,a+2)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$2.235701712$ |
0.377902562 |
\( \frac{111284641}{50625} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -10\) , \( -10\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-10{x}-10$ |
45.2-a5 |
45.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-35}) \) |
$2$ |
$[0, 1]$ |
45.2 |
\( 3^{2} \cdot 5 \) |
\( 3^{4} \cdot 5^{4} \) |
$1.36923$ |
$(3,a), (3,a+2), (5,a+2)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$4.471403425$ |
0.377902562 |
\( \frac{13997521}{225} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -5\) , \( 2\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-5{x}+2$ |
45.2-a6 |
45.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-35}) \) |
$2$ |
$[0, 1]$ |
45.2 |
\( 3^{2} \cdot 5 \) |
\( 3^{16} \cdot 5^{4} \) |
$1.36923$ |
$(3,a), (3,a+2), (5,a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$1.117850856$ |
0.377902562 |
\( \frac{272223782641}{164025} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -135\) , \( -660\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-135{x}-660$ |
*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.