| 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 |
| 15.1-a1 |
15.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-435}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{44} \cdot 5^{2} \) |
$3.66780$ |
$(3,a+1), (5,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$7.173953560$ |
$0.558925428$ |
3.076010285 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -990\) , \( 22765\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-990{x}+22765$ |
| 15.1-a2 |
15.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-435}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{14} \cdot 5^{2} \) |
$3.66780$ |
$(3,a+1), (5,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1.793488390$ |
$8.942806850$ |
3.076010285 |
\( -\frac{1}{15} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 0\) , \( -5\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-5$ |
| 15.1-a3 |
15.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-435}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{16} \cdot 5^{16} \) |
$3.66780$ |
$(3,a+1), (5,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$3.586976780$ |
$1.117850856$ |
3.076010285 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 315\) , \( 1066\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2+315{x}+1066$ |
| 15.1-a4 |
15.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-435}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{20} \cdot 5^{8} \) |
$3.66780$ |
$(3,a+1), (5,a+2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$16$ |
\( 2^{2} \) |
$1.793488390$ |
$2.235701712$ |
3.076010285 |
\( \frac{111284641}{50625} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -90\) , \( 175\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-90{x}+175$ |
| 15.1-a5 |
15.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-435}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{16} \cdot 5^{4} \) |
$3.66780$ |
$(3,a+1), (5,a+2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$3.586976780$ |
$4.471403425$ |
3.076010285 |
\( \frac{13997521}{225} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -45\) , \( -104\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-45{x}-104$ |
| 15.1-a6 |
15.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-435}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{28} \cdot 5^{4} \) |
$3.66780$ |
$(3,a+1), (5,a+2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$16$ |
\( 2^{2} \) |
$3.586976780$ |
$1.117850856$ |
3.076010285 |
\( \frac{272223782641}{164025} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -1215\) , \( 16600\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-1215{x}+16600$ |
| 15.1-a7 |
15.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-435}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{14} \cdot 5^{2} \) |
$3.66780$ |
$(3,a+1), (5,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$7.173953560$ |
$2.235701712$ |
3.076010285 |
\( \frac{56667352321}{15} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -720\) , \( -7259\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-720{x}-7259$ |
| 15.1-a8 |
15.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-435}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{20} \cdot 5^{2} \) |
$3.66780$ |
$(3,a+1), (5,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$7.173953560$ |
$0.558925428$ |
3.076010285 |
\( \frac{1114544804970241}{405} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -19440\) , \( 1048135\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-19440{x}+1048135$ |
| 15.1-b1 |
15.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-435}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{32} \cdot 5^{2} \) |
$3.66780$ |
$(3,a+1), (5,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$0.558925428$ |
0.214387384 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -110\) , \( -880\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-110{x}-880$ |
| 15.1-b2 |
15.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-435}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{2} \cdot 5^{2} \) |
$3.66780$ |
$(3,a+1), (5,a+2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$8.942806850$ |
0.214387384 |
\( -\frac{1}{15} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2$ |
| 15.1-b3 |
15.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-435}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{4} \cdot 5^{16} \) |
$3.66780$ |
$(3,a+1), (5,a+2)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{5} \) |
$1$ |
$1.117850856$ |
0.214387384 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 35\) , \( -28\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2+35{x}-28$ |
| 15.1-b4 |
15.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-435}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{8} \cdot 5^{8} \) |
$3.66780$ |
$(3,a+1), (5,a+2)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{4} \) |
$1$ |
$2.235701712$ |
0.214387384 |
\( \frac{111284641}{50625} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -10\) , \( -10\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-10{x}-10$ |
| 15.1-b5 |
15.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-435}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{4} \cdot 5^{4} \) |
$3.66780$ |
$(3,a+1), (5,a+2)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$1$ |
$4.471403425$ |
0.214387384 |
\( \frac{13997521}{225} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -5\) , \( 2\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-5{x}+2$ |
| 15.1-b6 |
15.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-435}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{16} \cdot 5^{4} \) |
$3.66780$ |
$(3,a+1), (5,a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$1$ |
$1.117850856$ |
0.214387384 |
\( \frac{272223782641}{164025} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -135\) , \( -660\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-135{x}-660$ |
| 15.1-b7 |
15.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-435}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{2} \cdot 5^{2} \) |
$3.66780$ |
$(3,a+1), (5,a+2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$2.235701712$ |
0.214387384 |
\( \frac{56667352321}{15} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -80\) , \( 242\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-80{x}+242$ |
| 15.1-b8 |
15.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-435}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{8} \cdot 5^{2} \) |
$3.66780$ |
$(3,a+1), (5,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$0.558925428$ |
0.214387384 |
\( \frac{1114544804970241}{405} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -2160\) , \( -39540\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-2160{x}-39540$ |
| 15.1-c1 |
15.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{-435}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{32} \cdot 5^{14} \) |
$3.66780$ |
$(3,a+1), (5,a+2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{6} \) |
$1$ |
$0.558925428$ |
0.857549539 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2751\) , \( -104477\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-2751{x}-104477$ |
| 15.1-c2 |
15.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{-435}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{2} \cdot 5^{14} \) |
$3.66780$ |
$(3,a+1), (5,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$8.942806850$ |
0.857549539 |
\( -\frac{1}{15} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( 23\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}+23$ |
| 15.1-c3 |
15.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{-435}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{4} \cdot 5^{28} \) |
$3.66780$ |
$(3,a+1), (5,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$1$ |
$1.117850856$ |
0.857549539 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 874\) , \( -5227\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+874{x}-5227$ |
| 15.1-c4 |
15.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{-435}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{8} \cdot 5^{20} \) |
$3.66780$ |
$(3,a+1), (5,a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{4} \) |
$1$ |
$2.235701712$ |
0.857549539 |
\( \frac{111284641}{50625} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -251\) , \( -727\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-251{x}-727$ |
| 15.1-c5 |
15.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{-435}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{4} \cdot 5^{16} \) |
$3.66780$ |
$(3,a+1), (5,a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$1$ |
$4.471403425$ |
0.857549539 |
\( \frac{13997521}{225} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -126\) , \( 523\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-126{x}+523$ |
| 15.1-c6 |
15.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{-435}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{16} \cdot 5^{16} \) |
$3.66780$ |
$(3,a+1), (5,a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{5} \) |
$1$ |
$1.117850856$ |
0.857549539 |
\( \frac{272223782641}{164025} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -3376\) , \( -75727\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-3376{x}-75727$ |
| 15.1-c7 |
15.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{-435}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{2} \cdot 5^{14} \) |
$3.66780$ |
$(3,a+1), (5,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$2.235701712$ |
0.857549539 |
\( \frac{56667352321}{15} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2001\) , \( 34273\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-2001{x}+34273$ |
| 15.1-c8 |
15.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{-435}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{8} \cdot 5^{14} \) |
$3.66780$ |
$(3,a+1), (5,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{4} \) |
$1$ |
$0.558925428$ |
0.857549539 |
\( \frac{1114544804970241}{405} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -54001\) , \( -4834477\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-54001{x}-4834477$ |
| 15.1-d1 |
15.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{-435}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{32} \cdot 5^{2} \cdot 11^{12} \) |
$3.66780$ |
$(3,a+1), (5,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$3.478323460$ |
$0.558925428$ |
5.965669363 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 737 a + 10436\) , \( -60696 a + 802332\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(a-1\right){x}^2+\left(737a+10436\right){x}-60696a+802332$ |
| 15.1-d2 |
15.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{-435}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{2} \cdot 5^{2} \cdot 11^{12} \) |
$3.66780$ |
$(3,a+1), (5,a+2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$13.91329384$ |
$8.942806850$ |
5.965669363 |
\( -\frac{1}{15} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -33 a + 206\) , \( 134 a - 8\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(a-1\right){x}^2+\left(-33a+206\right){x}+134a-8$ |
| 15.1-d3 |
15.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{-435}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{4} \cdot 5^{16} \cdot 11^{12} \) |
$3.66780$ |
$(3,a+1), (5,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1.739161730$ |
$1.117850856$ |
5.965669363 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -278 a - 3049\) , \( -2687 a + 94282\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(a-1\right){x}^2+\left(-278a-3049\right){x}-2687a+94282$ |
| 15.1-d4 |
15.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{-435}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{8} \cdot 5^{8} \cdot 11^{12} \) |
$3.66780$ |
$(3,a+1), (5,a+2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$3.478323460$ |
$2.235701712$ |
5.965669363 |
\( \frac{111284641}{50625} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 37 a + 1136\) , \( -356 a - 6518\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(a-1\right){x}^2+\left(37a+1136\right){x}-356a-6518$ |
| 15.1-d5 |
15.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{-435}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{4} \cdot 5^{4} \cdot 11^{12} \) |
$3.66780$ |
$(3,a+1), (5,a+2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$6.956646921$ |
$4.471403425$ |
5.965669363 |
\( \frac{13997521}{225} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 2 a + 671\) , \( 393 a - 11208\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(a-1\right){x}^2+\left(2a+671\right){x}+393a-11208$ |
| 15.1-d6 |
15.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{-435}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{16} \cdot 5^{4} \cdot 11^{12} \) |
$3.66780$ |
$(3,a+1), (5,a+2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$6.956646921$ |
$1.117850856$ |
5.965669363 |
\( \frac{272223782641}{164025} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 912 a + 12761\) , \( -44281 a + 507982\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(a-1\right){x}^2+\left(912a+12761\right){x}-44281a+507982$ |
| 15.1-d7 |
15.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{-435}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{2} \cdot 5^{2} \cdot 11^{12} \) |
$3.66780$ |
$(3,a+1), (5,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$13.91329384$ |
$2.235701712$ |
5.965669363 |
\( \frac{56667352321}{15} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 527 a + 7646\) , \( 19398 a - 417558\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(a-1\right){x}^2+\left(527a+7646\right){x}+19398a-417558$ |
| 15.1-d8 |
15.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{-435}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{8} \cdot 5^{2} \cdot 11^{12} \) |
$3.66780$ |
$(3,a+1), (5,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$13.91329384$ |
$0.558925428$ |
5.965669363 |
\( \frac{1114544804970241}{405} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 15087 a + 201086\) , \( -2797066 a + 41020132\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(a-1\right){x}^2+\left(15087a+201086\right){x}-2797066a+41020132$ |
| 60.1-a1 |
60.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{-435}) \) |
$2$ |
$[0, 1]$ |
60.1 |
\( 2^{2} \cdot 3 \cdot 5 \) |
\( 2^{24} \cdot 3^{2} \cdot 5^{6} \cdot 11^{12} \) |
$5.18706$ |
$(3,a+1), (5,a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$1.294290140$ |
1.489355097 |
\( -\frac{273359449}{1536000} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a\) , \( 98 a + 1535\) , \( -5461 a + 60436\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^3+\left(-a+1\right){x}^2+\left(98a+1535\right){x}-5461a+60436$ |
| 60.1-a2 |
60.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{-435}) \) |
$2$ |
$[0, 1]$ |
60.1 |
\( 2^{2} \cdot 3 \cdot 5 \) |
\( 2^{8} \cdot 3^{6} \cdot 5^{2} \cdot 11^{12} \) |
$5.18706$ |
$(3,a+1), (5,a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$3.882870421$ |
1.489355097 |
\( \frac{357911}{2160} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a\) , \( -7 a + 140\) , \( 236 a - 1919\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^3+\left(-a+1\right){x}^2+\left(-7a+140\right){x}+236a-1919$ |
| 60.1-a3 |
60.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{-435}) \) |
$2$ |
$[0, 1]$ |
60.1 |
\( 2^{2} \cdot 3 \cdot 5 \) |
\( 2^{6} \cdot 3^{2} \cdot 5^{24} \cdot 11^{12} \) |
$5.18706$ |
$(3,a+1), (5,a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$16$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$0.323572535$ |
1.489355097 |
\( \frac{10316097499609}{5859375000} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a\) , \( 3178 a + 42455\) , \( -67741 a + 236956\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^3+\left(-a+1\right){x}^2+\left(3178a+42455\right){x}-67741a+236956$ |
| 60.1-a4 |
60.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{-435}) \) |
$2$ |
$[0, 1]$ |
60.1 |
\( 2^{2} \cdot 3 \cdot 5 \) |
\( 2^{2} \cdot 3^{24} \cdot 5^{2} \cdot 11^{12} \) |
$5.18706$ |
$(3,a+1), (5,a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$16$ |
\( 2^{2} \) |
$1$ |
$0.970717605$ |
1.489355097 |
\( \frac{35578826569}{5314410} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a\) , \( 483 a + 6650\) , \( -18286 a + 161951\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^3+\left(-a+1\right){x}^2+\left(483a+6650\right){x}-18286a+161951$ |
| 60.1-a5 |
60.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{-435}) \) |
$2$ |
$[0, 1]$ |
60.1 |
\( 2^{2} \cdot 3 \cdot 5 \) |
\( 2^{4} \cdot 3^{12} \cdot 5^{4} \cdot 11^{12} \) |
$5.18706$ |
$(3,a+1), (5,a+2), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$16$ |
\( 2^{3} \) |
$1$ |
$1.941435210$ |
1.489355097 |
\( \frac{702595369}{72900} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a\) , \( 133 a + 2000\) , \( 704 a - 45899\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^3+\left(-a+1\right){x}^2+\left(133a+2000\right){x}+704a-45899$ |
| 60.1-a6 |
60.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{-435}) \) |
$2$ |
$[0, 1]$ |
60.1 |
\( 2^{2} \cdot 3 \cdot 5 \) |
\( 2^{12} \cdot 3^{4} \cdot 5^{12} \cdot 11^{12} \) |
$5.18706$ |
$(3,a+1), (5,a+2), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$16$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.647145070$ |
1.489355097 |
\( \frac{4102915888729}{9000000} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a\) , \( 2338 a + 31295\) , \( -191509 a + 2407636\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^3+\left(-a+1\right){x}^2+\left(2338a+31295\right){x}-191509a+2407636$ |
| 60.1-a7 |
60.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{-435}) \) |
$2$ |
$[0, 1]$ |
60.1 |
\( 2^{2} \cdot 3 \cdot 5 \) |
\( 2^{2} \cdot 3^{6} \cdot 5^{8} \cdot 11^{12} \) |
$5.18706$ |
$(3,a+1), (5,a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$16$ |
\( 2^{2} \) |
$1$ |
$0.970717605$ |
1.489355097 |
\( \frac{2656166199049}{33750} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a\) , \( 2023 a + 27110\) , \( 115886 a - 2355749\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^3+\left(-a+1\right){x}^2+\left(2023a+27110\right){x}+115886a-2355749$ |
| 60.1-a8 |
60.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{-435}) \) |
$2$ |
$[0, 1]$ |
60.1 |
\( 2^{2} \cdot 3 \cdot 5 \) |
\( 2^{6} \cdot 3^{8} \cdot 5^{6} \cdot 11^{12} \) |
$5.18706$ |
$(3,a+1), (5,a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$16$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$0.323572535$ |
1.489355097 |
\( \frac{16778985534208729}{81000} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a\) , \( 37338 a + 496295\) , \( -11162509 a + 166202636\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^3+\left(-a+1\right){x}^2+\left(37338a+496295\right){x}-11162509a+166202636$ |
| 60.1-b1 |
60.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{-435}) \) |
$2$ |
$[0, 1]$ |
60.1 |
\( 2^{2} \cdot 3 \cdot 5 \) |
\( 2^{24} \cdot 3^{2} \cdot 5^{18} \) |
$5.18706$ |
$(3,a+1), (5,a+2), (2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$3.081486993$ |
$1.294290140$ |
6.884142539 |
\( -\frac{273359449}{1536000} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -338\) , \( -7969\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-338{x}-7969$ |
| 60.1-b2 |
60.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{-435}) \) |
$2$ |
$[0, 1]$ |
60.1 |
\( 2^{2} \cdot 3 \cdot 5 \) |
\( 2^{8} \cdot 3^{6} \cdot 5^{14} \) |
$5.18706$ |
$(3,a+1), (5,a+2), (2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$9.244460979$ |
$3.882870421$ |
6.884142539 |
\( \frac{357911}{2160} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 37\) , \( 281\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2+37{x}+281$ |
| 60.1-b3 |
60.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{-435}) \) |
$2$ |
$[0, 1]$ |
60.1 |
\( 2^{2} \cdot 3 \cdot 5 \) |
\( 2^{6} \cdot 3^{2} \cdot 5^{36} \) |
$5.18706$ |
$(3,a+1), (5,a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{4} \cdot 3^{2} \) |
$0.770371748$ |
$0.323572535$ |
6.884142539 |
\( \frac{10316097499609}{5859375000} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -11338\) , \( -67969\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-11338{x}-67969$ |
| 60.1-b4 |
60.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{-435}) \) |
$2$ |
$[0, 1]$ |
60.1 |
\( 2^{2} \cdot 3 \cdot 5 \) |
\( 2^{2} \cdot 3^{24} \cdot 5^{14} \) |
$5.18706$ |
$(3,a+1), (5,a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{2} \) |
$9.244460979$ |
$0.970717605$ |
6.884142539 |
\( \frac{35578826569}{5314410} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -1713\) , \( -24219\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-1713{x}-24219$ |
| 60.1-b5 |
60.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{-435}) \) |
$2$ |
$[0, 1]$ |
60.1 |
\( 2^{2} \cdot 3 \cdot 5 \) |
\( 2^{4} \cdot 3^{12} \cdot 5^{16} \) |
$5.18706$ |
$(3,a+1), (5,a+2), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{4} \) |
$4.622230489$ |
$1.941435210$ |
6.884142539 |
\( \frac{702595369}{72900} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -463\) , \( 3281\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-463{x}+3281$ |
| 60.1-b6 |
60.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{-435}) \) |
$2$ |
$[0, 1]$ |
60.1 |
\( 2^{2} \cdot 3 \cdot 5 \) |
\( 2^{12} \cdot 3^{4} \cdot 5^{24} \) |
$5.18706$ |
$(3,a+1), (5,a+2), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{4} \cdot 3^{2} \) |
$1.540743496$ |
$0.647145070$ |
6.884142539 |
\( \frac{4102915888729}{9000000} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -8338\) , \( -295969\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-8338{x}-295969$ |
| 60.1-b7 |
60.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{-435}) \) |
$2$ |
$[0, 1]$ |
60.1 |
\( 2^{2} \cdot 3 \cdot 5 \) |
\( 2^{2} \cdot 3^{6} \cdot 5^{20} \) |
$5.18706$ |
$(3,a+1), (5,a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{4} \) |
$2.311115244$ |
$0.970717605$ |
6.884142539 |
\( \frac{2656166199049}{33750} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -7213\) , \( 232781\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-7213{x}+232781$ |
| 60.1-b8 |
60.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{-435}) \) |
$2$ |
$[0, 1]$ |
60.1 |
\( 2^{2} \cdot 3 \cdot 5 \) |
\( 2^{6} \cdot 3^{8} \cdot 5^{18} \) |
$5.18706$ |
$(3,a+1), (5,a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{2} \cdot 3^{2} \) |
$3.081486993$ |
$0.323572535$ |
6.884142539 |
\( \frac{16778985534208729}{81000} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -133338\) , \( -18795969\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-133338{x}-18795969$ |
| 60.1-c1 |
60.1-c |
$8$ |
$12$ |
\(\Q(\sqrt{-435}) \) |
$2$ |
$[0, 1]$ |
60.1 |
\( 2^{2} \cdot 3 \cdot 5 \) |
\( 2^{24} \cdot 3^{2} \cdot 5^{6} \) |
$5.18706$ |
$(3,a+1), (5,a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{4} \cdot 3 \) |
$2.887088615$ |
$1.294290140$ |
8.599800291 |
\( -\frac{273359449}{1536000} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -14\) , \( -64\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-14{x}-64$ |
| 60.1-c2 |
60.1-c |
$8$ |
$12$ |
\(\Q(\sqrt{-435}) \) |
$2$ |
$[0, 1]$ |
60.1 |
\( 2^{2} \cdot 3 \cdot 5 \) |
\( 2^{8} \cdot 3^{6} \cdot 5^{2} \) |
$5.18706$ |
$(3,a+1), (5,a+2), (2)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{4} \cdot 3 \) |
$8.661265847$ |
$3.882870421$ |
8.599800291 |
\( \frac{357911}{2160} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 1\) , \( 2\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}+2$ |
*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.
