| 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 |
$8$ |
$16$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 2^{12} \cdot 3^{32} \cdot 5^{2} \) |
$1.80201$ |
$(3,a+1), (2a-11)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$0.172294519$ |
$2.547989231$ |
1.370958724 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -68780293 a - 318003982\) , \( 1319401941438 a + 6100222396500\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-68780293a-318003982\right){x}+1319401941438a+6100222396500$ |
| 15.1-a2 |
15.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 2^{12} \cdot 3^{2} \cdot 5^{2} \) |
$1.80201$ |
$(3,a+1), (2a-11)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$2.756712307$ |
$10.19195692$ |
1.370958724 |
\( -\frac{1}{15} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -13023 a - 60202\) , \( -294878872 a - 1363365200\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-13023a-60202\right){x}-294878872a-1363365200$ |
| 15.1-a3 |
15.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 2^{12} \cdot 3^{4} \cdot 5^{16} \) |
$1.80201$ |
$(3,a+1), (2a-11)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.378356153$ |
$2.547989231$ |
1.370958724 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 21867472 a + 101103728\) , \( 67141172125 a + 310425556510\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(21867472a+101103728\right){x}+67141172125a+310425556510$ |
| 15.1-a4 |
15.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 2^{12} \cdot 3^{8} \cdot 5^{8} \) |
$1.80201$ |
$(3,a+1), (2a-11)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.689178076$ |
$10.19195692$ |
1.370958724 |
\( \frac{111284641}{50625} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -6264593 a - 28964182\) , \( 8918562808 a + 41234755600\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-6264593a-28964182\right){x}+8918562808a+41234755600$ |
| 15.1-a5 |
15.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 2^{12} \cdot 3^{4} \cdot 5^{4} \) |
$1.80201$ |
$(3,a+1), (2a-11)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1.378356153$ |
$10.19195692$ |
1.370958724 |
\( \frac{13997521}{225} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -3138808 a - 14512192\) , \( -6764057685 a - 31273454190\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-3138808a-14512192\right){x}-6764057685a-31273454190$ |
| 15.1-a6 |
15.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 2^{12} \cdot 3^{16} \cdot 5^{4} \) |
$1.80201$ |
$(3,a+1), (2a-11)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.344589038$ |
$10.19195692$ |
1.370958724 |
\( \frac{272223782641}{164025} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -84409218 a - 390263932\) , \( 954779057783 a + 4414397469850\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-84409218a-390263932\right){x}+954779057783a+4414397469850$ |
| 15.1-a7 |
15.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 2^{12} \cdot 3^{2} \cdot 5^{2} \) |
$1.80201$ |
$(3,a+1), (2a-11)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$2.756712307$ |
$2.547989231$ |
1.370958724 |
\( \frac{56667352321}{15} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -50025583 a - 231292042\) , \( -436078729470 a - 2016199270740\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-50025583a-231292042\right){x}-436078729470a-2016199270740$ |
| 15.1-a8 |
15.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 2^{12} \cdot 3^{8} \cdot 5^{2} \) |
$1.80201$ |
$(3,a+1), (2a-11)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.172294519$ |
$10.19195692$ |
1.370958724 |
\( \frac{1114544804970241}{405} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -1350352143 a - 6243319882\) , \( 61135112671028 a + 282656688470200\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-1350352143a-6243319882\right){x}+61135112671028a+282656688470200$ |
| 15.1-b1 |
15.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{32} \cdot 5^{2} \) |
$1.80201$ |
$(3,a+1), (2a-11)$ |
$0$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{6} \) |
$1$ |
$0.490422220$ |
3.063059717 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( -72173 a - 333684\) , \( -45020158 a - 208149599\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-72173a-333684\right){x}-45020158a-208149599$ |
| 15.1-b2 |
15.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{2} \cdot 5^{2} \) |
$1.80201$ |
$(3,a+1), (2a-11)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$31.38702211$ |
3.063059717 |
\( -\frac{1}{15} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( -13 a - 54\) , \( 9992 a + 46191\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-13a-54\right){x}+9992a+46191$ |
| 15.1-b3 |
15.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{4} \cdot 5^{16} \) |
$1.80201$ |
$(3,a+1), (2a-11)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$1.961688882$ |
3.063059717 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( 22947 a + 106101\) , \( -2227705 a - 10299746\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(22947a+106101\right){x}-2227705a-10299746$ |
| 15.1-b4 |
15.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{8} \cdot 5^{8} \) |
$1.80201$ |
$(3,a+1), (2a-11)$ |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$7.846755528$ |
3.063059717 |
\( \frac{111284641}{50625} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( -6573 a - 30384\) , \( -318778 a - 1473869\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-6573a-30384\right){x}-318778a-1473869$ |
| 15.1-b5 |
15.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{4} \cdot 5^{4} \) |
$1.80201$ |
$(3,a+1), (2a-11)$ |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$31.38702211$ |
3.063059717 |
\( \frac{13997521}{225} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( -3293 a - 15219\) , \( 222095 a + 1026844\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-3293a-15219\right){x}+222095a+1026844$ |
| 15.1-b6 |
15.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{16} \cdot 5^{4} \) |
$1.80201$ |
$(3,a+1), (2a-11)$ |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{6} \) |
$1$ |
$1.961688882$ |
3.063059717 |
\( \frac{272223782641}{164025} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( -88573 a - 409509\) , \( -32665003 a - 151025844\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-88573a-409509\right){x}-32665003a-151025844$ |
| 15.1-b7 |
15.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{2} \cdot 5^{2} \) |
$1.80201$ |
$(3,a+1), (2a-11)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$31.38702211$ |
3.063059717 |
\( \frac{56667352321}{15} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( -52493 a - 242694\) , \( 14698280 a + 67957129\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-52493a-242694\right){x}+14698280a+67957129$ |
| 15.1-b8 |
15.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{8} \cdot 5^{2} \) |
$1.80201$ |
$(3,a+1), (2a-11)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{4} \) |
$1$ |
$0.490422220$ |
3.063059717 |
\( \frac{1114544804970241}{405} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( -1416973 a - 6551334\) , \( -2081450248 a - 9623533989\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-1416973a-6551334\right){x}-2081450248a-9623533989$ |
| 15.1-c1 |
15.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{32} \cdot 5^{2} \) |
$1.80201$ |
$(3,a+1), (2a-11)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$2.617916422$ |
$0.490422220$ |
1.002354292 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -110\) , \( -880\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-110{x}-880$ |
| 15.1-c2 |
15.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{2} \cdot 5^{2} \) |
$1.80201$ |
$(3,a+1), (2a-11)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.654479105$ |
$31.38702211$ |
1.002354292 |
\( -\frac{1}{15} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}$ |
| 15.1-c3 |
15.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{4} \cdot 5^{16} \) |
$1.80201$ |
$(3,a+1), (2a-11)$ |
$1$ |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$5.235832845$ |
$1.961688882$ |
1.002354292 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 35\) , \( -28\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+35{x}-28$ |
| 15.1-c4 |
15.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{8} \cdot 5^{8} \) |
$1.80201$ |
$(3,a+1), (2a-11)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$2.617916422$ |
$7.846755528$ |
1.002354292 |
\( \frac{111284641}{50625} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -10\) , \( -10\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-10{x}-10$ |
| 15.1-c5 |
15.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{4} \cdot 5^{4} \) |
$1.80201$ |
$(3,a+1), (2a-11)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1.308958211$ |
$31.38702211$ |
1.002354292 |
\( \frac{13997521}{225} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -5\) , \( 2\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-5{x}+2$ |
| 15.1-c6 |
15.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{16} \cdot 5^{4} \) |
$1.80201$ |
$(3,a+1), (2a-11)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$1.308958211$ |
$1.961688882$ |
1.002354292 |
\( \frac{272223782641}{164025} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -135\) , \( -660\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-135{x}-660$ |
| 15.1-c7 |
15.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{2} \cdot 5^{2} \) |
$1.80201$ |
$(3,a+1), (2a-11)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.654479105$ |
$31.38702211$ |
1.002354292 |
\( \frac{56667352321}{15} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -80\) , \( 242\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-80{x}+242$ |
| 15.1-c8 |
15.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{8} \cdot 5^{2} \) |
$1.80201$ |
$(3,a+1), (2a-11)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$2.617916422$ |
$0.490422220$ |
1.002354292 |
\( \frac{1114544804970241}{405} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -2160\) , \( -39540\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-2160{x}-39540$ |
| 15.1-d1 |
15.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 2^{12} \cdot 3^{32} \cdot 5^{2} \) |
$1.80201$ |
$(3,a+1), (2a-11)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$2.547989231$ |
0.994633150 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[a\) , \( -a\) , \( 0\) , \( -10235 a - 47290\) , \( 2386570 a + 11034280\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(-10235a-47290\right){x}+2386570a+11034280$ |
| 15.1-d2 |
15.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 2^{12} \cdot 3^{2} \cdot 5^{2} \) |
$1.80201$ |
$(3,a+1), (2a-11)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$10.19195692$ |
0.994633150 |
\( -\frac{1}{15} \) |
\( \bigl[a\) , \( -a\) , \( 0\) , \( -5 a + 10\) , \( -540 a - 2460\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(-5a+10\right){x}-540a-2460$ |
| 15.1-d3 |
15.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 2^{12} \cdot 3^{4} \cdot 5^{16} \) |
$1.80201$ |
$(3,a+1), (2a-11)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$2.547989231$ |
0.994633150 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[a\) , \( -a\) , \( 0\) , \( 3250 a + 15060\) , \( 124193 a + 574242\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(3250a+15060\right){x}+124193a+574242$ |
| 15.1-d4 |
15.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 2^{12} \cdot 3^{8} \cdot 5^{8} \) |
$1.80201$ |
$(3,a+1), (2a-11)$ |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$10.19195692$ |
0.994633150 |
\( \frac{111284641}{50625} \) |
\( \bigl[a\) , \( -a\) , \( 0\) , \( -935 a - 4290\) , \( 15500 a + 71700\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(-935a-4290\right){x}+15500a+71700$ |
| 15.1-d5 |
15.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 2^{12} \cdot 3^{4} \cdot 5^{4} \) |
$1.80201$ |
$(3,a+1), (2a-11)$ |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$10.19195692$ |
0.994633150 |
\( \frac{13997521}{225} \) |
\( \bigl[a\) , \( -a\) , \( 0\) , \( -470 a - 2140\) , \( -12617 a - 58298\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(-470a-2140\right){x}-12617a-58298$ |
| 15.1-d6 |
15.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 2^{12} \cdot 3^{16} \cdot 5^{4} \) |
$1.80201$ |
$(3,a+1), (2a-11)$ |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$10.19195692$ |
0.994633150 |
\( \frac{272223782641}{164025} \) |
\( \bigl[a\) , \( -a\) , \( 0\) , \( -12560 a - 58040\) , \( 1723275 a + 7967550\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(-12560a-58040\right){x}+1723275a+7967550$ |
| 15.1-d7 |
15.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 2^{12} \cdot 3^{2} \cdot 5^{2} \) |
$1.80201$ |
$(3,a+1), (2a-11)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$2.547989231$ |
0.994633150 |
\( \frac{56667352321}{15} \) |
\( \bigl[a\) , \( -a\) , \( 0\) , \( -7445 a - 34390\) , \( -796682 a - 3683408\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(-7445a-34390\right){x}-796682a-3683408$ |
| 15.1-d8 |
15.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 2^{12} \cdot 3^{8} \cdot 5^{2} \) |
$1.80201$ |
$(3,a+1), (2a-11)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$10.19195692$ |
0.994633150 |
\( \frac{1114544804970241}{405} \) |
\( \bigl[a\) , \( -a\) , \( 0\) , \( -200885 a - 928790\) , \( 110782080 a + 512198220\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(-200885a-928790\right){x}+110782080a+512198220$ |
*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.
