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 |
$8$ |
$16$ |
\(\Q(\sqrt{30}) \) |
$2$ |
$[2, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{32} \cdot 5^{2} \) |
$1.92642$ |
$(3,a), (a+5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{6} \) |
$1$ |
$0.490422220$ |
2.865230004 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -4844 a - 26493\) , \( -813715 a - 4456859\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-4844a-26493\right){x}-813715a-4456859$ |
15.1-a2 |
15.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{30}) \) |
$2$ |
$[2, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{2} \cdot 5^{2} \) |
$1.92642$ |
$(3,a), (a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$31.38702211$ |
2.865230004 |
\( -\frac{1}{15} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -4 a + 17\) , \( 175 a + 1001\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-4a+17\right){x}+175a+1001$ |
15.1-a3 |
15.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{30}) \) |
$2$ |
$[2, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{4} \cdot 5^{16} \) |
$1.92642$ |
$(3,a), (a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$1.961688882$ |
2.865230004 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( 1536 a + 8452\) , \( -38388 a - 210217\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(1536a+8452\right){x}-38388a-210217$ |
15.1-a4 |
15.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{30}) \) |
$2$ |
$[2, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{8} \cdot 5^{8} \) |
$1.92642$ |
$(3,a), (a+5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$7.846755528$ |
2.865230004 |
\( \frac{111284641}{50625} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -444 a - 2393\) , \( -6195 a - 33889\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-444a-2393\right){x}-6195a-33889$ |
15.1-a5 |
15.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{30}) \) |
$2$ |
$[2, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{4} \cdot 5^{4} \) |
$1.92642$ |
$(3,a), (a+5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$31.38702211$ |
2.865230004 |
\( \frac{13997521}{225} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -224 a - 1188\) , \( 3752 a + 20593\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-224a-1188\right){x}+3752a+20593$ |
15.1-a6 |
15.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{30}) \) |
$2$ |
$[2, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{16} \cdot 5^{4} \) |
$1.92642$ |
$(3,a), (a+5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{6} \) |
$1$ |
$1.961688882$ |
2.865230004 |
\( \frac{272223782641}{164025} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -5944 a - 32518\) , \( -592970 a - 3247789\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-5944a-32518\right){x}-592970a-3247789$ |
15.1-a7 |
15.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{30}) \) |
$2$ |
$[2, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{2} \cdot 5^{2} \) |
$1.92642$ |
$(3,a), (a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$31.38702211$ |
2.865230004 |
\( \frac{56667352321}{15} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -3524 a - 19263\) , \( 260267 a + 1425583\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-3524a-19263\right){x}+260267a+1425583$ |
15.1-a8 |
15.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{30}) \) |
$2$ |
$[2, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{8} \cdot 5^{2} \) |
$1.92642$ |
$(3,a), (a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{4} \) |
$1$ |
$0.490422220$ |
2.865230004 |
\( \frac{1114544804970241}{405} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -95044 a - 520543\) , \( -37484825 a - 205312819\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-95044a-520543\right){x}-37484825a-205312819$ |
15.1-b1 |
15.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{30}) \) |
$2$ |
$[2, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 2^{12} \cdot 3^{32} \cdot 5^{2} \) |
$1.92642$ |
$(3,a), (a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$2.547989231$ |
0.930394118 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 9333283 a - 51120511\) , \( -68163727122 a + 373348109476\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(9333283a-51120511\right){x}-68163727122a+373348109476$ |
15.1-b2 |
15.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{30}) \) |
$2$ |
$[2, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 2^{12} \cdot 3^{2} \cdot 5^{2} \) |
$1.92642$ |
$(3,a), (a+5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$10.19195692$ |
0.930394118 |
\( -\frac{1}{15} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 1763 a - 9671\) , \( 15245718 a - 83504244\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(1763a-9671\right){x}+15245718a-83504244$ |
15.1-b3 |
15.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{30}) \) |
$2$ |
$[2, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 2^{12} \cdot 3^{4} \cdot 5^{16} \) |
$1.92642$ |
$(3,a), (a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$2.547989231$ |
0.930394118 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -2967357 a + 16252869\) , \( -3478975110 a + 19055131440\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-2967357a+16252869\right){x}-3478975110a+19055131440$ |
15.1-b4 |
15.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{30}) \) |
$2$ |
$[2, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 2^{12} \cdot 3^{8} \cdot 5^{8} \) |
$1.92642$ |
$(3,a), (a+5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$10.19195692$ |
0.930394118 |
\( \frac{111284641}{50625} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 850083 a - 4656111\) , \( -458404002 a + 2510782116\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(850083a-4656111\right){x}-458404002a+2510782116$ |
15.1-b5 |
15.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{30}) \) |
$2$ |
$[2, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 2^{12} \cdot 3^{4} \cdot 5^{4} \) |
$1.92642$ |
$(3,a), (a+5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$10.19195692$ |
0.930394118 |
\( \frac{13997521}{225} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 425923 a - 2332891\) , \( 350864730 a - 1921765280\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(425923a-2332891\right){x}+350864730a-1921765280$ |
15.1-b6 |
15.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{30}) \) |
$2$ |
$[2, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 2^{12} \cdot 3^{16} \cdot 5^{4} \) |
$1.92642$ |
$(3,a), (a+5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$10.19195692$ |
0.930394118 |
\( \frac{272223782641}{164025} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 11454083 a - 62736611\) , \( -49312315902 a + 270094677816\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(11454083a-62736611\right){x}-49312315902a+270094677816$ |
15.1-b7 |
15.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{30}) \) |
$2$ |
$[2, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 2^{12} \cdot 3^{2} \cdot 5^{2} \) |
$1.92642$ |
$(3,a), (a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$2.547989231$ |
0.930394118 |
\( \frac{56667352321}{15} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 6788323 a - 37181191\) , \( 22558466070 a - 123557807300\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(6788323a-37181191\right){x}+22558466070a-123557807300$ |
15.1-b8 |
15.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{30}) \) |
$2$ |
$[2, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 2^{12} \cdot 3^{8} \cdot 5^{2} \) |
$1.92642$ |
$(3,a), (a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$10.19195692$ |
0.930394118 |
\( \frac{1114544804970241}{405} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 183238883 a - 1003640711\) , \( -3159143370282 a + 17303340862956\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(183238883a-1003640711\right){x}-3159143370282a+17303340862956$ |
15.1-c1 |
15.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{30}) \) |
$2$ |
$[2, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 2^{12} \cdot 3^{32} \cdot 5^{2} \) |
$1.92642$ |
$(3,a), (a+5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$0.537222968$ |
$2.547989231$ |
3.998632720 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 19358 a - 106026\) , \( -6354792 a + 34806630\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(19358a-106026\right){x}-6354792a+34806630$ |
15.1-c2 |
15.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{30}) \) |
$2$ |
$[2, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 2^{12} \cdot 3^{2} \cdot 5^{2} \) |
$1.92642$ |
$(3,a), (a+5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$2.148891872$ |
$10.19195692$ |
3.998632720 |
\( -\frac{1}{15} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -2 a + 14\) , \( 1448 a - 7930\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2a+14\right){x}+1448a-7930$ |
15.1-c3 |
15.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{30}) \) |
$2$ |
$[2, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 2^{12} \cdot 3^{4} \cdot 5^{16} \) |
$1.92642$ |
$(3,a), (a+5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$4.297783744$ |
$2.547989231$ |
3.998632720 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -6162 a + 33754\) , \( -356336 a + 1951734\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-6162a+33754\right){x}-356336a+1951734$ |
15.1-c4 |
15.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{30}) \) |
$2$ |
$[2, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 2^{12} \cdot 3^{8} \cdot 5^{8} \) |
$1.92642$ |
$(3,a), (a+5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$2.148891872$ |
$10.19195692$ |
3.998632720 |
\( \frac{111284641}{50625} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 1758 a - 9626\) , \( -35432 a + 194070\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(1758a-9626\right){x}-35432a+194070$ |
15.1-c5 |
15.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{30}) \) |
$2$ |
$[2, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 2^{12} \cdot 3^{4} \cdot 5^{4} \) |
$1.92642$ |
$(3,a), (a+5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$4.297783744$ |
$10.19195692$ |
3.998632720 |
\( \frac{13997521}{225} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 878 a - 4806\) , \( 37104 a - 203226\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(878a-4806\right){x}+37104a-203226$ |
15.1-c6 |
15.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{30}) \) |
$2$ |
$[2, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 2^{12} \cdot 3^{16} \cdot 5^{4} \) |
$1.92642$ |
$(3,a), (a+5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1.074445936$ |
$10.19195692$ |
3.998632720 |
\( \frac{272223782641}{164025} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 23758 a - 130126\) , \( -4553632 a + 24941270\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(23758a-130126\right){x}-4553632a+24941270$ |
15.1-c7 |
15.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{30}) \) |
$2$ |
$[2, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 2^{12} \cdot 3^{2} \cdot 5^{2} \) |
$1.92642$ |
$(3,a), (a+5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$8.595567489$ |
$2.547989231$ |
3.998632720 |
\( \frac{56667352321}{15} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 14078 a - 77106\) , \( 2194824 a - 12021546\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(14078a-77106\right){x}+2194824a-12021546$ |
15.1-c8 |
15.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{30}) \) |
$2$ |
$[2, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 2^{12} \cdot 3^{8} \cdot 5^{2} \) |
$1.92642$ |
$(3,a), (a+5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.537222968$ |
$10.19195692$ |
3.998632720 |
\( \frac{1114544804970241}{405} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 380158 a - 2082226\) , \( -296837272 a + 1625844710\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(380158a-2082226\right){x}-296837272a+1625844710$ |
15.1-d1 |
15.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{30}) \) |
$2$ |
$[2, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{32} \cdot 5^{2} \) |
$1.92642$ |
$(3,a), (a+5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$5.036899059$ |
$0.490422220$ |
1.803984289 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -110\) , \( -880\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-110{x}-880$ |
15.1-d2 |
15.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{30}) \) |
$2$ |
$[2, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{2} \cdot 5^{2} \) |
$1.92642$ |
$(3,a), (a+5)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.259224764$ |
$31.38702211$ |
1.803984289 |
\( -\frac{1}{15} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}$ |
15.1-d3 |
15.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{30}) \) |
$2$ |
$[2, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{4} \cdot 5^{16} \) |
$1.92642$ |
$(3,a), (a+5)$ |
$1$ |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$10.07379811$ |
$1.961688882$ |
1.803984289 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 35\) , \( -28\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+35{x}-28$ |
15.1-d4 |
15.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{30}) \) |
$2$ |
$[2, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{8} \cdot 5^{8} \) |
$1.92642$ |
$(3,a), (a+5)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$5.036899059$ |
$7.846755528$ |
1.803984289 |
\( \frac{111284641}{50625} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -10\) , \( -10\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-10{x}-10$ |
15.1-d5 |
15.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{30}) \) |
$2$ |
$[2, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{4} \cdot 5^{4} \) |
$1.92642$ |
$(3,a), (a+5)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$2.518449529$ |
$31.38702211$ |
1.803984289 |
\( \frac{13997521}{225} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -5\) , \( 2\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-5{x}+2$ |
15.1-d6 |
15.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{30}) \) |
$2$ |
$[2, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{16} \cdot 5^{4} \) |
$1.92642$ |
$(3,a), (a+5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$2.518449529$ |
$1.961688882$ |
1.803984289 |
\( \frac{272223782641}{164025} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -135\) , \( -660\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-135{x}-660$ |
15.1-d7 |
15.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{30}) \) |
$2$ |
$[2, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{2} \cdot 5^{2} \) |
$1.92642$ |
$(3,a), (a+5)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.259224764$ |
$31.38702211$ |
1.803984289 |
\( \frac{56667352321}{15} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -80\) , \( 242\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-80{x}+242$ |
15.1-d8 |
15.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{30}) \) |
$2$ |
$[2, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{8} \cdot 5^{2} \) |
$1.92642$ |
$(3,a), (a+5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$5.036899059$ |
$0.490422220$ |
1.803984289 |
\( \frac{1114544804970241}{405} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -2160\) , \( -39540\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-2160{x}-39540$ |
*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.