| 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 |
| 2028.1-a1 |
2028.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2028.1 |
\( 2^{2} \cdot 3 \cdot 13^{2} \) |
\( - 2^{8} \cdot 3^{3} \cdot 13^{5} \) |
$2.07729$ |
$(a+1), (a), (a+4), (a-4)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$7.575150816$ |
2.186757681 |
\( -\frac{7050642069267500}{257049} a + \frac{1356896696001000}{28561} \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 2382 a - 4131\) , \( -81893 a + 141844\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(2382a-4131\right){x}-81893a+141844$ |
| 2028.1-a2 |
2028.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2028.1 |
\( 2^{2} \cdot 3 \cdot 13^{2} \) |
\( - 2^{8} \cdot 3 \cdot 13^{15} \) |
$2.07729$ |
$(a+1), (a), (a+4), (a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$0.841683424$ |
2.186757681 |
\( -\frac{106018707897405500}{69894255367443} a + \frac{63466734201825000}{23298085122481} \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 2512 a - 4341\) , \( -72563 a + 125602\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(2512a-4341\right){x}-72563a+125602$ |
| 2028.1-a3 |
2028.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2028.1 |
\( 2^{2} \cdot 3 \cdot 13^{2} \) |
\( 2^{8} \cdot 3^{12} \cdot 13^{2} \) |
$2.07729$ |
$(a+1), (a), (a+4), (a-4)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$7.575150816$ |
2.186757681 |
\( \frac{16384000}{9477} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -13\) , \( -4\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-13{x}-4$ |
| 2028.1-a4 |
2028.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2028.1 |
\( 2^{2} \cdot 3 \cdot 13^{2} \) |
\( - 2^{8} \cdot 3 \cdot 13^{15} \) |
$2.07729$ |
$(a+1), (a), (a+4), (a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$0.841683424$ |
2.186757681 |
\( \frac{106018707897405500}{69894255367443} a + \frac{63466734201825000}{23298085122481} \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -778 a + 1299\) , \( 61597 a - 106598\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-778a+1299\right){x}+61597a-106598$ |
| 2028.1-a5 |
2028.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2028.1 |
\( 2^{2} \cdot 3 \cdot 13^{2} \) |
\( 2^{4} \cdot 3^{2} \cdot 13^{12} \) |
$2.07729$ |
$(a+1), (a), (a+4), (a-4)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2Cs, 3B.1.2 |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$1.683366848$ |
2.186757681 |
\( \frac{181037698000}{14480427} \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 747 a - 1311\) , \( 14182 a - 24584\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(747a-1311\right){x}+14182a-24584$ |
| 2028.1-a6 |
2028.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2028.1 |
\( 2^{2} \cdot 3 \cdot 13^{2} \) |
\( 2^{4} \cdot 3^{6} \cdot 13^{4} \) |
$2.07729$ |
$(a+1), (a), (a+4), (a-4)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$15.15030163$ |
2.186757681 |
\( \frac{1409938000}{4563} \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 147 a - 261\) , \( -1208 a + 2092\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(147a-261\right){x}-1208a+2092$ |
| 2028.1-a7 |
2028.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2028.1 |
\( 2^{2} \cdot 3 \cdot 13^{2} \) |
\( 2^{8} \cdot 3^{4} \cdot 13^{6} \) |
$2.07729$ |
$(a+1), (a), (a+4), (a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$0.841683424$ |
2.186757681 |
\( \frac{2725888000000}{19773} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -733\) , \( -7888\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-733{x}-7888$ |
| 2028.1-a8 |
2028.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2028.1 |
\( 2^{2} \cdot 3 \cdot 13^{2} \) |
\( - 2^{8} \cdot 3^{3} \cdot 13^{5} \) |
$2.07729$ |
$(a+1), (a), (a+4), (a-4)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$7.575150816$ |
2.186757681 |
\( \frac{7050642069267500}{257049} a + \frac{1356896696001000}{28561} \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 72 a - 171\) , \( -2333 a + 4144\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(72a-171\right){x}-2333a+4144$ |
| 2028.1-b1 |
2028.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2028.1 |
\( 2^{2} \cdot 3 \cdot 13^{2} \) |
\( - 2^{8} \cdot 3 \cdot 13^{5} \) |
$2.07729$ |
$(a+1), (a), (a+4), (a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$10.01325960$ |
2.890579063 |
\( -\frac{1009266009620}{85683} a + \frac{582708026856}{28561} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 315 a - 545\) , \( -3812 a + 6603\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(315a-545\right){x}-3812a+6603$ |
| 2028.1-b2 |
2028.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2028.1 |
\( 2^{2} \cdot 3 \cdot 13^{2} \) |
\( 2^{4} \cdot 3^{2} \cdot 13^{4} \) |
$2.07729$ |
$(a+1), (a), (a+4), (a-4)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$20.02651920$ |
2.890579063 |
\( \frac{3631696}{507} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 20 a - 35\) , \( -45 a + 78\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(20a-35\right){x}-45a+78$ |
| 2028.1-b3 |
2028.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2028.1 |
\( 2^{2} \cdot 3 \cdot 13^{2} \) |
\( 2^{8} \cdot 3^{4} \cdot 13^{2} \) |
$2.07729$ |
$(a+1), (a), (a+4), (a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$10.01325960$ |
2.890579063 |
\( \frac{1048576}{117} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -5\) , \( -6\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-5{x}-6$ |
| 2028.1-b4 |
2028.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2028.1 |
\( 2^{2} \cdot 3 \cdot 13^{2} \) |
\( - 2^{8} \cdot 3 \cdot 13^{5} \) |
$2.07729$ |
$(a+1), (a), (a+4), (a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$10.01325960$ |
2.890579063 |
\( \frac{1009266009620}{85683} a + \frac{582708026856}{28561} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -35 a + 55\) , \( -328 a + 573\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-35a+55\right){x}-328a+573$ |
| 2028.1-c1 |
2028.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2028.1 |
\( 2^{2} \cdot 3 \cdot 13^{2} \) |
\( 2^{8} \cdot 3^{2} \cdot 13^{4} \) |
$2.07729$ |
$(a+1), (a), (a+4), (a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$3.675343036$ |
2.121960291 |
\( \frac{2277376}{507} a - \frac{3506176}{507} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 18 a - 28\) , \( 50 a - 85\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(18a-28\right){x}+50a-85$ |
| 2028.1-c2 |
2028.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2028.1 |
\( 2^{2} \cdot 3 \cdot 13^{2} \) |
\( 2^{4} \cdot 3^{4} \cdot 13^{2} \) |
$2.07729$ |
$(a+1), (a), (a+4), (a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$7.350686072$ |
2.121960291 |
\( -\frac{8038106816}{117} a + \frac{13922788144}{117} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 970 a - 1679\) , \( 21675 a - 37542\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(970a-1679\right){x}+21675a-37542$ |
| 2028.1-d1 |
2028.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2028.1 |
\( 2^{2} \cdot 3 \cdot 13^{2} \) |
\( 2^{8} \cdot 3^{2} \cdot 13^{4} \) |
$2.07729$ |
$(a+1), (a), (a+4), (a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$3.675343036$ |
2.121960291 |
\( -\frac{2277376}{507} a - \frac{3506176}{507} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -18 a - 28\) , \( -50 a - 85\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-18a-28\right){x}-50a-85$ |
| 2028.1-d2 |
2028.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2028.1 |
\( 2^{2} \cdot 3 \cdot 13^{2} \) |
\( 2^{4} \cdot 3^{4} \cdot 13^{2} \) |
$2.07729$ |
$(a+1), (a), (a+4), (a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$7.350686072$ |
2.121960291 |
\( \frac{8038106816}{117} a + \frac{13922788144}{117} \) |
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( -a - 15\) , \( -20 a - 14\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-a-15\right){x}-20a-14$ |
| 2028.1-e1 |
2028.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2028.1 |
\( 2^{2} \cdot 3 \cdot 13^{2} \) |
\( 2^{8} \cdot 3^{2} \cdot 13^{4} \) |
$2.07729$ |
$(a+1), (a), (a+4), (a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.089126448$ |
$9.104254095$ |
2.810875412 |
\( -\frac{2277376}{507} a - \frac{3506176}{507} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -18 a - 28\) , \( 50 a + 85\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-18a-28\right){x}+50a+85$ |
| 2028.1-e2 |
2028.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2028.1 |
\( 2^{2} \cdot 3 \cdot 13^{2} \) |
\( 2^{4} \cdot 3^{4} \cdot 13^{2} \) |
$2.07729$ |
$(a+1), (a), (a+4), (a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.178252897$ |
$18.20850819$ |
2.810875412 |
\( \frac{8038106816}{117} a + \frac{13922788144}{117} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -14\) , \( 4 a - 4\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}-14{x}+4a-4$ |
| 2028.1-f1 |
2028.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2028.1 |
\( 2^{2} \cdot 3 \cdot 13^{2} \) |
\( 2^{8} \cdot 3^{2} \cdot 13^{4} \) |
$2.07729$ |
$(a+1), (a), (a+4), (a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.089126448$ |
$9.104254095$ |
2.810875412 |
\( \frac{2277376}{507} a - \frac{3506176}{507} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 18 a - 28\) , \( -50 a + 85\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(18a-28\right){x}-50a+85$ |
| 2028.1-f2 |
2028.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2028.1 |
\( 2^{2} \cdot 3 \cdot 13^{2} \) |
\( 2^{4} \cdot 3^{4} \cdot 13^{2} \) |
$2.07729$ |
$(a+1), (a), (a+4), (a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.178252897$ |
$18.20850819$ |
2.810875412 |
\( -\frac{8038106816}{117} a + \frac{13922788144}{117} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 968 a - 1680\) , \( -20706 a + 35862\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(968a-1680\right){x}-20706a+35862$ |
| 2028.1-g1 |
2028.1-g |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2028.1 |
\( 2^{2} \cdot 3 \cdot 13^{2} \) |
\( - 2^{8} \cdot 3 \cdot 13^{5} \) |
$2.07729$ |
$(a+1), (a), (a+4), (a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.589657648$ |
$2.574453213$ |
2.629332847 |
\( -\frac{1009266009620}{85683} a + \frac{582708026856}{28561} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 315 a - 546\) , \( 4127 a - 7149\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(315a-546\right){x}+4127a-7149$ |
| 2028.1-g2 |
2028.1-g |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2028.1 |
\( 2^{2} \cdot 3 \cdot 13^{2} \) |
\( 2^{4} \cdot 3^{2} \cdot 13^{4} \) |
$2.07729$ |
$(a+1), (a), (a+4), (a-4)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.294828824$ |
$10.29781285$ |
2.629332847 |
\( \frac{3631696}{507} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 20 a - 36\) , \( 65 a - 114\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(20a-36\right){x}+65a-114$ |
| 2028.1-g3 |
2028.1-g |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2028.1 |
\( 2^{2} \cdot 3 \cdot 13^{2} \) |
\( 2^{8} \cdot 3^{4} \cdot 13^{2} \) |
$2.07729$ |
$(a+1), (a), (a+4), (a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.147414412$ |
$20.59562570$ |
2.629332847 |
\( \frac{1048576}{117} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -5\) , \( 6\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-5{x}+6$ |
| 2028.1-g4 |
2028.1-g |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2028.1 |
\( 2^{2} \cdot 3 \cdot 13^{2} \) |
\( - 2^{8} \cdot 3 \cdot 13^{5} \) |
$2.07729$ |
$(a+1), (a), (a+4), (a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.589657648$ |
$2.574453213$ |
2.629332847 |
\( \frac{1009266009620}{85683} a + \frac{582708026856}{28561} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -35 a + 54\) , \( 293 a - 519\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-35a+54\right){x}+293a-519$ |
| 2028.1-h1 |
2028.1-h |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2028.1 |
\( 2^{2} \cdot 3 \cdot 13^{2} \) |
\( - 2^{8} \cdot 3^{3} \cdot 13^{5} \) |
$2.07729$ |
$(a+1), (a), (a+4), (a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$5.325757738$ |
$0.936092452$ |
2.878322969 |
\( -\frac{7050642069267500}{257049} a + \frac{1356896696001000}{28561} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 2384 a - 4128\) , \( 84276 a - 145974\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(2384a-4128\right){x}+84276a-145974$ |
| 2028.1-h2 |
2028.1-h |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2028.1 |
\( 2^{2} \cdot 3 \cdot 13^{2} \) |
\( - 2^{8} \cdot 3 \cdot 13^{15} \) |
$2.07729$ |
$(a+1), (a), (a+4), (a-4)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{3} \) |
$1.775252579$ |
$0.936092452$ |
2.878322969 |
\( -\frac{106018707897405500}{69894255367443} a + \frac{63466734201825000}{23298085122481} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 2514 a - 4338\) , \( 75076 a - 129942\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(2514a-4338\right){x}+75076a-129942$ |
| 2028.1-h3 |
2028.1-h |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2028.1 |
\( 2^{2} \cdot 3 \cdot 13^{2} \) |
\( 2^{8} \cdot 3^{12} \cdot 13^{2} \) |
$2.07729$ |
$(a+1), (a), (a+4), (a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$1.331439434$ |
$7.488739620$ |
2.878322969 |
\( \frac{16384000}{9477} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -13\) , \( 4\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-13{x}+4$ |
| 2028.1-h4 |
2028.1-h |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2028.1 |
\( 2^{2} \cdot 3 \cdot 13^{2} \) |
\( - 2^{8} \cdot 3 \cdot 13^{15} \) |
$2.07729$ |
$(a+1), (a), (a+4), (a-4)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{3} \) |
$1.775252579$ |
$0.936092452$ |
2.878322969 |
\( \frac{106018707897405500}{69894255367443} a + \frac{63466734201825000}{23298085122481} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -776 a + 1302\) , \( -62374 a + 107898\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-776a+1302\right){x}-62374a+107898$ |
| 2028.1-h5 |
2028.1-h |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2028.1 |
\( 2^{2} \cdot 3 \cdot 13^{2} \) |
\( 2^{4} \cdot 3^{2} \cdot 13^{12} \) |
$2.07729$ |
$(a+1), (a), (a+4), (a-4)$ |
$1$ |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3^{3} \) |
$0.887626289$ |
$3.744369810$ |
2.878322969 |
\( \frac{181037698000}{14480427} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 749 a - 1308\) , \( -13434 a + 23274\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(749a-1308\right){x}-13434a+23274$ |
| 2028.1-h6 |
2028.1-h |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2028.1 |
\( 2^{2} \cdot 3 \cdot 13^{2} \) |
\( 2^{4} \cdot 3^{6} \cdot 13^{4} \) |
$2.07729$ |
$(a+1), (a), (a+4), (a-4)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2Cs, 3B.1.2 |
$1$ |
\( 2^{3} \) |
$2.662878869$ |
$3.744369810$ |
2.878322969 |
\( \frac{1409938000}{4563} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 149 a - 258\) , \( 1356 a - 2352\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(149a-258\right){x}+1356a-2352$ |
| 2028.1-h7 |
2028.1-h |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2028.1 |
\( 2^{2} \cdot 3 \cdot 13^{2} \) |
\( 2^{8} \cdot 3^{4} \cdot 13^{6} \) |
$2.07729$ |
$(a+1), (a), (a+4), (a-4)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3^{3} \) |
$0.443813144$ |
$7.488739620$ |
2.878322969 |
\( \frac{2725888000000}{19773} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -733\) , \( 7888\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-733{x}+7888$ |
| 2028.1-h8 |
2028.1-h |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2028.1 |
\( 2^{2} \cdot 3 \cdot 13^{2} \) |
\( - 2^{8} \cdot 3^{3} \cdot 13^{5} \) |
$2.07729$ |
$(a+1), (a), (a+4), (a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$5.325757738$ |
$0.936092452$ |
2.878322969 |
\( \frac{7050642069267500}{257049} a + \frac{1356896696001000}{28561} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 74 a - 168\) , \( 2406 a - 4314\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(74a-168\right){x}+2406a-4314$ |
*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.
