| 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 |
| 45.1-a1 |
45.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( - 3^{17} \cdot 5 \) |
$2.13379$ |
$(3,a), (3,a+2), (5,a+2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$3.987782348$ |
$22.83873331$ |
2.469642019 |
\( -\frac{7741}{135} a + \frac{90901}{45} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 5 a + 25\) , \( 6 a + 27\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(5a+25\right){x}+6a+27$ |
| 45.1-a2 |
45.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{22} \cdot 5^{2} \) |
$2.13379$ |
$(3,a), (3,a+2), (5,a+2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1.993891174$ |
$11.41936665$ |
2.469642019 |
\( -\frac{22118437}{3645} a + \frac{39774098}{1215} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -30 a - 125\) , \( -34 a - 156\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-30a-125\right){x}-34a-156$ |
| 45.1-a3 |
45.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{23} \cdot 5 \) |
$2.13379$ |
$(3,a), (3,a+2), (5,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$3.987782348$ |
$5.709683329$ |
2.469642019 |
\( -\frac{11530129542437}{32805} a + \frac{58925056413761}{32805} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -300 a - 1340\) , \( 6095 a + 24387\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-300a-1340\right){x}+6095a+24387$ |
| 45.1-a4 |
45.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( - 3^{26} \cdot 5^{4} \) |
$2.13379$ |
$(3,a), (3,a+2), (5,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.996945587$ |
$2.854841664$ |
2.469642019 |
\( \frac{448290634633}{13286025} a + \frac{122824820693}{885735} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -320 a - 1310\) , \( -6943 a - 28551\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-320a-1310\right){x}-6943a-28551$ |
| 45.1-b1 |
45.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{44} \cdot 5^{2} \) |
$2.13379$ |
$(3,a), (3,a+2), (5,a+2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{9} \) |
$1$ |
$0.490422220$ |
1.702200269 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 1215 a - 6254\) , \( 92278 a - 472418\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(1215a-6254\right){x}+92278a-472418$ |
| 45.1-b2 |
45.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{14} \cdot 5^{2} \) |
$2.13379$ |
$(3,a), (3,a+2), (5,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$31.38702211$ |
1.702200269 |
\( -\frac{1}{15} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 5 a + 16\) , \( -12 a + 142\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(5a+16\right){x}-12a+142$ |
| 45.1-b3 |
45.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{16} \cdot 5^{16} \) |
$2.13379$ |
$(3,a), (3,a+2), (5,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$1.961688882$ |
1.702200269 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -380 a + 2011\) , \( 5119 a - 25982\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-380a+2011\right){x}+5119a-25982$ |
| 45.1-b4 |
45.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{20} \cdot 5^{8} \) |
$2.13379$ |
$(3,a), (3,a+2), (5,a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$7.846755528$ |
1.702200269 |
\( \frac{111284641}{50625} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 115 a - 554\) , \( 538 a - 2708\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(115a-554\right){x}+538a-2708$ |
| 45.1-b5 |
45.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{16} \cdot 5^{4} \) |
$2.13379$ |
$(3,a), (3,a+2), (5,a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$31.38702211$ |
1.702200269 |
\( \frac{13997521}{225} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 60 a - 269\) , \( -521 a + 2728\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(60a-269\right){x}-521a+2728$ |
| 45.1-b6 |
45.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{28} \cdot 5^{4} \) |
$2.13379$ |
$(3,a), (3,a+2), (5,a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$1$ |
$1.961688882$ |
1.702200269 |
\( \frac{272223782641}{164025} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 1490 a - 7679\) , \( 66213 a - 339158\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(1490a-7679\right){x}+66213a-339158$ |
| 45.1-b7 |
45.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{14} \cdot 5^{2} \) |
$2.13379$ |
$(3,a), (3,a+2), (5,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$31.38702211$ |
1.702200269 |
\( \frac{56667352321}{15} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 885 a - 4544\) , \( -31676 a + 161848\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(885a-4544\right){x}-31676a+161848$ |
| 45.1-b8 |
45.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{20} \cdot 5^{2} \) |
$2.13379$ |
$(3,a), (3,a+2), (5,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{5} \) |
$1$ |
$0.490422220$ |
1.702200269 |
\( \frac{1114544804970241}{405} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 23765 a - 123104\) , \( 4305348 a - 22034198\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(23765a-123104\right){x}+4305348a-22034198$ |
| 45.1-c1 |
45.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{32} \cdot 5^{2} \) |
$2.13379$ |
$(3,a), (3,a+2), (5,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$9.091433220$ |
$0.490422220$ |
1.934430009 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -110\) , \( -880\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-110{x}-880$ |
| 45.1-c2 |
45.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{2} \cdot 5^{2} \) |
$2.13379$ |
$(3,a), (3,a+2), (5,a+2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$2.272858305$ |
$31.38702211$ |
1.934430009 |
\( -\frac{1}{15} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}$ |
| 45.1-c3 |
45.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{4} \cdot 5^{16} \) |
$2.13379$ |
$(3,a), (3,a+2), (5,a+2)$ |
$1$ |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$4.545716610$ |
$1.961688882$ |
1.934430009 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 35\) , \( -28\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+35{x}-28$ |
| 45.1-c4 |
45.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{8} \cdot 5^{8} \) |
$2.13379$ |
$(3,a), (3,a+2), (5,a+2)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$2.272858305$ |
$7.846755528$ |
1.934430009 |
\( \frac{111284641}{50625} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -10\) , \( -10\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-10{x}-10$ |
| 45.1-c5 |
45.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{4} \cdot 5^{4} \) |
$2.13379$ |
$(3,a), (3,a+2), (5,a+2)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1.136429152$ |
$31.38702211$ |
1.934430009 |
\( \frac{13997521}{225} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -5\) , \( 2\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-5{x}+2$ |
| 45.1-c6 |
45.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{16} \cdot 5^{4} \) |
$2.13379$ |
$(3,a), (3,a+2), (5,a+2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$4.545716610$ |
$1.961688882$ |
1.934430009 |
\( \frac{272223782641}{164025} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -135\) , \( -660\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-135{x}-660$ |
| 45.1-c7 |
45.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{2} \cdot 5^{2} \) |
$2.13379$ |
$(3,a), (3,a+2), (5,a+2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$2.272858305$ |
$31.38702211$ |
1.934430009 |
\( \frac{56667352321}{15} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -80\) , \( 242\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-80{x}+242$ |
| 45.1-c8 |
45.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{8} \cdot 5^{2} \) |
$2.13379$ |
$(3,a), (3,a+2), (5,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$9.091433220$ |
$0.490422220$ |
1.934430009 |
\( \frac{1114544804970241}{405} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -2160\) , \( -39540\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-2160{x}-39540$ |
| 45.1-d1 |
45.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( - 3^{5} \cdot 5 \) |
$2.13379$ |
$(3,a), (3,a+2), (5,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$22.83873331$ |
3.715812656 |
\( -\frac{7741}{135} a + \frac{90901}{45} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( 9 a + 37\) , \( 0\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(9a+37\right){x}$ |
| 45.1-d2 |
45.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{10} \cdot 5^{2} \) |
$2.13379$ |
$(3,a), (3,a+2), (5,a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$11.41936665$ |
3.715812656 |
\( -\frac{22118437}{3645} a + \frac{39774098}{1215} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -36 a - 148\) , \( -9 a - 37\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-36a-148\right){x}-9a-37$ |
| 45.1-d3 |
45.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{11} \cdot 5 \) |
$2.13379$ |
$(3,a), (3,a+2), (5,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$5.709683329$ |
3.715812656 |
\( -\frac{11530129542437}{32805} a + \frac{58925056413761}{32805} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -391 a - 1608\) , \( 8978 a + 36897\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-391a-1608\right){x}+8978a+36897$ |
| 45.1-d4 |
45.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( - 3^{14} \cdot 5^{4} \) |
$2.13379$ |
$(3,a), (3,a+2), (5,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$2.854841664$ |
3.715812656 |
\( \frac{448290634633}{13286025} a + \frac{122824820693}{885735} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -401 a - 1648\) , \( -9392 a - 38599\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-401a-1648\right){x}-9392a-38599$ |
| 45.1-e1 |
45.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( - 3^{26} \cdot 5^{4} \) |
$2.13379$ |
$(3,a), (3,a+2), (5,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.996945587$ |
$2.854841664$ |
2.469642019 |
\( -\frac{448290634633}{13286025} a + \frac{2290662945028}{13286025} \) |
\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( 5 a - 29\) , \( -834 a - 3646\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(5a-29\right){x}-834a-3646$ |
| 45.1-e2 |
45.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( - 3^{17} \cdot 5 \) |
$2.13379$ |
$(3,a), (3,a+2), (5,a+2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$3.987782348$ |
$22.83873331$ |
2.469642019 |
\( \frac{7741}{135} a + \frac{264962}{135} \) |
\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( -5 a - 14\) , \( 15 a + 62\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-5a-14\right){x}+15a+62$ |
| 45.1-e3 |
45.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{22} \cdot 5^{2} \) |
$2.13379$ |
$(3,a), (3,a+2), (5,a+2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1.993891174$ |
$11.41936665$ |
2.469642019 |
\( \frac{22118437}{3645} a + \frac{97203857}{3645} \) |
\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( -40 a - 164\) , \( -222 a - 919\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-40a-164\right){x}-222a-919$ |
| 45.1-e4 |
45.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{23} \cdot 5 \) |
$2.13379$ |
$(3,a), (3,a+2), (5,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$3.987782348$ |
$5.709683329$ |
2.469642019 |
\( \frac{11530129542437}{32805} a + \frac{15798308957108}{10935} \) |
\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( -645 a - 2699\) , \( -18158 a - 74536\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-645a-2699\right){x}-18158a-74536$ |
| 45.1-f1 |
45.1-f |
$4$ |
$4$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( - 3^{14} \cdot 5^{4} \) |
$2.13379$ |
$(3,a), (3,a+2), (5,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$2.854841664$ |
3.715812656 |
\( -\frac{448290634633}{13286025} a + \frac{2290662945028}{13286025} \) |
\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -5 a + 10\) , \( -1221 a - 4990\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-5a+10\right){x}-1221a-4990$ |
| 45.1-f2 |
45.1-f |
$4$ |
$4$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( - 3^{5} \cdot 5 \) |
$2.13379$ |
$(3,a), (3,a+2), (5,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$22.83873331$ |
3.715812656 |
\( \frac{7741}{135} a + \frac{264962}{135} \) |
\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -10 a - 10\) , \( a + 34\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-10a-10\right){x}+a+34$ |
| 45.1-f3 |
45.1-f |
$4$ |
$4$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{10} \cdot 5^{2} \) |
$2.13379$ |
$(3,a), (3,a+2), (5,a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$11.41936665$ |
3.715812656 |
\( \frac{22118437}{3645} a + \frac{97203857}{3645} \) |
\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -55 a - 195\) , \( -471 a - 1906\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-55a-195\right){x}-471a-1906$ |
| 45.1-f4 |
45.1-f |
$4$ |
$4$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{11} \cdot 5 \) |
$2.13379$ |
$(3,a), (3,a+2), (5,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$5.709683329$ |
3.715812656 |
\( \frac{11530129542437}{32805} a + \frac{15798308957108}{10935} \) |
\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -825 a - 3360\) , \( -28189 a - 115822\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-825a-3360\right){x}-28189a-115822$ |
*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.
