| 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 |
| 8.1-a1 |
8.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{16} \) |
$1.16409$ |
$(2,a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$2.176177662$ |
$21.87465325$ |
1.536384471 |
\( -432 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -8 a - 26\) , \( -64 a - 250\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-8a-26\right){x}-64a-250$ |
| 8.1-a2 |
8.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{22} \) |
$1.16409$ |
$(2,a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$2.176177662$ |
$21.87465325$ |
1.536384471 |
\( -128955875202 a + 499443959016 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -208 a - 806\) , \( -1388 a - 5366\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-208a-806\right){x}-1388a-5366$ |
| 8.1-a3 |
8.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{20} \) |
$1.16409$ |
$(2,a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1.088088831$ |
$21.87465325$ |
1.536384471 |
\( 1000188 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -168 a - 646\) , \( -2548 a - 9870\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-168a-646\right){x}-2548a-9870$ |
| 8.1-a4 |
8.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{22} \) |
$1.16409$ |
$(2,a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$2.176177662$ |
$5.468663313$ |
1.536384471 |
\( 128955875202 a + 499443959016 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -2688 a - 10406\) , \( -152764 a - 591654\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-2688a-10406\right){x}-152764a-591654$ |
| 8.1-b1 |
8.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{4} \) |
$1.16409$ |
$(2,a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$21.87465325$ |
1.412002795 |
\( -432 \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -125 a - 476\) , \( 3263 a + 12642\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-125a-476\right){x}+3263a+12642$ |
| 8.1-b2 |
8.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{10} \) |
$1.16409$ |
$(2,a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$5.468663313$ |
1.412002795 |
\( -128955875202 a + 499443959016 \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -3235 a - 12521\) , \( 67026 a + 259595\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-3235a-12521\right){x}+67026a+259595$ |
| 8.1-b3 |
8.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{8} \) |
$1.16409$ |
$(2,a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$4$ |
\( 2 \) |
$1$ |
$21.87465325$ |
1.412002795 |
\( 1000188 \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -2605 a - 10081\) , \( 141300 a + 547257\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-2605a-10081\right){x}+141300a+547257$ |
| 8.1-b4 |
8.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{10} \) |
$1.16409$ |
$(2,a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$21.87465325$ |
1.412002795 |
\( 128955875202 a + 499443959016 \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -41655 a - 161321\) , \( 9092142 a + 35213719\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-41655a-161321\right){x}+9092142a+35213719$ |
| 8.1-c1 |
8.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{16} \) |
$1.16409$ |
$(2,a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$2.176177662$ |
$21.87465325$ |
1.536384471 |
\( -432 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -8 a - 26\) , \( 64 a + 250\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-8a-26\right){x}+64a+250$ |
| 8.1-c2 |
8.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{22} \) |
$1.16409$ |
$(2,a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$2.176177662$ |
$5.468663313$ |
1.536384471 |
\( -128955875202 a + 499443959016 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -208 a - 806\) , \( 1388 a + 5366\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-208a-806\right){x}+1388a+5366$ |
| 8.1-c3 |
8.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{20} \) |
$1.16409$ |
$(2,a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1.088088831$ |
$21.87465325$ |
1.536384471 |
\( 1000188 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -168 a - 646\) , \( 2548 a + 9870\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-168a-646\right){x}+2548a+9870$ |
| 8.1-c4 |
8.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{22} \) |
$1.16409$ |
$(2,a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$2.176177662$ |
$21.87465325$ |
1.536384471 |
\( 128955875202 a + 499443959016 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -2688 a - 10406\) , \( 152764 a + 591654\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-2688a-10406\right){x}+152764a+591654$ |
| 8.1-d1 |
8.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{4} \) |
$1.16409$ |
$(2,a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$21.87465325$ |
1.412002795 |
\( -432 \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -4\) , \( -2\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}-4{x}-2$ |
| 8.1-d2 |
8.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{10} \) |
$1.16409$ |
$(2,a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$21.87465325$ |
1.412002795 |
\( -128955875202 a + 499443959016 \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 10 a - 49\) , \( -36 a + 125\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(10a-49\right){x}-36a+125$ |
| 8.1-d3 |
8.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{8} \) |
$1.16409$ |
$(2,a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$4$ |
\( 2 \) |
$1$ |
$21.87465325$ |
1.412002795 |
\( 1000188 \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -9\) , \( -2 a - 7\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}-9{x}-2a-7$ |
| 8.1-d4 |
8.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{10} \) |
$1.16409$ |
$(2,a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$5.468663313$ |
1.412002795 |
\( 128955875202 a + 499443959016 \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -10 a - 49\) , \( -56 a - 219\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-10a-49\right){x}-56a-219$ |
| 10.1-a1 |
10.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{2} \cdot 5^{2} \) |
$1.23088$ |
$(2,a+1), (5,a)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$22.35500709$ |
0.320668778 |
\( -\frac{368271}{10} a - \frac{713678}{5} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -3 a + 4\) , \( -2 a + 4\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-3a+4\right){x}-2a+4$ |
| 10.1-a2 |
10.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{6} \cdot 5^{6} \) |
$1.23088$ |
$(2,a+1), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$2.483889677$ |
0.320668778 |
\( \frac{22896613727}{1000} a - \frac{22169433439}{250} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 27 a - 111\) , \( 260 a - 1010\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(27a-111\right){x}+260a-1010$ |
| 10.1-a3 |
10.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{3} \cdot 5^{3} \) |
$1.23088$ |
$(2,a+1), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$4$ |
\( 1 \) |
$1$ |
$2.483889677$ |
0.320668778 |
\( -\frac{406087370211328559}{100} a + \frac{314553924386830927}{20} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 477 a - 1861\) , \( 12680 a - 49110\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(477a-1861\right){x}+12680a-49110$ |
| 10.1-a4 |
10.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2 \cdot 5 \) |
$1.23088$ |
$(2,a+1), (5,a)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 1 \) |
$1$ |
$22.35500709$ |
0.320668778 |
\( \frac{105678766089}{10} a + \frac{81859053049}{2} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 2 a - 21\) , \( 30 a - 116\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(2a-21\right){x}+30a-116$ |
| 10.1-b1 |
10.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{6} \cdot 5^{6} \) |
$1.23088$ |
$(2,a+1), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$11.26497123$ |
1.454301533 |
\( -\frac{22896613727}{1000} a - \frac{22169433439}{250} \) |
\( \bigl[a\) , \( a - 1\) , \( a\) , \( -402 a + 1564\) , \( 14377 a - 55675\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-402a+1564\right){x}+14377a-55675$ |
| 10.1-b2 |
10.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{2} \cdot 5^{2} \) |
$1.23088$ |
$(2,a+1), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$11.26497123$ |
1.454301533 |
\( \frac{368271}{10} a - \frac{713678}{5} \) |
\( \bigl[a\) , \( a - 1\) , \( a\) , \( 188 a - 721\) , \( 2661 a - 10299\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(188a-721\right){x}+2661a-10299$ |
| 10.1-b3 |
10.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2 \cdot 5 \) |
$1.23088$ |
$(2,a+1), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 1 \) |
$1$ |
$11.26497123$ |
1.454301533 |
\( -\frac{105678766089}{10} a + \frac{81859053049}{2} \) |
\( \bigl[a\) , \( a - 1\) , \( a\) , \( 2983 a - 11546\) , \( 173253 a - 670999\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(2983a-11546\right){x}+173253a-670999$ |
| 10.1-b4 |
10.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{3} \cdot 5^{3} \) |
$1.23088$ |
$(2,a+1), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 1 \) |
$1$ |
$11.26497123$ |
1.454301533 |
\( \frac{406087370211328559}{100} a + \frac{314553924386830927}{20} \) |
\( \bigl[a\) , \( a - 1\) , \( a\) , \( 3148 a - 12186\) , \( 152797 a - 591775\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(3148a-12186\right){x}+152797a-591775$ |
| 10.1-c1 |
10.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{18} \cdot 5^{6} \) |
$1.23088$ |
$(2,a+1), (5,a)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$11.26497123$ |
1.454301533 |
\( -\frac{22896613727}{1000} a - \frac{22169433439}{250} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -24 a + 110\) , \( 250 a - 960\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(-24a+110\right){x}+250a-960$ |
| 10.1-c2 |
10.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{14} \cdot 5^{2} \) |
$1.23088$ |
$(2,a+1), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$11.26497123$ |
1.454301533 |
\( \frac{368271}{10} a - \frac{713678}{5} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 16 a - 30\) , \( 42 a - 128\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(16a-30\right){x}+42a-128$ |
| 10.1-c3 |
10.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{13} \cdot 5 \) |
$1.23088$ |
$(2,a+1), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$4$ |
\( 1 \) |
$1$ |
$11.26497123$ |
1.454301533 |
\( -\frac{105678766089}{10} a + \frac{81859053049}{2} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 196 a - 730\) , \( 2746 a - 10608\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(196a-730\right){x}+2746a-10608$ |
| 10.1-c4 |
10.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{15} \cdot 5^{3} \) |
$1.23088$ |
$(2,a+1), (5,a)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 3^{2} \) |
$1$ |
$11.26497123$ |
1.454301533 |
\( \frac{406087370211328559}{100} a + \frac{314553924386830927}{20} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 176 a - 890\) , \( 2490 a - 8960\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(176a-890\right){x}+2490a-8960$ |
| 10.1-d1 |
10.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{14} \cdot 5^{2} \) |
$1.23088$ |
$(2,a+1), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$22.35500709$ |
2.886019006 |
\( -\frac{368271}{10} a - \frac{713678}{5} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 54 a - 205\) , \( 1800 a - 6965\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(54a-205\right){x}+1800a-6965$ |
| 10.1-d2 |
10.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{18} \cdot 5^{6} \) |
$1.23088$ |
$(2,a+1), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$2.483889677$ |
2.886019006 |
\( \frac{22896613727}{1000} a - \frac{22169433439}{250} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 7454 a - 28865\) , \( 696920 a - 2699153\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(7454a-28865\right){x}+696920a-2699153$ |
| 10.1-d3 |
10.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{15} \cdot 5^{3} \) |
$1.23088$ |
$(2,a+1), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 3^{2} \) |
$1$ |
$2.483889677$ |
2.886019006 |
\( -\frac{406087370211328559}{100} a + \frac{314553924386830927}{20} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 119254 a - 461865\) , \( 44237360 a - 171330553\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(119254a-461865\right){x}+44237360a-171330553$ |
| 10.1-d4 |
10.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{13} \cdot 5 \) |
$1.23088$ |
$(2,a+1), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 1 \) |
$1$ |
$22.35500709$ |
2.886019006 |
\( \frac{105678766089}{10} a + \frac{81859053049}{2} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 1474 a - 5705\) , \( 61924 a - 239825\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(1474a-5705\right){x}+61924a-239825$ |
| 10.1-e1 |
10.1-e |
$4$ |
$6$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{14} \cdot 5^{2} \) |
$1.23088$ |
$(2,a+1), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$11.26497123$ |
1.454301533 |
\( -\frac{368271}{10} a - \frac{713678}{5} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 52 a - 200\) , \( -1640 a + 6352\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(52a-200\right){x}-1640a+6352$ |
| 10.1-e2 |
10.1-e |
$4$ |
$6$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{18} \cdot 5^{6} \) |
$1.23088$ |
$(2,a+1), (5,a)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$11.26497123$ |
1.454301533 |
\( \frac{22896613727}{1000} a - \frac{22169433439}{250} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 7452 a - 28860\) , \( -674560 a + 2612560\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(7452a-28860\right){x}-674560a+2612560$ |
| 10.1-e3 |
10.1-e |
$4$ |
$6$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{15} \cdot 5^{3} \) |
$1.23088$ |
$(2,a+1), (5,a)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 3^{2} \) |
$1$ |
$11.26497123$ |
1.454301533 |
\( -\frac{406087370211328559}{100} a + \frac{314553924386830927}{20} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 119252 a - 461860\) , \( -43879600 a + 169944960\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(119252a-461860\right){x}-43879600a+169944960$ |
| 10.1-e4 |
10.1-e |
$4$ |
$6$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{13} \cdot 5 \) |
$1.23088$ |
$(2,a+1), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$4$ |
\( 1 \) |
$1$ |
$11.26497123$ |
1.454301533 |
\( \frac{105678766089}{10} a + \frac{81859053049}{2} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 1472 a - 5700\) , \( -57504 a + 222712\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(1472a-5700\right){x}-57504a+222712$ |
| 10.1-f1 |
10.1-f |
$4$ |
$6$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{18} \cdot 5^{6} \) |
$1.23088$ |
$(2,a+1), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$2.483889677$ |
2.886019006 |
\( -\frac{22896613727}{1000} a - \frac{22169433439}{250} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -23 a + 113\) , \( -230 a + 861\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-23a+113\right){x}-230a+861$ |
| 10.1-f2 |
10.1-f |
$4$ |
$6$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{14} \cdot 5^{2} \) |
$1.23088$ |
$(2,a+1), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$22.35500709$ |
2.886019006 |
\( \frac{368271}{10} a - \frac{713678}{5} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 17 a - 27\) , \( -42 a + 209\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(17a-27\right){x}-42a+209$ |
| 10.1-f3 |
10.1-f |
$4$ |
$6$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{13} \cdot 5 \) |
$1.23088$ |
$(2,a+1), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 1 \) |
$1$ |
$22.35500709$ |
2.886019006 |
\( -\frac{105678766089}{10} a + \frac{81859053049}{2} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 197 a - 727\) , \( -2906 a + 11289\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(197a-727\right){x}-2906a+11289$ |
| 10.1-f4 |
10.1-f |
$4$ |
$6$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{15} \cdot 5^{3} \) |
$1.23088$ |
$(2,a+1), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 3^{2} \) |
$1$ |
$2.483889677$ |
2.886019006 |
\( \frac{406087370211328559}{100} a + \frac{314553924386830927}{20} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 177 a - 887\) , \( -2870 a + 8861\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(177a-887\right){x}-2870a+8861$ |
| 10.1-g1 |
10.1-g |
$4$ |
$6$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{6} \cdot 5^{6} \) |
$1.23088$ |
$(2,a+1), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$2.483889677$ |
0.320668778 |
\( -\frac{22896613727}{1000} a - \frac{22169433439}{250} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( -404 a + 1569\) , \( -14780 a + 57241\bigr] \) |
${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(-404a+1569\right){x}-14780a+57241$ |
| 10.1-g2 |
10.1-g |
$4$ |
$6$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{2} \cdot 5^{2} \) |
$1.23088$ |
$(2,a+1), (5,a)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$22.35500709$ |
0.320668778 |
\( \frac{368271}{10} a - \frac{713678}{5} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( 186 a - 716\) , \( -2474 a + 9580\bigr] \) |
${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(186a-716\right){x}-2474a+9580$ |
| 10.1-g3 |
10.1-g |
$4$ |
$6$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2 \cdot 5 \) |
$1.23088$ |
$(2,a+1), (5,a)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 1 \) |
$1$ |
$22.35500709$ |
0.320668778 |
\( -\frac{105678766089}{10} a + \frac{81859053049}{2} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( 2981 a - 11541\) , \( -170271 a + 659455\bigr] \) |
${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(2981a-11541\right){x}-170271a+659455$ |
| 10.1-g4 |
10.1-g |
$4$ |
$6$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{3} \cdot 5^{3} \) |
$1.23088$ |
$(2,a+1), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$4$ |
\( 1 \) |
$1$ |
$2.483889677$ |
0.320668778 |
\( \frac{406087370211328559}{100} a + \frac{314553924386830927}{20} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( 3146 a - 12181\) , \( -149650 a + 579591\bigr] \) |
${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(3146a-12181\right){x}-149650a+579591$ |
| 10.1-h1 |
10.1-h |
$4$ |
$6$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{2} \cdot 5^{2} \) |
$1.23088$ |
$(2,a+1), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$11.26497123$ |
1.454301533 |
\( -\frac{368271}{10} a - \frac{713678}{5} \) |
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( a + 4\) , \( 4\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(a+4\right){x}+4$ |
| 10.1-h2 |
10.1-h |
$4$ |
$6$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{6} \cdot 5^{6} \) |
$1.23088$ |
$(2,a+1), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$11.26497123$ |
1.454301533 |
\( \frac{22896613727}{1000} a - \frac{22169433439}{250} \) |
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( 31 a - 111\) , \( -202 a + 788\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(31a-111\right){x}-202a+788$ |
| 10.1-h3 |
10.1-h |
$4$ |
$6$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{3} \cdot 5^{3} \) |
$1.23088$ |
$(2,a+1), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 1 \) |
$1$ |
$11.26497123$ |
1.454301533 |
\( -\frac{406087370211328559}{100} a + \frac{314553924386830927}{20} \) |
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( 481 a - 1861\) , \( -11722 a + 45388\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(481a-1861\right){x}-11722a+45388$ |
| 10.1-h4 |
10.1-h |
$4$ |
$6$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2 \cdot 5 \) |
$1.23088$ |
$(2,a+1), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 1 \) |
$1$ |
$11.26497123$ |
1.454301533 |
\( \frac{105678766089}{10} a + \frac{81859053049}{2} \) |
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( 6 a - 21\) , \( -22 a + 74\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(6a-21\right){x}-22a+74$ |
| 14.1-a1 |
14.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( - 2^{3} \cdot 7 \) |
$1.33889$ |
$(2,a+1), (7,a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$9$ |
\( 3 \) |
$1$ |
$0.760182873$ |
2.649758048 |
\( -\frac{632235090508565}{28} a - \frac{2448631469962925}{28} \) |
\( \bigl[a\) , \( 1\) , \( 1\) , \( 5060 a - 19593\) , \( 393664 a - 1524653\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(5060a-19593\right){x}+393664a-1524653$ |
| 14.1-a2 |
14.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( - 2^{9} \cdot 7^{3} \) |
$1.33889$ |
$(2,a+1), (7,a+1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 3^{3} \) |
$1$ |
$6.841645863$ |
2.649758048 |
\( -\frac{80643645}{10976} a - \frac{293363275}{10976} \) |
\( \bigl[a\) , \( 1\) , \( 1\) , \( 90 a - 343\) , \( 152 a - 585\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(90a-343\right){x}+152a-585$ |
*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.
