| 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 |
| 5.1-a1 |
5.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
5.1 |
\( 5 \) |
\( - 2^{12} \cdot 5^{3} \) |
$1.36923$ |
$(2a-11)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3Nn |
$1$ |
\( 3 \) |
$1.378497038$ |
$33.76254038$ |
1.703246763 |
\( -\frac{1145960298}{25} a + \frac{6444279999}{25} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 101 a + 507\) , \( 12625 a + 58420\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(101a+507\right){x}+12625a+58420$ |
| 5.1-a2 |
5.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
5.1 |
\( 5 \) |
\( 5^{12} \) |
$1.36923$ |
$(2a-11)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3Nn |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.344624259$ |
$8.440635095$ |
1.703246763 |
\( \frac{55306341}{15625} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( -426911 a - 1973810\) , \( -245763021 a - 1136279283\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-426911a-1973810\right){x}-245763021a-1136279283$ |
| 5.1-a3 |
5.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
5.1 |
\( 5 \) |
\( 5^{6} \) |
$1.36923$ |
$(2a-11)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2Cs, 3Nn |
$1$ |
\( 2 \cdot 3 \) |
$0.689248519$ |
$33.76254038$ |
1.703246763 |
\( \frac{2803221}{125} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( -157991 a - 730465\) , \( 74372212 a + 343858086\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-157991a-730465\right){x}+74372212a+343858086$ |
| 5.1-a4 |
5.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
5.1 |
\( 5 \) |
\( - 2^{12} \cdot 5^{3} \) |
$1.36923$ |
$(2a-11)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3Nn |
$1$ |
\( 3 \) |
$0.344624259$ |
$33.76254038$ |
1.703246763 |
\( \frac{1145960298}{25} a + \frac{5298319701}{25} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -2500155 a - 11559365\) , \( 4867995135 a + 22507055720\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2500155a-11559365\right){x}+4867995135a+22507055720$ |
| 5.1-b1 |
5.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
5.1 |
\( 5 \) |
\( - 5^{3} \) |
$1.36923$ |
$(2a-11)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3Nn |
$4$ |
\( 1 \) |
$1$ |
$6.686095992$ |
0.652496156 |
\( -\frac{1145960298}{25} a + \frac{6444279999}{25} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -2\) , \( -a - 10\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}-2{x}-a-10$ |
| 5.1-b2 |
5.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
5.1 |
\( 5 \) |
\( 2^{12} \cdot 5^{12} \) |
$1.36923$ |
$(2a-11)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3Nn |
$1$ |
\( 2 \) |
$1$ |
$13.37219198$ |
0.652496156 |
\( \frac{55306341}{15625} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -12 a - 37\) , \( 12 a + 69\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-12a-37\right){x}+12a+69$ |
| 5.1-b3 |
5.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
5.1 |
\( 5 \) |
\( 2^{12} \cdot 5^{6} \) |
$1.36923$ |
$(2a-11)$ |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2Cs, 3Nn |
$4$ |
\( 2 \) |
$1$ |
$13.37219198$ |
0.652496156 |
\( \frac{2803221}{125} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -7 a - 7\) , \( -14 a - 39\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-7a-7\right){x}-14a-39$ |
| 5.1-b4 |
5.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
5.1 |
\( 5 \) |
\( - 5^{3} \) |
$1.36923$ |
$(2a-11)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3Nn |
$4$ |
\( 1 \) |
$1$ |
$6.686095992$ |
0.652496156 |
\( \frac{1145960298}{25} a + \frac{5298319701}{25} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -2624 a - 12130\) , \( -164909 a - 762456\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-2624a-12130\right){x}-164909a-762456$ |
| 5.1-c1 |
5.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
5.1 |
\( 5 \) |
\( - 5^{3} \) |
$1.36923$ |
$(2a-11)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3Nn |
$4$ |
\( 1 \) |
$1$ |
$6.686095992$ |
0.652496156 |
\( -\frac{1145960298}{25} a + \frac{6444279999}{25} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( 2623 a - 14753\) , \( 164908 a - 927364\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(2623a-14753\right){x}+164908a-927364$ |
| 5.1-c2 |
5.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
5.1 |
\( 5 \) |
\( 2^{12} \cdot 5^{12} \) |
$1.36923$ |
$(2a-11)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3Nn |
$1$ |
\( 2 \) |
$1$ |
$13.37219198$ |
0.652496156 |
\( \frac{55306341}{15625} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 7164 a - 40283\) , \( -508682 a + 2860562\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(7164a-40283\right){x}-508682a+2860562$ |
| 5.1-c3 |
5.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
5.1 |
\( 5 \) |
\( 2^{12} \cdot 5^{6} \) |
$1.36923$ |
$(2a-11)$ |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2Cs, 3Nn |
$4$ |
\( 2 \) |
$1$ |
$13.37219198$ |
0.652496156 |
\( \frac{2803221}{125} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 2649 a - 14893\) , \( 171401 a - 963868\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(2649a-14893\right){x}+171401a-963868$ |
| 5.1-c4 |
5.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
5.1 |
\( 5 \) |
\( - 5^{3} \) |
$1.36923$ |
$(2a-11)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3Nn |
$4$ |
\( 1 \) |
$1$ |
$6.686095992$ |
0.652496156 |
\( \frac{1145960298}{25} a + \frac{5298319701}{25} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( -a - 1\) , \( -10\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-a-1\right){x}-10$ |
| 5.1-d1 |
5.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
5.1 |
\( 5 \) |
\( - 2^{12} \cdot 5^{3} \) |
$1.36923$ |
$(2a-11)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3Nn |
$1$ |
\( 3 \) |
$0.344624259$ |
$33.76254038$ |
1.703246763 |
\( -\frac{1145960298}{25} a + \frac{6444279999}{25} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 40 a - 237\) , \( -204 a + 1141\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(40a-237\right){x}-204a+1141$ |
| 5.1-d2 |
5.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
5.1 |
\( 5 \) |
\( 5^{12} \) |
$1.36923$ |
$(2a-11)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3Nn |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.344624259$ |
$8.440635095$ |
1.703246763 |
\( \frac{55306341}{15625} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -64 a - 294\) , \( -431 a - 1996\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-64a-294\right){x}-431a-1996$ |
| 5.1-d3 |
5.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
5.1 |
\( 5 \) |
\( 5^{6} \) |
$1.36923$ |
$(2a-11)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2Cs, 3Nn |
$1$ |
\( 2 \cdot 3 \) |
$0.689248519$ |
$33.76254038$ |
1.703246763 |
\( \frac{2803221}{125} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -24 a - 109\) , \( 140 a + 644\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-24a-109\right){x}+140a+644$ |
| 5.1-d4 |
5.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
5.1 |
\( 5 \) |
\( - 2^{12} \cdot 5^{3} \) |
$1.36923$ |
$(2a-11)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3Nn |
$1$ |
\( 3 \) |
$1.378497038$ |
$33.76254038$ |
1.703246763 |
\( \frac{1145960298}{25} a + \frac{5298319701}{25} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -376 a - 1709\) , \( 8426 a + 39001\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-376a-1709\right){x}+8426a+39001$ |
| 6.1-a1 |
6.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{3} \cdot 3 \) |
$1.43308$ |
$(2,a+1), (3,a+1)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$9$ |
\( 3 \) |
$1$ |
$1.013292176$ |
2.669954154 |
\( -\frac{305464256137}{24} a - \frac{481953441203}{12} \) |
\( \bigl[a\) , \( 0\) , \( a + 1\) , \( -10 a - 130\) , \( -101 a - 917\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-10a-130\right){x}-101a-917$ |
| 6.1-a2 |
6.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{9} \cdot 3^{3} \) |
$1.43308$ |
$(2,a+1), (3,a+1)$ |
$0$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 3^{3} \) |
$1$ |
$9.119629590$ |
2.669954154 |
\( -\frac{3411947}{4608} a + \frac{118391}{2304} \) |
\( \bigl[a\) , \( 0\) , \( a + 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}$ |
| 6.1-a3 |
6.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{27} \cdot 3 \) |
$1.43308$ |
$(2,a+1), (3,a+1)$ |
$0$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{3} \) |
$1$ |
$9.119629590$ |
2.669954154 |
\( -\frac{131406772321033}{402653184} a + \frac{369777222537421}{201326592} \) |
\( \bigl[a\) , \( 0\) , \( a + 1\) , \( 5 a - 10\) , \( 4 a + 37\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(5a-10\right){x}+4a+37$ |
| 6.1-b1 |
6.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{15} \cdot 3 \) |
$1.43308$ |
$(2,a+1), (3,a+1)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$2.089924069$ |
$30.88585248$ |
1.399854627 |
\( -\frac{305464256137}{24} a - \frac{481953441203}{12} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -17525 a - 81029\) , \( 2812460 a + 13003338\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-17525a-81029\right){x}+2812460a+13003338$ |
| 6.1-b2 |
6.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{21} \cdot 3^{3} \) |
$1.43308$ |
$(2,a+1), (3,a+1)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 3 \) |
$0.696641356$ |
$30.88585248$ |
1.399854627 |
\( -\frac{3411947}{4608} a + \frac{118391}{2304} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -205 a - 949\) , \( 3788 a + 17514\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-205a-949\right){x}+3788a+17514$ |
| 6.1-b3 |
6.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{39} \cdot 3 \) |
$1.43308$ |
$(2,a+1), (3,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$2.089924069$ |
$3.431761387$ |
1.399854627 |
\( -\frac{131406772321033}{402653184} a + \frac{369777222537421}{201326592} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 1480 a + 6841\) , \( -25504 a - 117918\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(1480a+6841\right){x}-25504a-117918$ |
| 6.1-c1 |
6.1-c |
$3$ |
$9$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{3} \cdot 3 \) |
$1.43308$ |
$(2,a+1), (3,a+1)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$9$ |
\( 1 \) |
$1$ |
$1.013292176$ |
0.889984718 |
\( -\frac{305464256137}{24} a - \frac{481953441203}{12} \) |
\( \bigl[a\) , \( 1\) , \( a + 1\) , \( -123620 a - 571549\) , \( -53919510 a - 249295521\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-123620a-571549\right){x}-53919510a-249295521$ |
| 6.1-c2 |
6.1-c |
$3$ |
$9$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{9} \cdot 3^{3} \) |
$1.43308$ |
$(2,a+1), (3,a+1)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs |
$1$ |
\( 1 \) |
$1$ |
$9.119629590$ |
0.889984718 |
\( -\frac{3411947}{4608} a + \frac{118391}{2304} \) |
\( \bigl[a\) , \( 1\) , \( a + 1\) , \( -1450 a - 6699\) , \( -85399 a - 394834\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-1450a-6699\right){x}-85399a-394834$ |
| 6.1-c3 |
6.1-c |
$3$ |
$9$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{27} \cdot 3 \) |
$1.43308$ |
$(2,a+1), (3,a+1)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$9.119629590$ |
0.889984718 |
\( -\frac{131406772321033}{402653184} a + \frac{369777222537421}{201326592} \) |
\( \bigl[a\) , \( 1\) , \( a + 1\) , \( 10435 a + 48251\) , \( 581811 a + 2689995\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(10435a+48251\right){x}+581811a+2689995$ |
| 6.1-d1 |
6.1-d |
$3$ |
$9$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{15} \cdot 3 \) |
$1.43308$ |
$(2,a+1), (3,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \) |
$0.115433659$ |
$30.88585248$ |
2.087606584 |
\( -\frac{305464256137}{24} a - \frac{481953441203}{12} \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( 929 a - 5265\) , \( -32129 a + 180702\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(929a-5265\right){x}-32129a+180702$ |
| 6.1-d2 |
6.1-d |
$3$ |
$9$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{21} \cdot 3^{3} \) |
$1.43308$ |
$(2,a+1), (3,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs |
$1$ |
\( 3^{2} \) |
$0.038477886$ |
$30.88585248$ |
2.087606584 |
\( -\frac{3411947}{4608} a + \frac{118391}{2304} \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( 9 a - 65\) , \( -a - 2\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(9a-65\right){x}-a-2$ |
| 6.1-d3 |
6.1-d |
$3$ |
$9$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{39} \cdot 3 \) |
$1.43308$ |
$(2,a+1), (3,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3^{3} \) |
$0.115433659$ |
$3.431761387$ |
2.087606584 |
\( -\frac{131406772321033}{402653184} a + \frac{369777222537421}{201326592} \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( 374 a - 2115\) , \( 10279 a - 57810\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(374a-2115\right){x}+10279a-57810$ |
| 6.2-a1 |
6.2-a |
$3$ |
$9$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( - 2^{9} \cdot 3^{3} \) |
$1.43308$ |
$(2,a), (3,a+1)$ |
$0$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 3^{3} \) |
$1$ |
$9.119629590$ |
2.669954154 |
\( \frac{3411947}{4608} a - \frac{3175165}{4608} \) |
\( \bigl[a + 1\) , \( -a\) , \( a\) , \( -2 a + 1\) , \( -a + 1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-2a+1\right){x}-a+1$ |
| 6.2-a2 |
6.2-a |
$3$ |
$9$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( - 2^{27} \cdot 3 \) |
$1.43308$ |
$(2,a), (3,a+1)$ |
$0$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{3} \) |
$1$ |
$9.119629590$ |
2.669954154 |
\( \frac{131406772321033}{402653184} a + \frac{608147672753809}{402653184} \) |
\( \bigl[a + 1\) , \( -a\) , \( a\) , \( -7 a - 4\) , \( -5 a + 42\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-7a-4\right){x}-5a+42$ |
| 6.2-a3 |
6.2-a |
$3$ |
$9$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( - 2^{3} \cdot 3 \) |
$1.43308$ |
$(2,a), (3,a+1)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$9$ |
\( 3 \) |
$1$ |
$1.013292176$ |
2.669954154 |
\( \frac{305464256137}{24} a - \frac{1269371138543}{24} \) |
\( \bigl[a + 1\) , \( -a\) , \( a\) , \( 8 a - 139\) , \( 100 a - 1017\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(8a-139\right){x}+100a-1017$ |
| 6.2-b1 |
6.2-b |
$3$ |
$9$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( - 2^{21} \cdot 3^{3} \) |
$1.43308$ |
$(2,a), (3,a+1)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 3 \) |
$0.696641356$ |
$30.88585248$ |
1.399854627 |
\( \frac{3411947}{4608} a - \frac{3175165}{4608} \) |
\( \bigl[0\) , \( -a\) , \( a\) , \( -106 a - 483\) , \( 1156 a + 5343\bigr] \) |
${y}^2+a{y}={x}^{3}-a{x}^{2}+\left(-106a-483\right){x}+1156a+5343$ |
| 6.2-b2 |
6.2-b |
$3$ |
$9$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( - 2^{39} \cdot 3 \) |
$1.43308$ |
$(2,a), (3,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$2.089924069$ |
$3.431761387$ |
1.399854627 |
\( \frac{131406772321033}{402653184} a + \frac{608147672753809}{402653184} \) |
\( \bigl[0\) , \( -a\) , \( a\) , \( -3186 a - 14723\) , \( -215575 a - 996707\bigr] \) |
${y}^2+a{y}={x}^{3}-a{x}^{2}+\left(-3186a-14723\right){x}-215575a-996707$ |
| 6.2-b3 |
6.2-b |
$3$ |
$9$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( - 2^{15} \cdot 3 \) |
$1.43308$ |
$(2,a), (3,a+1)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$2.089924069$ |
$30.88585248$ |
1.399854627 |
\( \frac{305464256137}{24} a - \frac{1269371138543}{24} \) |
\( \bigl[0\) , \( -a\) , \( a\) , \( -7896 a - 36503\) , \( 879389 a + 4065829\bigr] \) |
${y}^2+a{y}={x}^{3}-a{x}^{2}+\left(-7896a-36503\right){x}+879389a+4065829$ |
| 6.2-c1 |
6.2-c |
$3$ |
$9$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( - 2^{9} \cdot 3^{3} \) |
$1.43308$ |
$(2,a), (3,a+1)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs |
$1$ |
\( 1 \) |
$1$ |
$9.119629590$ |
0.889984718 |
\( \frac{3411947}{4608} a - \frac{3175165}{4608} \) |
\( \bigl[a + 1\) , \( -1\) , \( a\) , \( -748 a - 3465\) , \( -20434 a - 94481\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-748a-3465\right){x}-20434a-94481$ |
| 6.2-c2 |
6.2-c |
$3$ |
$9$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( - 2^{27} \cdot 3 \) |
$1.43308$ |
$(2,a), (3,a+1)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$9.119629590$ |
0.889984718 |
\( \frac{131406772321033}{402653184} a + \frac{608147672753809}{402653184} \) |
\( \bigl[a + 1\) , \( -1\) , \( a\) , \( -22473 a - 103910\) , \( 4075678 a + 18843792\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-22473a-103910\right){x}+4075678a+18843792$ |
| 6.2-c3 |
6.2-c |
$3$ |
$9$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( - 2^{3} \cdot 3 \) |
$1.43308$ |
$(2,a), (3,a+1)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$9$ |
\( 1 \) |
$1$ |
$1.013292176$ |
0.889984718 |
\( \frac{305464256137}{24} a - \frac{1269371138543}{24} \) |
\( \bigl[a + 1\) , \( -1\) , \( a\) , \( -55698 a - 257525\) , \( -16381853 a - 75741099\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-55698a-257525\right){x}-16381853a-75741099$ |
| 6.2-d1 |
6.2-d |
$3$ |
$9$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( - 2^{21} \cdot 3^{3} \) |
$1.43308$ |
$(2,a), (3,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs |
$1$ |
\( 3^{2} \) |
$0.038477886$ |
$30.88585248$ |
2.087606584 |
\( \frac{3411947}{4608} a - \frac{3175165}{4608} \) |
\( \bigl[0\) , \( -1\) , \( a\) , \( -714797 a - 3304846\) , \( 528167391 a + 2441968925\bigr] \) |
${y}^2+a{y}={x}^{3}-{x}^{2}+\left(-714797a-3304846\right){x}+528167391a+2441968925$ |
| 6.2-d2 |
6.2-d |
$3$ |
$9$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( - 2^{39} \cdot 3 \) |
$1.43308$ |
$(2,a), (3,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3^{3} \) |
$0.115433659$ |
$3.431761387$ |
2.087606584 |
\( \frac{131406772321033}{402653184} a + \frac{608147672753809}{402653184} \) |
\( \bigl[0\) , \( -1\) , \( a\) , \( -21418357 a - 99027246\) , \( -122091965992 a - 564489199229\bigr] \) |
${y}^2+a{y}={x}^{3}-{x}^{2}+\left(-21418357a-99027246\right){x}-122091965992a-564489199229$ |
| 6.2-d3 |
6.2-d |
$3$ |
$9$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( - 2^{15} \cdot 3 \) |
$1.43308$ |
$(2,a), (3,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \) |
$0.115433659$ |
$30.88585248$ |
2.087606584 |
\( \frac{305464256137}{24} a - \frac{1269371138543}{24} \) |
\( \bigl[0\) , \( -1\) , \( a\) , \( -53081227 a - 245419746\) , \( 476511048344 a + 2203137101731\bigr] \) |
${y}^2+a{y}={x}^{3}-{x}^{2}+\left(-53081227a-245419746\right){x}+476511048344a+2203137101731$ |
| 9.1-a1 |
9.1-a |
$4$ |
$14$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{6} \) |
$1.58597$ |
$(3,a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-7$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$3.458864173$ |
$5.709422123$ |
1.927218749 |
\( -3375 \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 50422 a - 283550\) , \( 17141097 a - 96392548\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(50422a-283550\right){x}+17141097a-96392548$ |
| 9.1-a2 |
9.1-a |
$4$ |
$14$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 2^{12} \cdot 3^{6} \) |
$1.58597$ |
$(3,a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-7$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.494123453$ |
$39.96595486$ |
1.927218749 |
\( -3375 \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 5690590 a - 32000905\) , \( -20545570618 a + 115537510593\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(5690590a-32000905\right){x}-20545570618a+115537510593$ |
| 9.1-a3 |
9.1-a |
$4$ |
$14$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{6} \) |
$1.58597$ |
$(3,a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-28$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1.729432086$ |
$5.709422123$ |
1.927218749 |
\( 16581375 \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 857182 a - 4820345\) , \( 977546796 a - 5497210354\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(857182a-4820345\right){x}+977546796a-5497210354$ |
| 9.1-a4 |
9.1-a |
$4$ |
$14$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 2^{12} \cdot 3^{6} \) |
$1.58597$ |
$(3,a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-28$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$0.247061726$ |
$39.96595486$ |
1.927218749 |
\( 16581375 \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 96740095 a - 544015555\) , \( -1171929687574 a + 6590317748649\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(96740095a-544015555\right){x}-1171929687574a+6590317748649$ |
| 9.1-b1 |
9.1-b |
$4$ |
$14$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{6} \) |
$1.58597$ |
$(3,a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-7$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$3.458864173$ |
$5.709422123$ |
1.927218749 |
\( -3375 \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( 7 a - 42\) , \( 29 a - 171\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(7a-42\right){x}+29a-171$ |
| 9.1-b2 |
9.1-b |
$4$ |
$14$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 2^{12} \cdot 3^{6} \) |
$1.58597$ |
$(3,a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-7$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.494123453$ |
$39.96595486$ |
1.927218749 |
\( -3375 \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 843 a - 4737\) , \( -34227 a + 192476\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(843a-4737\right){x}-34227a+192476$ |
| 9.1-b3 |
9.1-b |
$4$ |
$14$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{6} \) |
$1.58597$ |
$(3,a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-28$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1.729432086$ |
$5.709422123$ |
1.927218749 |
\( 16581375 \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( 127 a - 717\) , \( 1742 a - 9804\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(127a-717\right){x}+1742a-9804$ |
| 9.1-b4 |
9.1-b |
$4$ |
$14$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 2^{12} \cdot 3^{6} \) |
$1.58597$ |
$(3,a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-28$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$0.247061726$ |
$39.96595486$ |
1.927218749 |
\( 16581375 \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 14388 a - 80907\) , \( -2074476 a + 11665766\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(14388a-80907\right){x}-2074476a+11665766$ |
| 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 |
\( -\frac{1}{15} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -13023 a - 60202\) , \( -294878872 a - 1363365200\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-13023a-60202\right){x}-294878872a-1363365200$ |
*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.
