| 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 |
| 171.1-a1 |
171.1-a |
$2$ |
$5$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
171.1 |
\( 3^{2} \cdot 19 \) |
\( 3^{10} \cdot 19^{10} \) |
$2.43964$ |
$(4a+13), (10a-43)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B.4.2 |
$1$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$0.313808150$ |
0.831298097 |
\( -\frac{9358714467168256}{22284891} \) |
\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( 526841 a - 2252236\) , \( 404829173 a - 1730611020\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(526841a-2252236\right){x}+404829173a-1730611020$ |
| 171.1-a2 |
171.1-a |
$2$ |
$5$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
171.1 |
\( 3^{2} \cdot 19 \) |
\( 3^{26} \cdot 19^{2} \) |
$2.43964$ |
$(4a+13), (10a-43)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B.4.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$1.569040751$ |
0.831298097 |
\( \frac{841232384}{1121931} \) |
\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( -2359 a + 10094\) , \( 136703 a - 584400\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-2359a+10094\right){x}+136703a-584400$ |
| 171.1-b1 |
171.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
171.1 |
\( 3^{2} \cdot 19 \) |
\( 3^{8} \cdot 19^{2} \) |
$2.43964$ |
$(4a+13), (10a-43)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$0.494175486$ |
$3.113057546$ |
1.630124995 |
\( -\frac{1413120}{19} a - \frac{13791232}{57} \) |
\( \bigl[0\) , \( a + 1\) , \( 1\) , \( -34122 a + 145878\) , \( 1749942 a - 7480852\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-34122a+145878\right){x}+1749942a-7480852$ |
| 171.1-c1 |
171.1-c |
$3$ |
$9$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
171.1 |
\( 3^{2} \cdot 19 \) |
\( 3^{6} \cdot 19^{2} \) |
$2.43964$ |
$(4a+13), (10a-43)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$2.365058442$ |
$1.080001815$ |
2.706567867 |
\( -\frac{50357871050752}{19} \) |
\( \bigl[0\) , \( a + 1\) , \( 1\) , \( -92319 a - 302343\) , \( -29828922 a - 97687237\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-92319a-302343\right){x}-29828922a-97687237$ |
| 171.1-c2 |
171.1-c |
$3$ |
$9$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
171.1 |
\( 3^{2} \cdot 19 \) |
\( 3^{6} \cdot 19^{6} \) |
$2.43964$ |
$(4a+13), (10a-43)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3Cs |
$1$ |
\( 2^{2} \) |
$0.788352814$ |
$3.240005446$ |
2.706567867 |
\( -\frac{89915392}{6859} \) |
\( \bigl[0\) , \( a + 1\) , \( 1\) , \( -1119 a - 3663\) , \( -44142 a - 144562\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-1119a-3663\right){x}-44142a-144562$ |
| 171.1-c3 |
171.1-c |
$3$ |
$9$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
171.1 |
\( 3^{2} \cdot 19 \) |
\( 3^{6} \cdot 19^{2} \) |
$2.43964$ |
$(4a+13), (10a-43)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$0.262784271$ |
$9.720016340$ |
2.706567867 |
\( \frac{32768}{19} \) |
\( \bigl[0\) , \( a + 1\) , \( 1\) , \( 81 a + 267\) , \( 108 a + 353\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(81a+267\right){x}+108a+353$ |
| 171.1-d1 |
171.1-d |
$1$ |
$1$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
171.1 |
\( 3^{2} \cdot 19 \) |
\( 3^{10} \cdot 19^{2} \) |
$2.43964$ |
$(4a+13), (10a-43)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$6.152988229$ |
3.259932801 |
\( -\frac{1404928}{171} \) |
\( \bigl[0\) , \( a + 1\) , \( 1\) , \( 281 a - 1192\) , \( -5663 a + 24214\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(281a-1192\right){x}-5663a+24214$ |
| 171.1-e1 |
171.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
171.1 |
\( 3^{2} \cdot 19 \) |
\( 3^{8} \cdot 19^{8} \) |
$2.43964$ |
$(4a+13), (10a-43)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.884869071$ |
0.998628029 |
\( \frac{67419143}{390963} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( 1018 a + 3337\) , \( 104632 a + 342660\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(1018a+3337\right){x}+104632a+342660$ |
| 171.1-e2 |
171.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
171.1 |
\( 3^{2} \cdot 19 \) |
\( - 3^{7} \cdot 19 \) |
$2.43964$ |
$(4a+13), (10a-43)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$15.07895257$ |
0.998628029 |
\( -\frac{276137246}{57} a + \frac{1180481203}{57} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( 6 a - 18\) , \( -18 a + 81\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(6a-18\right){x}-18a+81$ |
| 171.1-e3 |
171.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
171.1 |
\( 3^{2} \cdot 19 \) |
\( 3^{8} \cdot 19^{2} \) |
$2.43964$ |
$(4a+13), (10a-43)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$15.07895257$ |
0.998628029 |
\( \frac{389017}{57} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( -182 a - 593\) , \( -2528 a - 8280\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(-182a-593\right){x}-2528a-8280$ |
| 171.1-e4 |
171.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
171.1 |
\( 3^{2} \cdot 19 \) |
\( 3^{10} \cdot 19^{4} \) |
$2.43964$ |
$(4a+13), (10a-43)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$7.539476287$ |
0.998628029 |
\( \frac{30664297}{3249} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( -782 a - 2558\) , \( 19744 a + 64659\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(-782a-2558\right){x}+19744a+64659$ |
| 171.1-e5 |
171.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
171.1 |
\( 3^{2} \cdot 19 \) |
\( - 3^{7} \cdot 19 \) |
$2.43964$ |
$(4a+13), (10a-43)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$7.539476287$ |
0.998628029 |
\( \frac{276137246}{57} a + \frac{904343957}{57} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( -9960 a + 42585\) , \( -2264742 a + 9681588\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(-9960a+42585\right){x}-2264742a+9681588$ |
| 171.1-e6 |
171.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
171.1 |
\( 3^{2} \cdot 19 \) |
\( 3^{14} \cdot 19^{2} \) |
$2.43964$ |
$(4a+13), (10a-43)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$3.769738143$ |
0.998628029 |
\( \frac{115714886617}{1539} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( -12182 a - 39893\) , \( 1403704 a + 4597014\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(-12182a-39893\right){x}+1403704a+4597014$ |
| 171.1-f1 |
171.1-f |
$1$ |
$1$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
171.1 |
\( 3^{2} \cdot 19 \) |
\( 3^{8} \cdot 19^{2} \) |
$2.43964$ |
$(4a+13), (10a-43)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$0.434454973$ |
$14.02540668$ |
6.456732522 |
\( \frac{1413120}{19} a - \frac{18030592}{57} \) |
\( \bigl[0\) , \( a + 1\) , \( 1\) , \( 4 a - 5\) , \( -5 a + 32\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(4a-5\right){x}-5a+32$ |
| 171.1-g1 |
171.1-g |
$1$ |
$1$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
171.1 |
\( 3^{2} \cdot 19 \) |
\( 3^{8} \cdot 19^{2} \) |
$2.43964$ |
$(4a+13), (10a-43)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$0.434454973$ |
$14.02540668$ |
6.456732522 |
\( -\frac{1413120}{19} a - \frac{13791232}{57} \) |
\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( -2 a - 2\) , \( 8 a + 29\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-2a-2\right){x}+8a+29$ |
| 171.1-h1 |
171.1-h |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
171.1 |
\( 3^{2} \cdot 19 \) |
\( 3^{8} \cdot 19^{8} \) |
$2.43964$ |
$(4a+13), (10a-43)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.884869071$ |
0.998628029 |
\( \frac{67419143}{390963} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -1018 a + 4355\) , \( -104632 a + 447292\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-1018a+4355\right){x}-104632a+447292$ |
| 171.1-h2 |
171.1-h |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
171.1 |
\( 3^{2} \cdot 19 \) |
\( - 3^{7} \cdot 19 \) |
$2.43964$ |
$(4a+13), (10a-43)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$7.539476287$ |
0.998628029 |
\( -\frac{276137246}{57} a + \frac{1180481203}{57} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( 9960 a + 32625\) , \( 2264742 a + 7416846\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(9960a+32625\right){x}+2264742a+7416846$ |
| 171.1-h3 |
171.1-h |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
171.1 |
\( 3^{2} \cdot 19 \) |
\( 3^{8} \cdot 19^{2} \) |
$2.43964$ |
$(4a+13), (10a-43)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$15.07895257$ |
0.998628029 |
\( \frac{389017}{57} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( 182 a - 775\) , \( 2528 a - 10808\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(182a-775\right){x}+2528a-10808$ |
| 171.1-h4 |
171.1-h |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
171.1 |
\( 3^{2} \cdot 19 \) |
\( 3^{10} \cdot 19^{4} \) |
$2.43964$ |
$(4a+13), (10a-43)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$7.539476287$ |
0.998628029 |
\( \frac{30664297}{3249} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( 782 a - 3340\) , \( -19744 a + 84403\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(782a-3340\right){x}-19744a+84403$ |
| 171.1-h5 |
171.1-h |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
171.1 |
\( 3^{2} \cdot 19 \) |
\( - 3^{7} \cdot 19 \) |
$2.43964$ |
$(4a+13), (10a-43)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$15.07895257$ |
0.998628029 |
\( \frac{276137246}{57} a + \frac{904343957}{57} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -6 a - 12\) , \( 18 a + 63\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-6a-12\right){x}+18a+63$ |
| 171.1-h6 |
171.1-h |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
171.1 |
\( 3^{2} \cdot 19 \) |
\( 3^{14} \cdot 19^{2} \) |
$2.43964$ |
$(4a+13), (10a-43)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$3.769738143$ |
0.998628029 |
\( \frac{115714886617}{1539} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( 12182 a - 52075\) , \( -1403704 a + 6000718\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(12182a-52075\right){x}-1403704a+6000718$ |
| 171.1-i1 |
171.1-i |
$1$ |
$1$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
171.1 |
\( 3^{2} \cdot 19 \) |
\( 3^{10} \cdot 19^{2} \) |
$2.43964$ |
$(4a+13), (10a-43)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$6.152988229$ |
3.259932801 |
\( -\frac{1404928}{171} \) |
\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( -279 a - 912\) , \( 5943 a + 19463\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-279a-912\right){x}+5943a+19463$ |
| 171.1-j1 |
171.1-j |
$3$ |
$9$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
171.1 |
\( 3^{2} \cdot 19 \) |
\( 3^{6} \cdot 19^{2} \) |
$2.43964$ |
$(4a+13), (10a-43)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$2.365058442$ |
$1.080001815$ |
2.706567867 |
\( -\frac{50357871050752}{19} \) |
\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( 92321 a - 394663\) , \( 29736602 a - 127121496\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(92321a-394663\right){x}+29736602a-127121496$ |
| 171.1-j2 |
171.1-j |
$3$ |
$9$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
171.1 |
\( 3^{2} \cdot 19 \) |
\( 3^{6} \cdot 19^{6} \) |
$2.43964$ |
$(4a+13), (10a-43)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3Cs |
$1$ |
\( 2^{2} \) |
$0.788352814$ |
$3.240005446$ |
2.706567867 |
\( -\frac{89915392}{6859} \) |
\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( 1121 a - 4783\) , \( 43022 a - 183921\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(1121a-4783\right){x}+43022a-183921$ |
| 171.1-j3 |
171.1-j |
$3$ |
$9$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
171.1 |
\( 3^{2} \cdot 19 \) |
\( 3^{6} \cdot 19^{2} \) |
$2.43964$ |
$(4a+13), (10a-43)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$0.262784271$ |
$9.720016340$ |
2.706567867 |
\( \frac{32768}{19} \) |
\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( -79 a + 347\) , \( -28 a + 114\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-79a+347\right){x}-28a+114$ |
| 171.1-k1 |
171.1-k |
$1$ |
$1$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
171.1 |
\( 3^{2} \cdot 19 \) |
\( 3^{8} \cdot 19^{2} \) |
$2.43964$ |
$(4a+13), (10a-43)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$0.494175486$ |
$3.113057546$ |
1.630124995 |
\( \frac{1413120}{19} a - \frac{18030592}{57} \) |
\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( 34124 a + 111755\) , \( -1784065 a - 5842665\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(34124a+111755\right){x}-1784065a-5842665$ |
| 171.1-l1 |
171.1-l |
$2$ |
$5$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
171.1 |
\( 3^{2} \cdot 19 \) |
\( 3^{10} \cdot 19^{10} \) |
$2.43964$ |
$(4a+13), (10a-43)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B.4.2 |
$1$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$0.313808150$ |
0.831298097 |
\( -\frac{9358714467168256}{22284891} \) |
\( \bigl[0\) , \( a + 1\) , \( 1\) , \( -526839 a - 1725396\) , \( -405356013 a - 1327507243\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-526839a-1725396\right){x}-405356013a-1327507243$ |
| 171.1-l2 |
171.1-l |
$2$ |
$5$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
171.1 |
\( 3^{2} \cdot 19 \) |
\( 3^{26} \cdot 19^{2} \) |
$2.43964$ |
$(4a+13), (10a-43)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B.4.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$1.569040751$ |
0.831298097 |
\( \frac{841232384}{1121931} \) |
\( \bigl[0\) , \( a + 1\) , \( 1\) , \( 2361 a + 7734\) , \( -134343 a - 439963\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(2361a+7734\right){x}-134343a-439963$ |
*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.
