| 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 |
| 8.4-a5 |
8.4-a |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
8.4 |
\( 2^{3} \) |
\( 2^{11} \) |
$0.61963$ |
$(-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$12.69057434$ |
0.769479095 |
\( -21069823 a + 54821634 \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( 7 a - 20\) , \( 15 a - 40\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(7a-20\right){x}+15a-40$ |
| 16.4-a5 |
16.4-a |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
16.4 |
\( 2^{4} \) |
\( 2^{11} \) |
$0.73687$ |
$(-a+2)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$36.94092262$ |
0.559968109 |
\( -21069823 a + 54821634 \) |
\( \bigl[a\) , \( a\) , \( a\) , \( -124 a - 195\) , \( 916 a + 1430\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-124a-195\right){x}+916a+1430$ |
| 64.7-a5 |
64.7-a |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
64.7 |
\( 2^{6} \) |
\( 2^{17} \) |
$1.04210$ |
$(-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$12.02171134$ |
1.457846637 |
\( -21069823 a + 54821634 \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -38 a - 65\) , \( -203 a - 311\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-38a-65\right){x}-203a-311$ |
| 64.7-b5 |
64.7-b |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
64.7 |
\( 2^{6} \) |
\( 2^{17} \) |
$1.04210$ |
$(-a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.986670162$ |
$4.129902846$ |
0.988296755 |
\( -21069823 a + 54821634 \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 90 a - 233\) , \( 779 a - 1997\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(90a-233\right){x}+779a-1997$ |
| 128.2-b5 |
128.2-b |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
128.2 |
\( 2^{7} \) |
\( 2^{23} \) |
$1.23927$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$2.920282308$ |
1.416544989 |
\( -21069823 a + 54821634 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 43 a - 127\) , \( 218 a - 606\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(43a-127\right){x}+218a-606$ |
| 256.1-f5 |
256.1-f |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{23} \) |
$1.47375$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.539799292$ |
$8.500633610$ |
2.225815404 |
\( -21069823 a + 54821634 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -303 a - 476\) , \( -3792 a - 5920\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-303a-476\right){x}-3792a-5920$ |
| 512.3-e5 |
512.3-e |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.3 |
\( 2^{9} \) |
\( 2^{29} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$6.010855670$ |
1.457846637 |
\( -21069823 a + 54821634 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -44 a - 128\) , \( -352 a - 416\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-44a-128\right){x}-352a-416$ |
| 512.3-h5 |
512.3-h |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.3 |
\( 2^{9} \) |
\( 2^{29} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$13.06058844$ |
1.583828990 |
\( -21069823 a + 54821634 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 984 a - 2520\) , \( -24304 a + 62256\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(984a-2520\right){x}-24304a+62256$ |
| 648.4-d5 |
648.4-d |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
648.4 |
\( 2^{3} \cdot 3^{4} \) |
\( 2^{11} \cdot 3^{12} \) |
$1.85890$ |
$(-a+2), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1.361629101$ |
$5.667089073$ |
1.871519699 |
\( -21069823 a + 54821634 \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 48 a - 192\) , \( -427 a + 912\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(48a-192\right){x}-427a+912$ |
*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.
