| 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 |
| 8.3-a2 |
8.3-a |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
8.3 |
\( 2^{3} \) |
\( - 2^{10} \) |
$0.61963$ |
$(-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$6.345287171$ |
0.769479095 |
\( -2701312025 a + 6919553753 \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 80 a + 125\) , \( 1186 a + 1852\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(80a+125\right){x}+1186a+1852$ |
| 16.5-a2 |
16.5-a |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
16.5 |
\( 2^{4} \) |
\( - 2^{10} \) |
$0.73687$ |
$(-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$4.617615327$ |
0.559968109 |
\( -2701312025 a + 6919553753 \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 7 a - 2\) , \( 5 a - 5\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(7a-2\right){x}+5a-5$ |
| 64.6-a2 |
64.6-a |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
64.6 |
\( 2^{6} \) |
\( - 2^{16} \) |
$1.04210$ |
$(-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$12.02171134$ |
1.457846637 |
\( -2701312025 a + 6919553753 \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 20 a + 27\) , \( -59 a - 88\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(20a+27\right){x}-59a-88$ |
| 64.6-b2 |
64.6-b |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
64.6 |
\( 2^{6} \) |
\( - 2^{16} \) |
$1.04210$ |
$(-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.123333770$ |
$16.51961138$ |
0.988296755 |
\( -2701312025 a + 6919553753 \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 68 a - 178\) , \( -469 a + 1200\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(68a-178\right){x}-469a+1200$ |
| 128.1-b2 |
128.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
128.1 |
\( 2^{7} \) |
\( - 2^{22} \) |
$1.23927$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$11.68112923$ |
1.416544989 |
\( -2701312025 a + 6919553753 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 533 a - 1364\) , \( -10078 a + 25816\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(533a-1364\right){x}-10078a+25816$ |
| 256.1-e2 |
256.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( - 2^{22} \) |
$1.47375$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.079598584$ |
$8.500633610$ |
2.225815404 |
\( -2701312025 a + 6919553753 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 16 a - 8\) , \( -48 a - 12\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(16a-8\right){x}-48a-12$ |
| 512.4-e2 |
512.4-e |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.4 |
\( 2^{9} \) |
\( - 2^{28} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$6.010855670$ |
1.457846637 |
\( -2701312025 a + 6919553753 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 166 a + 255\) , \( -3275 a - 5103\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(166a+255\right){x}-3275a-5103$ |
| 512.4-h2 |
512.4-h |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.4 |
\( 2^{9} \) |
\( - 2^{28} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$1.632573555$ |
1.583828990 |
\( -2701312025 a + 6919553753 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 106 a - 257\) , \( 789 a - 2033\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(106a-257\right){x}+789a-2033$ |
| 648.3-d2 |
648.3-d |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
648.3 |
\( 2^{3} \cdot 3^{4} \) |
\( - 2^{10} \cdot 3^{12} \) |
$1.85890$ |
$(-a-1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.680814550$ |
$5.667089073$ |
1.871519699 |
\( -2701312025 a + 6919553753 \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 717 a + 1118\) , \( -29467 a - 46014\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(717a+1118\right){x}-29467a-46014$ |
*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.
