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 |
1.1-a1 |
1.1-a |
$4$ |
$15$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$0.48121$ |
$\textsf{none}$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
✓ |
$3, 5$ |
3B.1.2, 5B |
$1$ |
\( 1 \) |
$1$ |
$2.044974771$ |
0.379742281 |
\( -1407628760845 a - 3086342051803 \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( -23 a - 53\) , \( -169 a - 372\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-23a-53\right){x}-169a-372$ |
25.2-a1 |
25.2-a |
$4$ |
$15$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{6} \) |
$1.07603$ |
$(-a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 5$ |
3B, 5B |
$9$ |
\( 1 \) |
$1$ |
$0.914540520$ |
1.528433200 |
\( -1407628760845 a - 3086342051803 \) |
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -16 a - 38\) , \( -64 a - 195\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-16a-38\right){x}-64a-195$ |
25.3-a1 |
25.3-a |
$4$ |
$15$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
25.3 |
\( 5^{2} \) |
\( 5^{6} \) |
$1.07603$ |
$(-a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 5$ |
3B, 5B |
$9$ |
\( 1 \) |
$1$ |
$0.914540520$ |
1.528433200 |
\( -1407628760845 a - 3086342051803 \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 13 a - 53\) , \( 480 a - 1546\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(13a-53\right){x}+480a-1546$ |
49.2-b1 |
49.2-b |
$4$ |
$15$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
49.2 |
\( 7^{2} \) |
\( 7^{6} \) |
$1.27317$ |
$(-a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 5$ |
3B, 5B |
$1$ |
\( 2 \) |
$0.315073727$ |
$7.296424013$ |
1.707588603 |
\( -1407628760845 a - 3086342051803 \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 1\) , \( 107 a - 344\) , \( 9766 a - 31179\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(107a-344\right){x}+9766a-31179$ |
49.3-b1 |
49.3-b |
$4$ |
$15$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
49.3 |
\( 7^{2} \) |
\( 7^{6} \) |
$1.27317$ |
$(a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 5$ |
3B, 5B |
$1$ |
\( 2 \) |
$1.575368639$ |
$1.459284802$ |
1.707588603 |
\( -1407628760845 a - 3086342051803 \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -122 a - 265\) , \( -1292 a - 2825\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-122a-265\right){x}-1292a-2825$ |
81.1-a1 |
81.1-a |
$4$ |
$15$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
81.1 |
\( 3^{4} \) |
\( 3^{12} \) |
$1.44364$ |
$(3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 5$ |
3B.1.1, 5B |
$9$ |
\( 1 \) |
$1$ |
$12.14895586$ |
2.256004467 |
\( -1407628760845 a - 3086342051803 \) |
\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( -229 a - 503\) , \( 3200 a + 7022\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-229a-503\right){x}+3200a+7022$ |
169.2-a1 |
169.2-a |
$4$ |
$15$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
169.2 |
\( 13^{2} \) |
\( 13^{6} \) |
$1.73504$ |
$(a-5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 5$ |
3B, 5B |
$1$ |
\( 1 \) |
$1$ |
$10.10854230$ |
1.877109181 |
\( -1407628760845 a - 3086342051803 \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -82 a - 189\) , \( 561 a + 1325\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-82a-189\right){x}+561a+1325$ |
169.3-a1 |
169.3-a |
$4$ |
$15$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
169.3 |
\( 13^{2} \) |
\( 13^{6} \) |
$1.73504$ |
$(a+4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 5$ |
3B, 5B |
$1$ |
\( 1 \) |
$1$ |
$10.10854230$ |
1.877109181 |
\( -1407628760845 a - 3086342051803 \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( 71 a - 238\) , \( -5335 a + 17040\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(71a-238\right){x}-5335a+17040$ |
256.1-d1 |
256.1-d |
$4$ |
$15$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{24} \) |
$1.92485$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 5$ |
3B, 5B |
$1$ |
\( 2 \) |
$0.556634139$ |
$4.826130850$ |
1.995399799 |
\( -1407628760845 a - 3086342051803 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -2 a - 73\) , \( 495 a - 1241\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2a-73\right){x}+495a-1241$ |
256.1-h1 |
256.1-h |
$4$ |
$15$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{24} \) |
$1.92485$ |
$(2)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 5$ |
3B, 5B |
$1$ |
\( 2^{2} \) |
$0.103947800$ |
$9.111716899$ |
2.814080433 |
\( -1407628760845 a - 3086342051803 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -404 a - 888\) , \( 6724 a + 14760\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-404a-888\right){x}+6724a+14760$ |
256.1-i1 |
256.1-i |
$4$ |
$15$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{24} \) |
$1.92485$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 5$ |
3B, 5B |
$1$ |
\( 2 \) |
$2.783170698$ |
$0.965226170$ |
1.995399799 |
\( -1407628760845 a - 3086342051803 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -2 a - 73\) , \( -495 a + 1241\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-2a-73\right){x}-495a+1241$ |
529.2-a1 |
529.2-a |
$4$ |
$15$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
529.2 |
\( 23^{2} \) |
\( 23^{6} \) |
$2.30782$ |
$(a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 5$ |
3B, 5B |
$1$ |
\( 2 \) |
$5.642831631$ |
$0.805054277$ |
3.374296536 |
\( -1407628760845 a - 3086342051803 \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -57 a - 157\) , \( -544 a - 454\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-57a-157\right){x}-544a-454$ |
529.3-a1 |
529.3-a |
$4$ |
$15$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
529.3 |
\( 23^{2} \) |
\( 23^{6} \) |
$2.30782$ |
$(a-6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 5$ |
3B, 5B |
$1$ |
\( 2 \) |
$1.128566326$ |
$4.025271385$ |
3.374296536 |
\( -1407628760845 a - 3086342051803 \) |
\( \bigl[a\) , \( -a\) , \( 0\) , \( 48 a - 193\) , \( 3674 a - 11624\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(48a-193\right){x}+3674a-11624$ |
625.1-f1 |
625.1-f |
$4$ |
$15$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
625.1 |
\( 5^{4} \) |
\( 5^{12} \) |
$2.40607$ |
$(-a-1), (-a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 5$ |
3B, 5B |
$9$ |
\( 1 \) |
$1$ |
$0.408994954$ |
0.683536107 |
\( -1407628760845 a - 3086342051803 \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -633 a - 1394\) , \( -14777 a - 32434\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-633a-1394\right){x}-14777a-32434$ |
841.1-a1 |
841.1-a |
$4$ |
$15$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
841.1 |
\( 29^{2} \) |
\( 29^{6} \) |
$2.59141$ |
$(-2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 5$ |
3B, 5B |
$1$ |
\( 2^{2} \) |
$1$ |
$6.768013403$ |
5.027154151 |
\( -1407628760845 a - 3086342051803 \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -131\) , \( -974 a + 3393\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}-131{x}-974a+3393$ |
*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.