| 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-a2 |
1.1-a |
$4$ |
$15$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$0.48121$ |
$\textsf{none}$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
✓ |
$3, 5$ |
3B.1.1, 5B |
$1$ |
\( 1 \) |
$1$ |
$18.40477294$ |
0.379742281 |
\( -3515 a - 7688 \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( 2 a + 2\) , \( a + 1\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(2a+2\right){x}+a+1$ |
| 25.2-a2 |
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 |
$1$ |
\( 1 \) |
$1$ |
$8.230864683$ |
1.528433200 |
\( -3515 a - 7688 \) |
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -a + 2\) , \( -a - 2\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-a+2\right){x}-a-2$ |
| 25.3-a2 |
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 |
$1$ |
\( 1 \) |
$1$ |
$8.230864683$ |
1.528433200 |
\( -3515 a - 7688 \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -2 a + 2\) , \( -18 a + 55\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-2a+2\right){x}-18a+55$ |
| 49.2-b2 |
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 |
$1$ |
\( 2 \) |
$0.105024575$ |
$21.88927204$ |
1.707588603 |
\( -3515 a - 7688 \) |
\( \bigl[1\) , \( -a\) , \( 1\) , \( -3 a - 5\) , \( 8 a + 18\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-3a-5\right){x}+8a+18$ |
| 49.3-b2 |
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 |
$1$ |
\( 2 \) |
$0.525122879$ |
$4.377854408$ |
1.707588603 |
\( -3515 a - 7688 \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -2 a\) , \( -3 a - 5\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}-2a{x}-3a-5$ |
| 81.1-a2 |
81.1-a |
$4$ |
$15$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
81.1 |
\( 3^{4} \) |
\( 3^{12} \) |
$1.44364$ |
$(3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 5$ |
3B.1.2, 5B |
$1$ |
\( 1 \) |
$1$ |
$12.14895586$ |
2.256004467 |
\( -3515 a - 7688 \) |
\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( -4 a - 8\) , \( 5 a + 11\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-4a-8\right){x}+5a+11$ |
| 169.2-a2 |
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 |
\( -3515 a - 7688 \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -2 a - 4\) , \( -4\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-2a-4\right){x}-4$ |
| 169.3-a2 |
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 |
\( -3515 a - 7688 \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -16 a - 35\) , \( 53 a + 116\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-16a-35\right){x}+53a+116$ |
| 256.1-d2 |
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 |
$1$ |
\( 2 \) |
$0.185544713$ |
$14.47839255$ |
1.995399799 |
\( -3515 a - 7688 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -2 a + 7\) , \( -17 a + 55\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2a+7\right){x}-17a+55$ |
| 256.1-h2 |
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 |
\( -3515 a - 7688 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -4 a - 8\) , \( 4 a + 8\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-4a-8\right){x}+4a+8$ |
| 256.1-i2 |
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 |
$1$ |
\( 2 \) |
$0.927723566$ |
$2.895678510$ |
1.995399799 |
\( -3515 a - 7688 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -2 a + 7\) , \( 17 a - 55\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-2a+7\right){x}+17a-55$ |
| 529.2-a2 |
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 |
$1$ |
\( 2 \) |
$1.880943877$ |
$2.415162831$ |
3.374296536 |
\( -3515 a - 7688 \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -2 a + 3\) , \( 4 a - 14\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2a+3\right){x}+4a-14$ |
| 529.3-a2 |
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 |
$1$ |
\( 2 \) |
$0.376188775$ |
$12.07581415$ |
3.374296536 |
\( -3515 a - 7688 \) |
\( \bigl[a\) , \( -a\) , \( 0\) , \( -7 a + 22\) , \( -139 a + 444\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(-7a+22\right){x}-139a+444$ |
| 625.1-f2 |
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 |
$1$ |
\( 1 \) |
$1$ |
$3.680954588$ |
0.683536107 |
\( -3515 a - 7688 \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -8 a - 19\) , \( -27 a - 59\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-8a-19\right){x}-27a-59$ |
| 841.1-a2 |
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 |
\( -3515 a - 7688 \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 14\) , \( 41 a - 116\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+14{x}+41a-116$ |
*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.
