| 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 |
| 725.1-a1 |
725.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
725.1 |
\( 5^{2} \cdot 29 \) |
\( - 5^{8} \cdot 29 \) |
$2.49702$ |
$(-a-1), (-a+2), (-2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \) |
$1$ |
$6.647831697$ |
3.703414065 |
\( -\frac{335860066}{90625} a + \frac{1138409117}{90625} \) |
\( \bigl[1\) , \( a\) , \( 1\) , \( 10 a - 28\) , \( 19 a - 59\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(10a-28\right){x}+19a-59$ |
| 725.1-b1 |
725.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
725.1 |
\( 5^{2} \cdot 29 \) |
\( 5^{10} \cdot 29^{8} \) |
$2.49702$ |
$(-a-1), (-a+2), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$2.141176370$ |
2.385638820 |
\( \frac{260036963574168}{55256328125} a + \frac{3121329996689473}{55256328125} \) |
\( \bigl[a + 1\) , \( -a\) , \( a\) , \( 3747 a - 12023\) , \( -198697 a + 634484\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(3747a-12023\right){x}-198697a+634484$ |
| 725.1-b2 |
725.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
725.1 |
\( 5^{2} \cdot 29 \) |
\( - 5^{20} \cdot 29^{4} \) |
$2.49702$ |
$(-a-1), (-a+2), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$1.070588185$ |
2.385638820 |
\( \frac{4773348938382503604562}{5133056640625} a + \frac{10465960888870619616557}{5133056640625} \) |
\( \bigl[a + 1\) , \( -a\) , \( a\) , \( -458 a + 592\) , \( -613310 a + 1967469\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-458a+592\right){x}-613310a+1967469$ |
| 725.1-c1 |
725.1-c |
$2$ |
$3$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
725.1 |
\( 5^{2} \cdot 29 \) |
\( - 5^{6} \cdot 29^{3} \) |
$2.49702$ |
$(-a-1), (-a+2), (-2a+1)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{3} \) |
$0.688788084$ |
$4.300789297$ |
3.300547924 |
\( \frac{278586546127}{105125} a + \frac{610823956159}{105125} \) |
\( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( 4 a - 6\) , \( -907 a + 2898\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(4a-6\right){x}-907a+2898$ |
| 725.1-c2 |
725.1-c |
$2$ |
$3$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
725.1 |
\( 5^{2} \cdot 29 \) |
\( - 5^{2} \cdot 29 \) |
$2.49702$ |
$(-a-1), (-a+2), (-2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$9$ |
\( 1 \) |
$2.066364252$ |
$0.477865477$ |
3.300547924 |
\( \frac{78245696574194732586727}{145} a + \frac{171560137463441783660674}{145} \) |
\( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( -46 a + 19\) , \( 24333 a - 78597\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-46a+19\right){x}+24333a-78597$ |
| 725.1-d1 |
725.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
725.1 |
\( 5^{2} \cdot 29 \) |
\( - 5^{20} \cdot 29^{4} \) |
$2.49702$ |
$(-a-1), (-a+2), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$1.070588185$ |
2.385638820 |
\( -\frac{4773348938382503604562}{5133056640625} a + \frac{15239309827253123221119}{5133056640625} \) |
\( \bigl[a\) , \( 0\) , \( a + 1\) , \( 456 a + 135\) , \( 613309 a + 1354159\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(456a+135\right){x}+613309a+1354159$ |
| 725.1-d2 |
725.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
725.1 |
\( 5^{2} \cdot 29 \) |
\( 5^{10} \cdot 29^{8} \) |
$2.49702$ |
$(-a-1), (-a+2), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$2.141176370$ |
2.385638820 |
\( -\frac{260036963574168}{55256328125} a + \frac{3381366960263641}{55256328125} \) |
\( \bigl[a\) , \( 0\) , \( a + 1\) , \( -3749 a - 8275\) , \( 198696 a + 435787\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-3749a-8275\right){x}+198696a+435787$ |
| 725.1-e1 |
725.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
725.1 |
\( 5^{2} \cdot 29 \) |
\( 5^{4} \cdot 29^{4} \) |
$2.49702$ |
$(-a-1), (-a+2), (-2a+1)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.271508854$ |
$8.098518157$ |
3.266484080 |
\( \frac{1367631}{21025} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 2\) , \( 6\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+2{x}+6$ |
| 725.1-e2 |
725.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
725.1 |
\( 5^{2} \cdot 29 \) |
\( 5^{2} \cdot 29^{2} \) |
$2.49702$ |
$(-a-1), (-a+2), (-2a+1)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.271508854$ |
$32.39407262$ |
3.266484080 |
\( \frac{2146689}{145} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -3\) , \( 2\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-3{x}+2$ |
| 725.1-f1 |
725.1-f |
$2$ |
$3$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
725.1 |
\( 5^{2} \cdot 29 \) |
\( - 5^{6} \cdot 29^{3} \) |
$2.49702$ |
$(-a-1), (-a+2), (-2a+1)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{3} \) |
$0.688788084$ |
$4.300789297$ |
3.300547924 |
\( -\frac{278586546127}{105125} a + \frac{889410502286}{105125} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 1\) , \( 904 a + 1982\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+{x}+904a+1982$ |
| 725.1-f2 |
725.1-f |
$2$ |
$3$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
725.1 |
\( 5^{2} \cdot 29 \) |
\( - 5^{2} \cdot 29 \) |
$2.49702$ |
$(-a-1), (-a+2), (-2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$9$ |
\( 1 \) |
$2.066364252$ |
$0.477865477$ |
3.300547924 |
\( -\frac{78245696574194732586727}{145} a + \frac{249805834037636516247401}{145} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 50 a - 24\) , \( -24361 a - 53898\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(50a-24\right){x}-24361a-53898$ |
| 725.1-g1 |
725.1-g |
$1$ |
$1$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
725.1 |
\( 5^{2} \cdot 29 \) |
\( - 5^{8} \cdot 29 \) |
$2.49702$ |
$(-a-1), (-a+2), (-2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \) |
$1$ |
$6.647831697$ |
3.703414065 |
\( \frac{335860066}{90625} a + \frac{802549051}{90625} \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -10 a - 18\) , \( -19 a - 40\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-10a-18\right){x}-19a-40$ |
*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.
