| 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 |
| 175.1-a1 |
175.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
175.1 |
\( 5^{2} \cdot 7 \) |
\( 5^{2} \cdot 7^{8} \) |
$1.71980$ |
$(a), (5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$1.083405971$ |
0.409488967 |
\( \frac{414670848}{1715} a - \frac{8020135936}{12005} \) |
\( \bigl[0\) , \( -a\) , \( 1\) , \( 62 a - 164\) , \( 492 a - 1302\bigr] \) |
${y}^2+{y}={x}^{3}-a{x}^{2}+\left(62a-164\right){x}+492a-1302$ |
| 175.1-b1 |
175.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
175.1 |
\( 5^{2} \cdot 7 \) |
\( 5^{8} \cdot 7^{2} \) |
$1.71980$ |
$(a), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.997738387$ |
$4.288775605$ |
3.238343538 |
\( -\frac{191840064}{4375} a - \frac{509066839}{4375} \) |
\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( -26 a - 64\) , \( -96 a - 253\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-26a-64\right){x}-96a-253$ |
| 175.1-b2 |
175.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
175.1 |
\( 5^{2} \cdot 7 \) |
\( 5^{4} \cdot 7^{4} \) |
$1.71980$ |
$(a), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.998869193$ |
$4.288775605$ |
3.238343538 |
\( \frac{12580331521029}{1225} a + \frac{33285407658056}{1225} \) |
\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( -401 a - 1064\) , \( -6871 a - 18178\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-401a-1064\right){x}-6871a-18178$ |
| 175.1-c1 |
175.1-c |
$1$ |
$1$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
175.1 |
\( 5^{2} \cdot 7 \) |
\( 5^{2} \cdot 7^{8} \) |
$1.71980$ |
$(a), (5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{3} \) |
$0.028394727$ |
$15.89055595$ |
1.364324749 |
\( \frac{414670848}{1715} a - \frac{8020135936}{12005} \) |
\( \bigl[0\) , \( a\) , \( a\) , \( 62 a - 164\) , \( -492 a + 1300\bigr] \) |
${y}^2+a{y}={x}^{3}+a{x}^{2}+\left(62a-164\right){x}-492a+1300$ |
| 175.1-d1 |
175.1-d |
$1$ |
$1$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
175.1 |
\( 5^{2} \cdot 7 \) |
\( 5^{2} \cdot 7^{4} \) |
$1.71980$ |
$(a), (5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$0.041084180$ |
$16.80631910$ |
1.043898337 |
\( \frac{8192}{35} a + \frac{139264}{245} \) |
\( \bigl[0\) , \( -a + 1\) , \( a\) , \( a + 7\) , \( 0\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(a+7\right){x}$ |
| 175.1-e1 |
175.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
175.1 |
\( 5^{2} \cdot 7 \) |
\( 5^{8} \cdot 7^{2} \) |
$1.71980$ |
$(a), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$7.800504445$ |
1.474156775 |
\( -\frac{191840064}{4375} a - \frac{509066839}{4375} \) |
\( \bigl[1\) , \( a - 1\) , \( a\) , \( -26 a - 64\) , \( 96 a + 251\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-26a-64\right){x}+96a+251$ |
| 175.1-e2 |
175.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
175.1 |
\( 5^{2} \cdot 7 \) |
\( 5^{4} \cdot 7^{4} \) |
$1.71980$ |
$(a), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$7.800504445$ |
1.474156775 |
\( \frac{12580331521029}{1225} a + \frac{33285407658056}{1225} \) |
\( \bigl[1\) , \( a - 1\) , \( a\) , \( -401 a - 1064\) , \( 6871 a + 18176\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-401a-1064\right){x}+6871a+18176$ |
| 175.1-f1 |
175.1-f |
$1$ |
$1$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
175.1 |
\( 5^{2} \cdot 7 \) |
\( 5^{2} \cdot 7^{4} \) |
$1.71980$ |
$(a), (5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$7.341413625$ |
2.774793532 |
\( \frac{8192}{35} a + \frac{139264}{245} \) |
\( \bigl[0\) , \( a - 1\) , \( 1\) , \( a + 7\) , \( -2\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(a+7\right){x}-2$ |
| 175.1-g1 |
175.1-g |
$2$ |
$2$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
175.1 |
\( 5^{2} \cdot 7 \) |
\( 5^{8} \cdot 7^{2} \) |
$1.71980$ |
$(a), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$7.800504445$ |
1.474156775 |
\( \frac{191840064}{4375} a - \frac{509066839}{4375} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 25 a - 64\) , \( -96 a + 251\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(25a-64\right){x}-96a+251$ |
| 175.1-g2 |
175.1-g |
$2$ |
$2$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
175.1 |
\( 5^{2} \cdot 7 \) |
\( 5^{4} \cdot 7^{4} \) |
$1.71980$ |
$(a), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$7.800504445$ |
1.474156775 |
\( -\frac{12580331521029}{1225} a + \frac{33285407658056}{1225} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 400 a - 1064\) , \( -6871 a + 18176\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(400a-1064\right){x}-6871a+18176$ |
| 175.1-h1 |
175.1-h |
$1$ |
$1$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
175.1 |
\( 5^{2} \cdot 7 \) |
\( 5^{2} \cdot 7^{4} \) |
$1.71980$ |
$(a), (5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$7.341413625$ |
2.774793532 |
\( -\frac{8192}{35} a + \frac{139264}{245} \) |
\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( -a + 7\) , \( -2\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-a+7\right){x}-2$ |
| 175.1-i1 |
175.1-i |
$3$ |
$9$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
175.1 |
\( 5^{2} \cdot 7 \) |
\( 5^{18} \cdot 7^{2} \) |
$1.71980$ |
$(a), (5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$0.494084210$ |
1.680716502 |
\( -\frac{250523582464}{13671875} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -131\) , \( -650\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}-131{x}-650$ |
| 175.1-i2 |
175.1-i |
$3$ |
$9$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
175.1 |
\( 5^{2} \cdot 7 \) |
\( 5^{2} \cdot 7^{2} \) |
$1.71980$ |
$(a), (5)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$40.02082101$ |
1.680716502 |
\( -\frac{262144}{35} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -1\) , \( 0\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}-{x}$ |
| 175.1-i3 |
175.1-i |
$3$ |
$9$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
175.1 |
\( 5^{2} \cdot 7 \) |
\( 5^{6} \cdot 7^{6} \) |
$1.71980$ |
$(a), (5)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$4.446757890$ |
1.680716502 |
\( \frac{71991296}{42875} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( 9\) , \( 1\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}+9{x}+1$ |
| 175.1-j1 |
175.1-j |
$3$ |
$9$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
175.1 |
\( 5^{2} \cdot 7 \) |
\( 5^{18} \cdot 7^{2} \) |
$1.71980$ |
$(a), (5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3^{2} \) |
$0.040819755$ |
$4.862220259$ |
1.350294553 |
\( -\frac{250523582464}{13671875} \) |
\( \bigl[0\) , \( -1\) , \( a\) , \( -131\) , \( 648\bigr] \) |
${y}^2+a{y}={x}^{3}-{x}^{2}-131{x}+648$ |
| 175.1-j2 |
175.1-j |
$3$ |
$9$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
175.1 |
\( 5^{2} \cdot 7 \) |
\( 5^{2} \cdot 7^{2} \) |
$1.71980$ |
$(a), (5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \) |
$0.367377802$ |
$4.862220259$ |
1.350294553 |
\( -\frac{262144}{35} \) |
\( \bigl[0\) , \( -1\) , \( a\) , \( -1\) , \( -2\bigr] \) |
${y}^2+a{y}={x}^{3}-{x}^{2}-{x}-2$ |
| 175.1-j3 |
175.1-j |
$3$ |
$9$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
175.1 |
\( 5^{2} \cdot 7 \) |
\( 5^{6} \cdot 7^{6} \) |
$1.71980$ |
$(a), (5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs |
$1$ |
\( 2 \cdot 3 \) |
$0.122459267$ |
$4.862220259$ |
1.350294553 |
\( \frac{71991296}{42875} \) |
\( \bigl[0\) , \( -1\) , \( a\) , \( 9\) , \( -3\bigr] \) |
${y}^2+a{y}={x}^{3}-{x}^{2}+9{x}-3$ |
| 175.1-k1 |
175.1-k |
$1$ |
$1$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
175.1 |
\( 5^{2} \cdot 7 \) |
\( 5^{2} \cdot 7^{8} \) |
$1.71980$ |
$(a), (5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{3} \) |
$0.028394727$ |
$15.89055595$ |
1.364324749 |
\( -\frac{414670848}{1715} a - \frac{8020135936}{12005} \) |
\( \bigl[0\) , \( -a\) , \( a\) , \( -62 a - 164\) , \( 492 a + 1300\bigr] \) |
${y}^2+a{y}={x}^{3}-a{x}^{2}+\left(-62a-164\right){x}+492a+1300$ |
| 175.1-l1 |
175.1-l |
$2$ |
$2$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
175.1 |
\( 5^{2} \cdot 7 \) |
\( 5^{8} \cdot 7^{2} \) |
$1.71980$ |
$(a), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.997738387$ |
$4.288775605$ |
3.238343538 |
\( \frac{191840064}{4375} a - \frac{509066839}{4375} \) |
\( \bigl[a\) , \( a - 1\) , \( 1\) , \( 25 a - 64\) , \( 96 a - 253\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(25a-64\right){x}+96a-253$ |
| 175.1-l2 |
175.1-l |
$2$ |
$2$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
175.1 |
\( 5^{2} \cdot 7 \) |
\( 5^{4} \cdot 7^{4} \) |
$1.71980$ |
$(a), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.998869193$ |
$4.288775605$ |
3.238343538 |
\( -\frac{12580331521029}{1225} a + \frac{33285407658056}{1225} \) |
\( \bigl[a\) , \( a - 1\) , \( 1\) , \( 400 a - 1064\) , \( 6871 a - 18178\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(400a-1064\right){x}+6871a-18178$ |
| 175.1-m1 |
175.1-m |
$1$ |
$1$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
175.1 |
\( 5^{2} \cdot 7 \) |
\( 5^{2} \cdot 7^{4} \) |
$1.71980$ |
$(a), (5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$0.041084180$ |
$16.80631910$ |
1.043898337 |
\( -\frac{8192}{35} a + \frac{139264}{245} \) |
\( \bigl[0\) , \( a + 1\) , \( a\) , \( -a + 7\) , \( 0\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-a+7\right){x}$ |
| 175.1-n1 |
175.1-n |
$1$ |
$1$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
175.1 |
\( 5^{2} \cdot 7 \) |
\( 5^{2} \cdot 7^{8} \) |
$1.71980$ |
$(a), (5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$1.083405971$ |
0.409488967 |
\( -\frac{414670848}{1715} a - \frac{8020135936}{12005} \) |
\( \bigl[0\) , \( a\) , \( 1\) , \( -62 a - 164\) , \( -492 a - 1302\bigr] \) |
${y}^2+{y}={x}^{3}+a{x}^{2}+\left(-62a-164\right){x}-492a-1302$ |
*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.
