| 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 |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
175.1 |
\( 5^{2} \cdot 7 \) |
\( 5^{18} \cdot 7^{2} \) |
$0.85990$ |
$(-2a+1), (5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \cdot 3^{2} \) |
$0.040819755$ |
$0.774975202$ |
0.860878149 |
\( -\frac{250523582464}{13671875} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -131\) , \( -650\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}-131{x}-650$ |
| 4375.1-b1 |
4375.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4375.1 |
\( 5^{4} \cdot 7 \) |
\( 5^{30} \cdot 7^{2} \) |
$1.92279$ |
$(-2a+1), (5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B |
$1$ |
\( 2^{3} \) |
$0.833160004$ |
$0.154995040$ |
1.561878237 |
\( -\frac{250523582464}{13671875} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -3283\) , \( -74657\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}-3283{x}-74657$ |
| 11200.1-e1 |
11200.1-e |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
11200.1 |
\( 2^{6} \cdot 5^{2} \cdot 7 \) |
\( 2^{6} \cdot 5^{18} \cdot 7^{2} \) |
$2.43216$ |
$(a), (-2a+1), (5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1.996104087$ |
$0.547990220$ |
3.307477963 |
\( -\frac{250523582464}{13671875} \) |
\( \bigl[0\) , \( -a\) , \( a\) , \( -131 a + 262\) , \( -650 a - 1299\bigr] \) |
${y}^2+a{y}={x}^{3}-a{x}^{2}+\left(-131a+262\right){x}-650a-1299$ |
| 11200.7-e1 |
11200.7-e |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
11200.7 |
\( 2^{6} \cdot 5^{2} \cdot 7 \) |
\( 2^{6} \cdot 5^{18} \cdot 7^{2} \) |
$2.43216$ |
$(-a+1), (-2a+1), (5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1.996104087$ |
$0.547990220$ |
3.307477963 |
\( -\frac{250523582464}{13671875} \) |
\( \bigl[0\) , \( a - 1\) , \( a + 1\) , \( 131 a + 131\) , \( 649 a - 1949\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(131a+131\right){x}+649a-1949$ |
| 14175.1-b1 |
14175.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
14175.1 |
\( 3^{4} \cdot 5^{2} \cdot 7 \) |
\( 3^{12} \cdot 5^{18} \cdot 7^{2} \) |
$2.57969$ |
$(-2a+1), (3), (5)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$4.057165837$ |
$0.258325067$ |
3.169058661 |
\( -\frac{250523582464}{13671875} \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -1182\) , \( 16362\bigr] \) |
${y}^2+{y}={x}^{3}-1182{x}+16362$ |
| 19600.1-c1 |
19600.1-c |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
19600.1 |
\( 2^{4} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{12} \cdot 5^{18} \cdot 7^{8} \) |
$2.79738$ |
$(a), (-2a+1), (5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B |
$1$ |
\( 2 \) |
$6.395326012$ |
$0.146456546$ |
2.832125182 |
\( -\frac{250523582464}{13671875} \) |
\( \bigl[0\) , \( 1\) , \( a\) , \( -2758 a + 1839\) , \( 37259 a - 92712\bigr] \) |
${y}^2+a{y}={x}^{3}+{x}^{2}+\left(-2758a+1839\right){x}+37259a-92712$ |
| 19600.5-c1 |
19600.5-c |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
19600.5 |
\( 2^{4} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{12} \cdot 5^{18} \cdot 7^{8} \) |
$2.79738$ |
$(-a+1), (-2a+1), (5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B |
$1$ |
\( 2 \) |
$6.395326012$ |
$0.146456546$ |
2.832125182 |
\( -\frac{250523582464}{13671875} \) |
\( \bigl[0\) , \( 1\) , \( a + 1\) , \( 2758 a - 919\) , \( -37260 a - 55453\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(2758a-919\right){x}-37260a-55453$ |
| 44800.5-b1 |
44800.5-b |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
44800.5 |
\( 2^{8} \cdot 5^{2} \cdot 7 \) |
\( 2^{24} \cdot 5^{18} \cdot 7^{2} \) |
$3.43959$ |
$(a), (-a+1), (-2a+1), (5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$0.193743800$ |
2.636217845 |
\( -\frac{250523582464}{13671875} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -2101\) , \( 39485\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-2101{x}+39485$ |
*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.
