| 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-a3 |
175.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
175.1 |
\( 5^{2} \cdot 7 \) |
\( 5^{6} \cdot 7^{6} \) |
$0.85990$ |
$(-2a+1), (5)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$0.122459267$ |
$2.324925606$ |
0.860878149 |
\( \frac{71991296}{42875} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( 9\) , \( 1\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}+9{x}+1$ |
| 4375.1-b3 |
4375.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4375.1 |
\( 5^{4} \cdot 7 \) |
\( 5^{18} \cdot 7^{6} \) |
$1.92279$ |
$(-2a+1), (5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3Cs |
$1$ |
\( 2^{3} \) |
$0.277720001$ |
$0.464985121$ |
1.561878237 |
\( \frac{71991296}{42875} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( 217\) , \( -282\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}+217{x}-282$ |
| 11200.1-e3 |
11200.1-e |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
11200.1 |
\( 2^{6} \cdot 5^{2} \cdot 7 \) |
\( 2^{6} \cdot 5^{6} \cdot 7^{6} \) |
$2.43216$ |
$(a), (-2a+1), (5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3Cs |
$1$ |
\( 2 \) |
$0.665368029$ |
$1.643970662$ |
3.307477963 |
\( \frac{71991296}{42875} \) |
\( \bigl[0\) , \( -a\) , \( a\) , \( 9 a - 18\) , \( a + 3\bigr] \) |
${y}^2+a{y}={x}^{3}-a{x}^{2}+\left(9a-18\right){x}+a+3$ |
| 11200.7-e3 |
11200.7-e |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
11200.7 |
\( 2^{6} \cdot 5^{2} \cdot 7 \) |
\( 2^{6} \cdot 5^{6} \cdot 7^{6} \) |
$2.43216$ |
$(-a+1), (-2a+1), (5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3Cs |
$1$ |
\( 2 \) |
$0.665368029$ |
$1.643970662$ |
3.307477963 |
\( \frac{71991296}{42875} \) |
\( \bigl[0\) , \( a - 1\) , \( a + 1\) , \( -9 a - 9\) , \( -2 a + 4\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-9a-9\right){x}-2a+4$ |
| 14175.1-b3 |
14175.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
14175.1 |
\( 3^{4} \cdot 5^{2} \cdot 7 \) |
\( 3^{12} \cdot 5^{6} \cdot 7^{6} \) |
$2.57969$ |
$(-2a+1), (3), (5)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1.352388612$ |
$0.774975202$ |
3.169058661 |
\( \frac{71991296}{42875} \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 78\) , \( 45\bigr] \) |
${y}^2+{y}={x}^{3}+78{x}+45$ |
| 19600.1-c3 |
19600.1-c |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
19600.1 |
\( 2^{4} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{12} \cdot 5^{6} \cdot 7^{12} \) |
$2.79738$ |
$(a), (-2a+1), (5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3Cs |
$1$ |
\( 2 \) |
$2.131775337$ |
$0.439369640$ |
2.832125182 |
\( \frac{71991296}{42875} \) |
\( \bigl[0\) , \( 1\) , \( a\) , \( 182 a - 121\) , \( 166 a - 298\bigr] \) |
${y}^2+a{y}={x}^{3}+{x}^{2}+\left(182a-121\right){x}+166a-298$ |
| 19600.5-c3 |
19600.5-c |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
19600.5 |
\( 2^{4} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{12} \cdot 5^{6} \cdot 7^{12} \) |
$2.79738$ |
$(-a+1), (-2a+1), (5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3Cs |
$1$ |
\( 2 \) |
$2.131775337$ |
$0.439369640$ |
2.832125182 |
\( \frac{71991296}{42875} \) |
\( \bigl[0\) , \( 1\) , \( a + 1\) , \( -182 a + 61\) , \( -167 a - 132\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-182a+61\right){x}-167a-132$ |
| 44800.5-b3 |
44800.5-b |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
44800.5 |
\( 2^{8} \cdot 5^{2} \cdot 7 \) |
\( 2^{24} \cdot 5^{6} \cdot 7^{6} \) |
$3.43959$ |
$(a), (-a+1), (-2a+1), (5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3Cs |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$0.581231401$ |
2.636217845 |
\( \frac{71991296}{42875} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 139\) , \( 61\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+139{x}+61$ |
*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.
