| 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-a1 |
1.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$0.43777$ |
$\textsf{none}$ |
0 |
$\Z/6\Z$ |
$\textsf{potential}$ |
$-8$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
$3$ |
3Cs.1.1 |
$1$ |
\( 1 \) |
$1$ |
$50.75994773$ |
0.287814748 |
\( 8000 \) |
\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( -3 a - 1\) , \( -2 a - 1\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-3a-1\right){x}-2a-1$ |
| 1.1-a2 |
1.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$0.43777$ |
$\textsf{none}$ |
0 |
$\Z/6\Z$ |
$\textsf{potential}$ |
$-8$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
$3$ |
3Cs.1.1 |
$1$ |
\( 1 \) |
$1$ |
$50.75994773$ |
0.287814748 |
\( 8000 \) |
\( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( 2 a - 1\) , \( a - 1\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(2a-1\right){x}+a-1$ |
| 16.1-a1 |
16.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$0.87554$ |
$(-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-8$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3$ |
3Cs |
$1$ |
\( 1 \) |
$1$ |
$25.37997386$ |
1.295166367 |
\( 8000 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 4 a - 6\) , \( 6 a - 16\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(4a-6\right){x}+6a-16$ |
| 16.1-a2 |
16.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$0.87554$ |
$(-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-8$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3$ |
3Cs |
$1$ |
\( 1 \) |
$1$ |
$25.37997386$ |
1.295166367 |
\( 8000 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -4 a - 6\) , \( -6 a - 16\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-4a-6\right){x}-6a-16$ |
| 225.2-e1 |
225.2-e |
$6$ |
$18$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
225.2 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{6} \cdot 5^{6} \) |
$1.69547$ |
$(a+3), (-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-8$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3$ |
3Cs |
$1$ |
\( 2^{2} \) |
$0.597533156$ |
$9.267456131$ |
2.260720761 |
\( 8000 \) |
\( \bigl[a\) , \( -a\) , \( 1\) , \( -54 a - 126\) , \( -271 a - 662\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-54a-126\right){x}-271a-662$ |
| 225.2-e2 |
225.2-e |
$6$ |
$18$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
225.2 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{6} \cdot 5^{6} \) |
$1.69547$ |
$(a+3), (-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-8$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3$ |
3Cs |
$1$ |
\( 2^{2} \) |
$0.298766578$ |
$18.53491226$ |
2.260720761 |
\( 8000 \) |
\( \bigl[a\) , \( -a\) , \( 1\) , \( a - 6\) , \( 2\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(a-6\right){x}+2$ |
| 225.3-e1 |
225.3-e |
$6$ |
$18$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
225.3 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{6} \cdot 5^{6} \) |
$1.69547$ |
$(a+3), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-8$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3$ |
3Cs |
$1$ |
\( 2^{2} \) |
$0.597533156$ |
$9.267456131$ |
2.260720761 |
\( 8000 \) |
\( \bigl[a\) , \( a\) , \( 1\) , \( 53 a - 126\) , \( 271 a - 662\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(53a-126\right){x}+271a-662$ |
| 225.3-e2 |
225.3-e |
$6$ |
$18$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
225.3 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{6} \cdot 5^{6} \) |
$1.69547$ |
$(a+3), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-8$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3$ |
3Cs |
$1$ |
\( 2^{2} \) |
$0.298766578$ |
$18.53491226$ |
2.260720761 |
\( 8000 \) |
\( \bigl[a\) , \( a\) , \( 1\) , \( -2 a - 6\) , \( 2\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-2a-6\right){x}+2$ |
| 529.2-e1 |
529.2-e |
$6$ |
$18$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
529.2 |
\( 23^{2} \) |
\( 23^{6} \) |
$2.09946$ |
$(-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-8$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3$ |
3Cs |
$1$ |
\( 2^{2} \) |
$1.252155738$ |
$7.484145988$ |
3.825823879 |
\( 8000 \) |
\( \bigl[a\) , \( -1\) , \( a + 1\) , \( -13 a - 35\) , \( -37 a - 92\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-13a-35\right){x}-37a-92$ |
| 529.2-e2 |
529.2-e |
$6$ |
$18$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
529.2 |
\( 23^{2} \) |
\( 23^{6} \) |
$2.09946$ |
$(-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-8$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3$ |
3Cs |
$1$ |
\( 2^{2} \) |
$0.626077869$ |
$14.96829197$ |
3.825823879 |
\( 8000 \) |
\( \bigl[a\) , \( a - 1\) , \( a + 1\) , \( 29 a - 73\) , \( -139 a + 338\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(29a-73\right){x}-139a+338$ |
| 529.3-e1 |
529.3-e |
$6$ |
$18$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
529.3 |
\( 23^{2} \) |
\( 23^{6} \) |
$2.09946$ |
$(2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-8$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3$ |
3Cs |
$1$ |
\( 2^{2} \) |
$0.626077869$ |
$14.96829197$ |
3.825823879 |
\( 8000 \) |
\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( -30 a - 73\) , \( 138 a + 338\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-30a-73\right){x}+138a+338$ |
| 529.3-e2 |
529.3-e |
$6$ |
$18$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
529.3 |
\( 23^{2} \) |
\( 23^{6} \) |
$2.09946$ |
$(2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-8$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3$ |
3Cs |
$1$ |
\( 2^{2} \) |
$1.252155738$ |
$7.484145988$ |
3.825823879 |
\( 8000 \) |
\( \bigl[a\) , \( -1\) , \( a + 1\) , \( 12 a - 35\) , \( 36 a - 92\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(12a-35\right){x}+36a-92$ |
| 625.1-b1 |
625.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
625.1 |
\( 5^{4} \) |
\( 5^{12} \) |
$2.18884$ |
$(-a-1), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-8$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3$ |
3Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$10.15198954$ |
2.072266188 |
\( 8000 \) |
\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( 20 a - 53\) , \( 93 a - 230\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(20a-53\right){x}+93a-230$ |
| 625.1-b2 |
625.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
625.1 |
\( 5^{4} \) |
\( 5^{12} \) |
$2.18884$ |
$(-a-1), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-8$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3$ |
3Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$10.15198954$ |
2.072266188 |
\( 8000 \) |
\( \bigl[a\) , \( a - 1\) , \( a + 1\) , \( -21 a - 53\) , \( -94 a - 230\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-21a-53\right){x}-94a-230$ |
*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.
