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 |
25.2-d1 |
25.2-d |
$2$ |
$3$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{10} \) |
$0.97888$ |
$(-a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$7.346204439$ |
1.499537701 |
\( 0 \) |
\( \bigl[0\) , \( -a\) , \( 1\) , \( 2\) , \( -192 a - 470\bigr] \) |
${y}^2+{y}={x}^{3}-a{x}^{2}+2{x}-192a-470$ |
25.2-d2 |
25.2-d |
$2$ |
$3$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{10} \) |
$0.97888$ |
$(-a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$7.346204439$ |
1.499537701 |
\( 0 \) |
\( \bigl[0\) , \( -a\) , \( a + 1\) , \( 2\) , \( a - 5\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}-a{x}^{2}+2{x}+a-5$ |
25.3-d1 |
25.3-d |
$2$ |
$3$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
25.3 |
\( 5^{2} \) |
\( 5^{10} \) |
$0.97888$ |
$(-a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$7.346204439$ |
1.499537701 |
\( 0 \) |
\( \bigl[0\) , \( a\) , \( 1\) , \( 2\) , \( 192 a - 470\bigr] \) |
${y}^2+{y}={x}^{3}+a{x}^{2}+2{x}+192a-470$ |
25.3-d2 |
25.3-d |
$2$ |
$3$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
25.3 |
\( 5^{2} \) |
\( 5^{10} \) |
$0.97888$ |
$(-a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$7.346204439$ |
1.499537701 |
\( 0 \) |
\( \bigl[0\) , \( a\) , \( a + 1\) , \( 2\) , \( -2 a - 5\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+a{x}^{2}+2{x}-2a-5$ |
36.1-a1 |
36.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{6} \) |
$1.07231$ |
$(-a+2), (a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$5.898343969$ |
1.203994421 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( 198 a - 485\bigr] \) |
${y}^2={x}^{3}+198a-485$ |
36.1-a2 |
36.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{6} \) |
$1.07231$ |
$(-a+2), (a+3)$ |
0 |
$\Z/6\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$17.69503190$ |
1.203994421 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( 1\bigr] \) |
${y}^2={x}^{3}+1$ |
81.1-b3 |
81.1-b |
$4$ |
$27$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
81.1 |
\( 3^{4} \) |
\( 3^{6} \) |
$1.31330$ |
$(a+3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3Cs.1.1 |
$1$ |
\( 3 \) |
$0.449858945$ |
$28.08911226$ |
1.719560635 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+{y}={x}^{3}$ |
81.1-b4 |
81.1-b |
$4$ |
$27$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
81.1 |
\( 3^{4} \) |
\( 3^{6} \) |
$1.31330$ |
$(a+3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3Cs.1.1 |
$1$ |
\( 3 \) |
$1.349576835$ |
$9.363037422$ |
1.719560635 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( a + 1\) , \( 0\) , \( 49 a - 123\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+49a-123$ |
100.2-a1 |
100.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
100.2 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{2} \) |
$1.38434$ |
$(-a+2), (-a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$0.199657850$ |
$17.04903024$ |
1.389666049 |
\( 0 \) |
\( \bigl[0\) , \( -a\) , \( a\) , \( 2\) , \( -2\bigr] \) |
${y}^2+a{y}={x}^{3}-a{x}^{2}+2{x}-2$ |
100.2-a2 |
100.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
100.2 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{2} \) |
$1.38434$ |
$(-a+2), (-a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 3 \) |
$0.066552616$ |
$17.04903024$ |
1.389666049 |
\( 0 \) |
\( \bigl[0\) , \( -a\) , \( a\) , \( 2\) , \( -9 a - 23\bigr] \) |
${y}^2+a{y}={x}^{3}-a{x}^{2}+2{x}-9a-23$ |
100.2-b1 |
100.2-b |
$4$ |
$6$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
100.2 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{6} \) |
$1.38434$ |
$(-a+2), (-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1.276191853$ |
$7.913458842$ |
2.061468462 |
\( 0 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 2\) , \( 50 a - 123\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+2{x}+50a-123$ |
100.2-b2 |
100.2-b |
$4$ |
$6$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
100.2 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{6} \) |
$1.38434$ |
$(-a+2), (-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.425397284$ |
$7.913458842$ |
2.061468462 |
\( 0 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 2\) , \( -4 a - 9\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+2{x}-4a-9$ |
100.3-a1 |
100.3-a |
$2$ |
$3$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
100.3 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{2} \) |
$1.38434$ |
$(-a+2), (-a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$0.199657850$ |
$17.04903024$ |
1.389666049 |
\( 0 \) |
\( \bigl[0\) , \( a\) , \( a\) , \( 2\) , \( -2\bigr] \) |
${y}^2+a{y}={x}^{3}+a{x}^{2}+2{x}-2$ |
100.3-a2 |
100.3-a |
$2$ |
$3$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
100.3 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{2} \) |
$1.38434$ |
$(-a+2), (-a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 3 \) |
$0.066552616$ |
$17.04903024$ |
1.389666049 |
\( 0 \) |
\( \bigl[0\) , \( a\) , \( a\) , \( 2\) , \( 9 a - 23\bigr] \) |
${y}^2+a{y}={x}^{3}+a{x}^{2}+2{x}+9a-23$ |
100.3-b1 |
100.3-b |
$4$ |
$6$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
100.3 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{6} \) |
$1.38434$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1.276191853$ |
$7.913458842$ |
2.061468462 |
\( 0 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 2\) , \( -50 a - 123\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+2{x}-50a-123$ |
100.3-b2 |
100.3-b |
$4$ |
$6$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
100.3 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{6} \) |
$1.38434$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.425397284$ |
$7.913458842$ |
2.061468462 |
\( 0 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 2\) , \( 4 a - 9\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+2{x}+4a-9$ |
144.1-c1 |
144.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{6} \) |
$1.51647$ |
$(-a+2), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.489926008$ |
$5.898343969$ |
2.359472722 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( -1\bigr] \) |
${y}^2={x}^{3}-1$ |
144.1-c2 |
144.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{6} \) |
$1.51647$ |
$(-a+2), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.163308669$ |
$17.69503190$ |
2.359472722 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( 198 a + 485\bigr] \) |
${y}^2={x}^{3}+198a+485$ |
225.2-i1 |
225.2-i |
$2$ |
$3$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
225.2 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{6} \cdot 5^{4} \) |
$1.69547$ |
$(a+3), (-a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$5.475537501$ |
1.117689412 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 6 a - 15\bigr] \) |
${y}^2+{y}={x}^{3}+6a-15$ |
225.2-i2 |
225.2-i |
$2$ |
$3$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
225.2 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{6} \cdot 5^{4} \) |
$1.69547$ |
$(a+3), (-a+1)$ |
0 |
$\Z/3\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$16.42661250$ |
1.117689412 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( a + 1\) , \( 0\) , \( 10 a + 24\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+10a+24$ |
225.3-i1 |
225.3-i |
$2$ |
$3$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
225.3 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{6} \cdot 5^{4} \) |
$1.69547$ |
$(a+3), (-a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$5.475537501$ |
1.117689412 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( -6 a - 15\bigr] \) |
${y}^2+{y}={x}^{3}-6a-15$ |
225.3-i2 |
225.3-i |
$2$ |
$3$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
225.3 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{6} \cdot 5^{4} \) |
$1.69547$ |
$(a+3), (-a-1)$ |
0 |
$\Z/3\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$16.42661250$ |
1.117689412 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( a + 1\) , \( 0\) , \( -11 a + 24\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}-11a+24$ |
256.1-c1 |
256.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{8} \) |
$1.75107$ |
$(-a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$2.579744927$ |
$10.21623143$ |
2.689873605 |
\( 0 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 2\) , \( -a - 3\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+2{x}-a-3$ |
256.1-c2 |
256.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{8} \) |
$1.75107$ |
$(-a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$0.859914975$ |
$30.64869430$ |
2.689873605 |
\( 0 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 2\) , \( -a + 3\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+2{x}-a+3$ |
256.1-f1 |
256.1-f |
$4$ |
$6$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{8} \) |
$1.75107$ |
$(-a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$2.579744927$ |
$10.21623143$ |
2.689873605 |
\( 0 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 2\) , \( a - 3\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+2{x}+a-3$ |
256.1-f2 |
256.1-f |
$4$ |
$6$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{8} \) |
$1.75107$ |
$(-a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$0.859914975$ |
$30.64869430$ |
2.689873605 |
\( 0 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 2\) , \( a + 3\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+2{x}+a+3$ |
324.1-a1 |
324.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( 2^{4} \cdot 3^{6} \) |
$1.85729$ |
$(-a+2), (a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$7.431447726$ |
1.516937915 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( a\) , \( 0\) , \( -2\bigr] \) |
${y}^2+a{y}={x}^{3}-2$ |
324.1-a2 |
324.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( 2^{4} \cdot 3^{6} \) |
$1.85729$ |
$(-a+2), (a+3)$ |
0 |
$\Z/3\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$22.29434318$ |
1.516937915 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( a\) , \( 0\) , \( 99 a + 241\bigr] \) |
${y}^2+a{y}={x}^{3}+99a+241$ |
400.2-c1 |
400.2-c |
$2$ |
$3$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
400.2 |
\( 2^{4} \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{2} \) |
$1.95776$ |
$(-a+2), (-a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$17.04903024$ |
3.480118726 |
\( 0 \) |
\( \bigl[0\) , \( a\) , \( a\) , \( 2\) , \( -1\bigr] \) |
${y}^2+a{y}={x}^{3}+a{x}^{2}+2{x}-1$ |
400.2-c2 |
400.2-c |
$2$ |
$3$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
400.2 |
\( 2^{4} \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{2} \) |
$1.95776$ |
$(-a+2), (-a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$17.04903024$ |
3.480118726 |
\( 0 \) |
\( \bigl[0\) , \( a\) , \( a\) , \( 2\) , \( 9 a + 20\bigr] \) |
${y}^2+a{y}={x}^{3}+a{x}^{2}+2{x}+9a+20$ |
400.2-e1 |
400.2-e |
$4$ |
$6$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
400.2 |
\( 2^{4} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{6} \) |
$1.95776$ |
$(-a+2), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$7.913458842$ |
1.615328022 |
\( 0 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 2\) , \( 4 a + 9\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+2{x}+4a+9$ |
400.2-e2 |
400.2-e |
$4$ |
$6$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
400.2 |
\( 2^{4} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{6} \) |
$1.95776$ |
$(-a+2), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$7.913458842$ |
1.615328022 |
\( 0 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 2\) , \( -50 a + 123\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+2{x}-50a+123$ |
400.2-g1 |
400.2-g |
$2$ |
$3$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
400.2 |
\( 2^{4} \cdot 5^{2} \) |
\( 2^{12} \cdot 5^{10} \) |
$1.95776$ |
$(-a+2), (-a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$3.673102219$ |
0.749768850 |
\( 0 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 2\) , \( -1534 a - 3758\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+2{x}-1534a-3758$ |
400.2-g2 |
400.2-g |
$2$ |
$3$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
400.2 |
\( 2^{4} \cdot 5^{2} \) |
\( 2^{12} \cdot 5^{10} \) |
$1.95776$ |
$(-a+2), (-a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$3.673102219$ |
0.749768850 |
\( 0 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 2\) , \( 14 a - 26\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+2{x}+14a-26$ |
400.3-c1 |
400.3-c |
$2$ |
$3$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
400.3 |
\( 2^{4} \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{2} \) |
$1.95776$ |
$(-a+2), (-a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$17.04903024$ |
3.480118726 |
\( 0 \) |
\( \bigl[0\) , \( -a\) , \( a\) , \( 2\) , \( -1\bigr] \) |
${y}^2+a{y}={x}^{3}-a{x}^{2}+2{x}-1$ |
400.3-c2 |
400.3-c |
$2$ |
$3$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
400.3 |
\( 2^{4} \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{2} \) |
$1.95776$ |
$(-a+2), (-a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$17.04903024$ |
3.480118726 |
\( 0 \) |
\( \bigl[0\) , \( -a\) , \( a\) , \( 2\) , \( -9 a + 20\bigr] \) |
${y}^2+a{y}={x}^{3}-a{x}^{2}+2{x}-9a+20$ |
400.3-e1 |
400.3-e |
$4$ |
$6$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
400.3 |
\( 2^{4} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{6} \) |
$1.95776$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$7.913458842$ |
1.615328022 |
\( 0 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 2\) , \( -4 a + 9\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+2{x}-4a+9$ |
400.3-e2 |
400.3-e |
$4$ |
$6$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
400.3 |
\( 2^{4} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{6} \) |
$1.95776$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$7.913458842$ |
1.615328022 |
\( 0 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 2\) , \( 50 a + 123\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+2{x}+50a+123$ |
400.3-g1 |
400.3-g |
$2$ |
$3$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
400.3 |
\( 2^{4} \cdot 5^{2} \) |
\( 2^{12} \cdot 5^{10} \) |
$1.95776$ |
$(-a+2), (-a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$3.673102219$ |
0.749768850 |
\( 0 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 2\) , \( 1534 a - 3758\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+2{x}+1534a-3758$ |
400.3-g2 |
400.3-g |
$2$ |
$3$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
400.3 |
\( 2^{4} \cdot 5^{2} \) |
\( 2^{12} \cdot 5^{10} \) |
$1.95776$ |
$(-a+2), (-a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$3.673102219$ |
0.749768850 |
\( 0 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 2\) , \( -14 a - 26\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+2{x}-14a-26$ |
625.1-a1 |
625.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
625.1 |
\( 5^{4} \) |
\( 5^{10} \) |
$2.18884$ |
$(-a-1), (-a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.269498295$ |
$7.346204439$ |
1.616491420 |
\( 0 \) |
\( \bigl[0\) , \( a\) , \( 1\) , \( 2\) , \( 3 a + 6\bigr] \) |
${y}^2+{y}={x}^{3}+a{x}^{2}+2{x}+3a+6$ |
625.1-a2 |
625.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
625.1 |
\( 5^{4} \) |
\( 5^{10} \) |
$2.18884$ |
$(-a-1), (-a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \cdot 3 \) |
$0.089832765$ |
$7.346204439$ |
1.616491420 |
\( 0 \) |
\( \bigl[0\) , \( a\) , \( a + 1\) , \( 2\) , \( -110 a + 267\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+a{x}^{2}+2{x}-110a+267$ |
625.1-d1 |
625.1-d |
$2$ |
$3$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
625.1 |
\( 5^{4} \) |
\( 5^{10} \) |
$2.18884$ |
$(-a-1), (-a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5$ |
5Ns.2.1 |
$1$ |
\( 1 \) |
$0.891744475$ |
$7.346204439$ |
2.674408923 |
\( 0 \) |
\( \bigl[0\) , \( a\) , \( 1\) , \( 2\) , \( 63 a - 154\bigr] \) |
${y}^2+{y}={x}^{3}+a{x}^{2}+2{x}+63a-154$ |
625.1-d2 |
625.1-d |
$2$ |
$3$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
625.1 |
\( 5^{4} \) |
\( 5^{10} \) |
$2.18884$ |
$(-a-1), (-a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5$ |
5Ns.2.1 |
$1$ |
\( 3 \) |
$0.297248158$ |
$7.346204439$ |
2.674408923 |
\( 0 \) |
\( \bigl[0\) , \( a\) , \( a + 1\) , \( 2\) , \( -5 a - 13\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+a{x}^{2}+2{x}-5a-13$ |
625.1-g1 |
625.1-g |
$2$ |
$3$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
625.1 |
\( 5^{4} \) |
\( 5^{10} \) |
$2.18884$ |
$(-a-1), (-a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5$ |
5Ns.2.1 |
$1$ |
\( 1 \) |
$0.891744475$ |
$7.346204439$ |
2.674408923 |
\( 0 \) |
\( \bigl[0\) , \( -a\) , \( 1\) , \( 2\) , \( -63 a - 154\bigr] \) |
${y}^2+{y}={x}^{3}-a{x}^{2}+2{x}-63a-154$ |
625.1-g2 |
625.1-g |
$2$ |
$3$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
625.1 |
\( 5^{4} \) |
\( 5^{10} \) |
$2.18884$ |
$(-a-1), (-a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5$ |
5Ns.2.1 |
$1$ |
\( 3 \) |
$0.297248158$ |
$7.346204439$ |
2.674408923 |
\( 0 \) |
\( \bigl[0\) , \( -a\) , \( a + 1\) , \( 2\) , \( 4 a - 13\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}-a{x}^{2}+2{x}+4a-13$ |
625.1-i1 |
625.1-i |
$2$ |
$3$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
625.1 |
\( 5^{4} \) |
\( 5^{10} \) |
$2.18884$ |
$(-a-1), (-a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.269498295$ |
$7.346204439$ |
1.616491420 |
\( 0 \) |
\( \bigl[0\) , \( -a\) , \( 1\) , \( 2\) , \( -3 a + 6\bigr] \) |
${y}^2+{y}={x}^{3}-a{x}^{2}+2{x}-3a+6$ |
625.1-i2 |
625.1-i |
$2$ |
$3$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
625.1 |
\( 5^{4} \) |
\( 5^{10} \) |
$2.18884$ |
$(-a-1), (-a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \cdot 3 \) |
$0.089832765$ |
$7.346204439$ |
1.616491420 |
\( 0 \) |
\( \bigl[0\) , \( -a\) , \( a + 1\) , \( 2\) , \( 109 a + 267\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}-a{x}^{2}+2{x}+109a+267$ |
729.1-b1 |
729.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
729.1 |
\( 3^{6} \) |
\( 3^{6} \) |
$2.27471$ |
$(a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$0.781767729$ |
$9.363037422$ |
2.988263384 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( a + 1\) , \( 0\) , \( -a - 3\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}-a-3$ |
729.1-b2 |
729.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
729.1 |
\( 3^{6} \) |
\( 3^{6} \) |
$2.27471$ |
$(a+3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$2.345303189$ |
$28.08911226$ |
2.988263384 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( -5 a + 12\bigr] \) |
${y}^2+{y}={x}^{3}-5a+12$ |
*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.