| 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 |
| 2.1-a1 |
2.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{46}) \) |
$2$ |
$[2, 0]$ |
2.1 |
\( 2 \) |
\( 2^{5} \) |
$1.44147$ |
$(-23a+156)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$23.18869278$ |
1.709493112 |
\( \frac{497681}{8} a - \frac{844747}{2} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( 2082 a - 14114\) , \( -129362 a + 877358\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(2082a-14114\right){x}-129362a+877358$ |
| 2.1-b1 |
2.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{46}) \) |
$2$ |
$[2, 0]$ |
2.1 |
\( 2 \) |
\( 2^{5} \) |
$1.44147$ |
$(-23a+156)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$11.76067635$ |
0.867008564 |
\( -\frac{497681}{8} a - \frac{844747}{2} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( 6140 a - 41622\) , \( -1519636 a + 10306692\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(6140a-41622\right){x}-1519636a+10306692$ |
| 2.1-c1 |
2.1-c |
$1$ |
$1$ |
\(\Q(\sqrt{46}) \) |
$2$ |
$[2, 0]$ |
2.1 |
\( 2 \) |
\( 2^{5} \) |
$1.44147$ |
$(-23a+156)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$23.18869278$ |
1.709493112 |
\( -\frac{497681}{8} a - \frac{844747}{2} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( -2083 a - 14114\) , \( 129362 a + 877358\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-2083a-14114\right){x}+129362a+877358$ |
| 2.1-d1 |
2.1-d |
$1$ |
$1$ |
\(\Q(\sqrt{46}) \) |
$2$ |
$[2, 0]$ |
2.1 |
\( 2 \) |
\( 2^{5} \) |
$1.44147$ |
$(-23a+156)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$11.76067635$ |
0.867008564 |
\( \frac{497681}{8} a - \frac{844747}{2} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -6140 a - 41622\) , \( 1519636 a + 10306692\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-6140a-41622\right){x}+1519636a+10306692$ |
| 4.1-a1 |
4.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{46}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{8} \) |
$1.71420$ |
$(-23a+156)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 3 \) |
$0.108426512$ |
$35.16072020$ |
1.686302914 |
\( 165376 a - 1121536 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 32868472 a - 222924812\) , \( -267317636924 a + 1813036423935\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(32868472a-222924812\right){x}-267317636924a+1813036423935$ |
| 4.1-b1 |
4.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{46}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{8} \) |
$1.71420$ |
$(-23a+156)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 3 \) |
$0.991227685$ |
$5.069265675$ |
2.222597468 |
\( -165376 a - 1121536 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 20\) , \( -17\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+20{x}-17$ |
| 4.1-c1 |
4.1-c |
$1$ |
$1$ |
\(\Q(\sqrt{46}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{8} \) |
$1.71420$ |
$(-23a+156)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 3 \) |
$0.991227685$ |
$5.069265675$ |
2.222597468 |
\( 165376 a - 1121536 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 20\) , \( -17\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+20{x}-17$ |
| 4.1-d1 |
4.1-d |
$1$ |
$1$ |
\(\Q(\sqrt{46}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{8} \) |
$1.71420$ |
$(-23a+156)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 3 \) |
$0.108426512$ |
$35.16072020$ |
1.686302914 |
\( -165376 a - 1121536 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -32868472 a - 222924812\) , \( 267317636924 a + 1813036423935\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-32868472a-222924812\right){x}+267317636924a+1813036423935$ |
| 6.1-a1 |
6.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{46}) \) |
$2$ |
$[2, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{8} \cdot 3^{6} \) |
$1.89708$ |
$(-23a+156), (a-7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$2.855685675$ |
$2.174972395$ |
2.747302561 |
\( -\frac{3535318439}{5832} a - \frac{47959064233}{11664} \) |
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 186 a - 1189\) , \( 9426 a - 63802\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(186a-1189\right){x}+9426a-63802$ |
| 6.1-a2 |
6.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{46}) \) |
$2$ |
$[2, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{4} \cdot 3^{3} \) |
$1.89708$ |
$(-23a+156), (a-7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$5.711371350$ |
$2.174972395$ |
2.747302561 |
\( \frac{538476234670117}{108} a + \frac{3652123591000837}{108} \) |
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 4046 a - 27369\) , \( 375214 a - 2544698\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(4046a-27369\right){x}+375214a-2544698$ |
| 6.1-b1 |
6.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{46}) \) |
$2$ |
$[2, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{8} \cdot 3^{6} \) |
$1.89708$ |
$(-23a+156), (a-7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.231145592$ |
$23.69682198$ |
2.422802775 |
\( -\frac{3535318439}{5832} a - \frac{47959064233}{11664} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -2401233 a - 16285948\) , \( 5263220671 a + 35696899378\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-2401233a-16285948\right){x}+5263220671a+35696899378$ |
| 6.1-b2 |
6.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{46}) \) |
$2$ |
$[2, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{4} \cdot 3^{3} \) |
$1.89708$ |
$(-23a+156), (a-7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.462291185$ |
$23.69682198$ |
2.422802775 |
\( \frac{538476234670117}{108} a + \frac{3652123591000837}{108} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -38420893 a - 260583168\) , \( 337407147143 a + 2288406610602\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-38420893a-260583168\right){x}+337407147143a+2288406610602$ |
| 6.2-a1 |
6.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{46}) \) |
$2$ |
$[2, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( 2^{8} \cdot 3^{6} \) |
$1.89708$ |
$(-23a+156), (a+7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$2.855685675$ |
$2.174972395$ |
2.747302561 |
\( \frac{3535318439}{5832} a - \frac{47959064233}{11664} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -187 a - 1189\) , \( -9426 a - 63802\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-187a-1189\right){x}-9426a-63802$ |
| 6.2-a2 |
6.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{46}) \) |
$2$ |
$[2, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( 2^{4} \cdot 3^{3} \) |
$1.89708$ |
$(-23a+156), (a+7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$5.711371350$ |
$2.174972395$ |
2.747302561 |
\( -\frac{538476234670117}{108} a + \frac{3652123591000837}{108} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -4047 a - 27369\) , \( -375214 a - 2544698\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-4047a-27369\right){x}-375214a-2544698$ |
| 6.2-b1 |
6.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{46}) \) |
$2$ |
$[2, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( 2^{8} \cdot 3^{6} \) |
$1.89708$ |
$(-23a+156), (a+7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.231145592$ |
$23.69682198$ |
2.422802775 |
\( \frac{3535318439}{5832} a - \frac{47959064233}{11664} \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 2401231 a - 16285948\) , \( -5263220672 a + 35696899378\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(2401231a-16285948\right){x}-5263220672a+35696899378$ |
| 6.2-b2 |
6.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{46}) \) |
$2$ |
$[2, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( 2^{4} \cdot 3^{3} \) |
$1.89708$ |
$(-23a+156), (a+7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.462291185$ |
$23.69682198$ |
2.422802775 |
\( -\frac{538476234670117}{108} a + \frac{3652123591000837}{108} \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 38420891 a - 260583168\) , \( -337407147144 a + 2288406610602\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(38420891a-260583168\right){x}-337407147144a+2288406610602$ |
| 8.1-a1 |
8.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{46}) \) |
$2$ |
$[2, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{8} \) |
$2.03854$ |
$(-23a+156)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.809972776$ |
$17.55912210$ |
4.193960162 |
\( 256 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -1196 a + 8112\) , \( -140998 a + 956295\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-1196a+8112\right){x}-140998a+956295$ |
| 8.1-b1 |
8.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{46}) \) |
$2$ |
$[2, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{8} \) |
$2.03854$ |
$(-23a+156)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.809972776$ |
$17.55912210$ |
4.193960162 |
\( 256 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 1196 a + 8112\) , \( 140998 a + 956295\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(1196a+8112\right){x}+140998a+956295$ |
| 9.1-a1 |
9.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{46}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{8} \) |
$2.09946$ |
$(a+7), (a-7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$11.01298155$ |
3.247551087 |
\( -\frac{2924207}{81} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( -10679 a - 72448\) , \( 1529184 a + 10371419\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-10679a-72448\right){x}+1529184a+10371419$ |
| 9.1-a2 |
9.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{46}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{4} \) |
$2.09946$ |
$(a+7), (a-7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$11.01298155$ |
3.247551087 |
\( \frac{12214672127}{9} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( -172139 a - 1167523\) , \( 100052859 a + 678591494\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-172139a-1167523\right){x}+100052859a+678591494$ |
| 9.1-b1 |
9.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{46}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{8} \) |
$2.09946$ |
$(a+7), (a-7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$11.01298155$ |
3.247551087 |
\( -\frac{2924207}{81} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 10700 a - 72425\) , \( -1601632 a + 10863136\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(10700a-72425\right){x}-1601632a+10863136$ |
| 9.1-b2 |
9.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{46}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{4} \) |
$2.09946$ |
$(a+7), (a-7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$11.01298155$ |
3.247551087 |
\( \frac{12214672127}{9} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 172160 a - 1167500\) , \( -101220382 a + 686510371\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(172160a-1167500\right){x}-101220382a+686510371$ |
| 9.2-a1 |
9.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{46}) \) |
$2$ |
$[2, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{6} \) |
$2.09946$ |
$(a+7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-8$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$2.504311477$ |
$20.72266188$ |
3.825823879 |
\( 8000 \) |
\( \bigl[a\) , \( a\) , \( a + 1\) , \( -283972 a - 1926004\) , \( -191681032 a - 1300044015\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-283972a-1926004\right){x}-191681032a-1300044015$ |
| 9.2-a2 |
9.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{46}) \) |
$2$ |
$[2, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{6} \) |
$2.09946$ |
$(a+7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-8$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1.252155738$ |
$41.44532377$ |
3.825823879 |
\( 8000 \) |
\( \bigl[a\) , \( a\) , \( a + 1\) , \( 78 a - 444\) , \( -621 a + 4423\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(78a-444\right){x}-621a+4423$ |
| 9.3-a1 |
9.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{46}) \) |
$2$ |
$[2, 0]$ |
9.3 |
\( 3^{2} \) |
\( 3^{6} \) |
$2.09946$ |
$(a-7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-8$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$2.504311477$ |
$20.72266188$ |
3.825823879 |
\( 8000 \) |
\( \bigl[a\) , \( -a\) , \( a + 1\) , \( 283971 a - 1926004\) , \( 191681031 a - 1300044015\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(283971a-1926004\right){x}+191681031a-1300044015$ |
| 9.3-a2 |
9.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{46}) \) |
$2$ |
$[2, 0]$ |
9.3 |
\( 3^{2} \) |
\( 3^{6} \) |
$2.09946$ |
$(a-7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-8$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1.252155738$ |
$41.44532377$ |
3.825823879 |
\( 8000 \) |
\( \bigl[a\) , \( -a\) , \( a + 1\) , \( -79 a - 444\) , \( 620 a + 4423\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-79a-444\right){x}+620a+4423$ |
| 10.1-a1 |
10.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{46}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2 \cdot 5^{3} \) |
$2.15550$ |
$(-23a+156), (9a+61)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \) |
$0.298859460$ |
$19.55351800$ |
2.584843496 |
\( -\frac{59899811}{250} a + \frac{201658777}{125} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( 85 a - 555\) , \( 941 a - 6363\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(85a-555\right){x}+941a-6363$ |
| 10.1-b1 |
10.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{46}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{9} \cdot 5^{12} \) |
$2.15550$ |
$(-23a+156), (9a+61)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 2 \) |
$1$ |
$5.798023056$ |
0.854871861 |
\( -\frac{13777032407}{7812500000} a - \frac{3369992913}{1953125000} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -508516327 a - 3448925531\) , \( 183383033227434 a + 1243764244654883\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(-508516327a-3448925531\right){x}+183383033227434a+1243764244654883$ |
| 10.1-c1 |
10.1-c |
$1$ |
$1$ |
\(\Q(\sqrt{46}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{13} \cdot 5^{6} \) |
$2.15550$ |
$(-23a+156), (9a+61)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$5.046478788$ |
0.744062704 |
\( -\frac{3776907459758737}{2000000} a - \frac{800507282019751}{62500} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( 1194937761 a - 8104462185\) , \( 202073642980310 a - 1370530127584686\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(1194937761a-8104462185\right){x}+202073642980310a-1370530127584686$ |
| 10.1-d1 |
10.1-d |
$1$ |
$1$ |
\(\Q(\sqrt{46}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{13} \cdot 5^{6} \) |
$2.15550$ |
$(-23a+156), (9a+61)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \cdot 3 \) |
$2.527378401$ |
$1.362540458$ |
3.046435665 |
\( -\frac{3776907459758737}{2000000} a - \frac{800507282019751}{62500} \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -42 a - 232\) , \( -439 a - 2868\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-42a-232\right){x}-439a-2868$ |
| 10.1-e1 |
10.1-e |
$1$ |
$1$ |
\(\Q(\sqrt{46}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{9} \cdot 5^{12} \) |
$2.15550$ |
$(-23a+156), (9a+61)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.996707357$ |
$1.919163130$ |
3.384401555 |
\( -\frac{13777032407}{7812500000} a - \frac{3369992913}{1953125000} \) |
\( \bigl[1\) , \( 1\) , \( a\) , \( -a + 1\) , \( a - 41\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-a+1\right){x}+a-41$ |
| 10.1-f1 |
10.1-f |
$1$ |
$1$ |
\(\Q(\sqrt{46}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2 \cdot 5^{3} \) |
$2.15550$ |
$(-23a+156), (9a+61)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$15.53590747$ |
1.145322294 |
\( -\frac{59899811}{250} a + \frac{201658777}{125} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( -1407458 a - 9545831\) , \( -2538606312 a - 17217665723\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-1407458a-9545831\right){x}-2538606312a-17217665723$ |
| 10.2-a1 |
10.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{46}) \) |
$2$ |
$[2, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2 \cdot 5^{3} \) |
$2.15550$ |
$(-23a+156), (-9a+61)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \) |
$0.298859460$ |
$19.55351800$ |
2.584843496 |
\( \frac{59899811}{250} a + \frac{201658777}{125} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -85 a - 555\) , \( -941 a - 6363\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-85a-555\right){x}-941a-6363$ |
| 10.2-b1 |
10.2-b |
$1$ |
$1$ |
\(\Q(\sqrt{46}) \) |
$2$ |
$[2, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2^{9} \cdot 5^{12} \) |
$2.15550$ |
$(-23a+156), (-9a+61)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 2 \) |
$1$ |
$5.798023056$ |
0.854871861 |
\( \frac{13777032407}{7812500000} a - \frac{3369992913}{1953125000} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( 508516327 a - 3448925531\) , \( -183383033227434 a + 1243764244654883\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(508516327a-3448925531\right){x}-183383033227434a+1243764244654883$ |
| 10.2-c1 |
10.2-c |
$1$ |
$1$ |
\(\Q(\sqrt{46}) \) |
$2$ |
$[2, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2^{13} \cdot 5^{6} \) |
$2.15550$ |
$(-23a+156), (-9a+61)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$5.046478788$ |
0.744062704 |
\( \frac{3776907459758737}{2000000} a - \frac{800507282019751}{62500} \) |
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -1194937762 a - 8104462185\) , \( -202073642980310 a - 1370530127584686\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-1194937762a-8104462185\right){x}-202073642980310a-1370530127584686$ |
| 10.2-d1 |
10.2-d |
$1$ |
$1$ |
\(\Q(\sqrt{46}) \) |
$2$ |
$[2, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2^{13} \cdot 5^{6} \) |
$2.15550$ |
$(-23a+156), (-9a+61)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \cdot 3 \) |
$2.527378401$ |
$1.362540458$ |
3.046435665 |
\( \frac{3776907459758737}{2000000} a - \frac{800507282019751}{62500} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 40 a - 232\) , \( 438 a - 2868\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(40a-232\right){x}+438a-2868$ |
| 10.2-e1 |
10.2-e |
$1$ |
$1$ |
\(\Q(\sqrt{46}) \) |
$2$ |
$[2, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2^{9} \cdot 5^{12} \) |
$2.15550$ |
$(-23a+156), (-9a+61)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.996707357$ |
$1.919163130$ |
3.384401555 |
\( \frac{13777032407}{7812500000} a - \frac{3369992913}{1953125000} \) |
\( \bigl[1\) , \( 1\) , \( a\) , \( 1\) , \( -a - 41\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+{x}^{2}+{x}-a-41$ |
| 10.2-f1 |
10.2-f |
$1$ |
$1$ |
\(\Q(\sqrt{46}) \) |
$2$ |
$[2, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2 \cdot 5^{3} \) |
$2.15550$ |
$(-23a+156), (-9a+61)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$15.53590747$ |
1.145322294 |
\( \frac{59899811}{250} a + \frac{201658777}{125} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( 1407457 a - 9545831\) , \( 2538606312 a - 17217665723\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(1407457a-9545831\right){x}+2538606312a-17217665723$ |
| 14.1-a1 |
14.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{46}) \) |
$2$ |
$[2, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{13} \cdot 7^{2} \) |
$2.34466$ |
$(-23a+156), (-4a+27)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$5.794569323$ |
0.854362636 |
\( \frac{3621929}{6272} a - \frac{4226507}{1568} \) |
\( \bigl[1\) , \( -a\) , \( 1\) , \( 4 a + 43\) , \( -3 a - 8\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(4a+43\right){x}-3a-8$ |
| 14.1-b1 |
14.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{46}) \) |
$2$ |
$[2, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{13} \cdot 7^{2} \) |
$2.34466$ |
$(-23a+156), (-4a+27)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.371815243$ |
$14.07641912$ |
1.543371442 |
\( \frac{3621929}{6272} a - \frac{4226507}{1568} \) |
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( 19885746 a - 134871681\) , \( -141136021647 a + 957231071290\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(19885746a-134871681\right){x}-141136021647a+957231071290$ |
| 14.2-a1 |
14.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{46}) \) |
$2$ |
$[2, 0]$ |
14.2 |
\( 2 \cdot 7 \) |
\( 2^{13} \cdot 7^{2} \) |
$2.34466$ |
$(-23a+156), (-4a-27)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$5.794569323$ |
0.854362636 |
\( -\frac{3621929}{6272} a - \frac{4226507}{1568} \) |
\( \bigl[1\) , \( a\) , \( 1\) , \( -4 a + 43\) , \( 3 a - 8\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-4a+43\right){x}+3a-8$ |
| 14.2-b1 |
14.2-b |
$1$ |
$1$ |
\(\Q(\sqrt{46}) \) |
$2$ |
$[2, 0]$ |
14.2 |
\( 2 \cdot 7 \) |
\( 2^{13} \cdot 7^{2} \) |
$2.34466$ |
$(-23a+156), (-4a-27)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.371815243$ |
$14.07641912$ |
1.543371442 |
\( -\frac{3621929}{6272} a - \frac{4226507}{1568} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( -19885747 a - 134871681\) , \( 141136021646 a + 957231071290\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-19885747a-134871681\right){x}+141136021646a+957231071290$ |
| 15.2-a1 |
15.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{46}) \) |
$2$ |
$[2, 0]$ |
15.2 |
\( 3 \cdot 5 \) |
\( - 3^{9} \cdot 5^{3} \) |
$2.38545$ |
$(a+7), (9a+61)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 1 \) |
$1$ |
$7.915134328$ |
0.583511444 |
\( \frac{34150648704512}{2460375} a + \frac{231619278154432}{2460375} \) |
\( \bigl[a\) , \( 1\) , \( 1\) , \( 660184220 a - 4477587181\) , \( 45085488471578 a - 305784660264560\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(660184220a-4477587181\right){x}+45085488471578a-305784660264560$ |
| 15.2-b1 |
15.2-b |
$1$ |
$1$ |
\(\Q(\sqrt{46}) \) |
$2$ |
$[2, 0]$ |
15.2 |
\( 3 \cdot 5 \) |
\( - 3^{9} \cdot 5^{3} \) |
$2.38545$ |
$(a+7), (9a+61)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 3 \) |
$0.880149407$ |
$5.951477578$ |
2.316986703 |
\( \frac{34150648704512}{2460375} a + \frac{231619278154432}{2460375} \) |
\( \bigl[a\) , \( 1\) , \( 1\) , \( -6 a + 11\) , \( -43 a - 230\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-6a+11\right){x}-43a-230$ |
| 15.3-a1 |
15.3-a |
$1$ |
$1$ |
\(\Q(\sqrt{46}) \) |
$2$ |
$[2, 0]$ |
15.3 |
\( 3 \cdot 5 \) |
\( - 3^{9} \cdot 5^{3} \) |
$2.38545$ |
$(a-7), (-9a+61)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 1 \) |
$1$ |
$7.915134328$ |
0.583511444 |
\( -\frac{34150648704512}{2460375} a + \frac{231619278154432}{2460375} \) |
\( \bigl[a\) , \( 1\) , \( 1\) , \( -660184221 a - 4477587181\) , \( -45085488471578 a - 305784660264560\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-660184221a-4477587181\right){x}-45085488471578a-305784660264560$ |
| 15.3-b1 |
15.3-b |
$1$ |
$1$ |
\(\Q(\sqrt{46}) \) |
$2$ |
$[2, 0]$ |
15.3 |
\( 3 \cdot 5 \) |
\( - 3^{9} \cdot 5^{3} \) |
$2.38545$ |
$(a-7), (-9a+61)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 3 \) |
$0.880149407$ |
$5.951477578$ |
2.316986703 |
\( -\frac{34150648704512}{2460375} a + \frac{231619278154432}{2460375} \) |
\( \bigl[a\) , \( 1\) , \( 1\) , \( 5 a + 11\) , \( 43 a - 230\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(5a+11\right){x}+43a-230$ |
| 16.1-a1 |
16.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{46}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$2.42425$ |
$(-23a+156)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$5.069265675$ |
0.747422447 |
\( -165376 a - 1121536 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -32868472 a - 222924812\) , \( -267317636924 a - 1813036423935\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-32868472a-222924812\right){x}-267317636924a-1813036423935$ |
| 16.1-b1 |
16.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{46}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{17} \) |
$2.42425$ |
$(-23a+156)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$5.880338179$ |
0.867008564 |
\( -\frac{497681}{8} a - \frac{844747}{2} \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( 24549 a - 166515\) , \( -11916898 a + 80824327\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(24549a-166515\right){x}-11916898a+80824327$ |
| 16.1-c1 |
16.1-c |
$1$ |
$1$ |
\(\Q(\sqrt{46}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$2.42425$ |
$(-23a+156)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$5.069265675$ |
0.747422447 |
\( 165376 a - 1121536 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 32868472 a - 222924812\) , \( 267317636924 a - 1813036423935\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(32868472a-222924812\right){x}+267317636924a-1813036423935$ |
| 16.1-d1 |
16.1-d |
$1$ |
$1$ |
\(\Q(\sqrt{46}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{17} \) |
$2.42425$ |
$(-23a+156)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$11.59434639$ |
1.709493112 |
\( \frac{497681}{8} a - \frac{844747}{2} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( 8341 a - 56483\) , \( -1066384 a + 7232783\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(8341a-56483\right){x}-1066384a+7232783$ |
*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.
