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 |
3584.7-a1 |
3584.7-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3584.7 |
\( 2^{9} \cdot 7 \) |
\( 2^{31} \cdot 7 \) |
$1.82928$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$0.691848366$ |
1.045976412 |
\( \frac{4096655365}{28} a - \frac{2878658051}{14} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -468 a + 384\) , \( -2140 a + 7060\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-468a+384\right){x}-2140a+7060$ |
3584.7-a2 |
3584.7-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3584.7 |
\( 2^{9} \cdot 7 \) |
\( 2^{23} \cdot 7^{2} \) |
$1.82928$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.383696732$ |
1.045976412 |
\( -\frac{13647889}{14} a - \frac{40536829}{7} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 55 a - 105\) , \( 282 a - 254\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(55a-105\right){x}+282a-254$ |
3584.7-a3 |
3584.7-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3584.7 |
\( 2^{9} \cdot 7 \) |
\( 2^{32} \cdot 7^{2} \) |
$1.82928$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$1.383696732$ |
1.045976412 |
\( -\frac{1145925}{112} a - \frac{72257}{56} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -28 a + 24\) , \( -44 a + 132\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-28a+24\right){x}-44a+132$ |
3584.7-a4 |
3584.7-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3584.7 |
\( 2^{9} \cdot 7 \) |
\( 2^{37} \cdot 7 \) |
$1.82928$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.383696732$ |
1.045976412 |
\( -\frac{138325}{1792} a - \frac{317937}{896} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 11 a - 10\) , \( 33 a + 6\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(11a-10\right){x}+33a+6$ |
3584.7-a5 |
3584.7-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3584.7 |
\( 2^{9} \cdot 7 \) |
\( 2^{29} \cdot 7^{8} \) |
$1.82928$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.691848366$ |
1.045976412 |
\( -\frac{5786513}{4802} a + \frac{263001}{343} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -5 a - 90\) , \( 99 a - 466\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-5a-90\right){x}+99a-466$ |
3584.7-a6 |
3584.7-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3584.7 |
\( 2^{9} \cdot 7 \) |
\( 2^{28} \cdot 7^{4} \) |
$1.82928$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$1.383696732$ |
1.045976412 |
\( \frac{361845}{196} a - \frac{43727}{98} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 15 a + 10\) , \( 3 a - 50\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(15a+10\right){x}+3a-50$ |
3584.7-b1 |
3584.7-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3584.7 |
\( 2^{9} \cdot 7 \) |
\( 2^{26} \cdot 7^{2} \) |
$1.82928$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$2.261235310$ |
1.709333224 |
\( -\frac{4}{7} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 0\) , \( 4 a - 12\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+4a-12$ |
3584.7-b2 |
3584.7-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3584.7 |
\( 2^{9} \cdot 7 \) |
\( 2^{25} \cdot 7 \) |
$1.82928$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.261235310$ |
1.709333224 |
\( -\frac{59930}{7} a + \frac{346862}{7} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 14 a - 3\) , \( -13 a - 14\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(14a-3\right){x}-13a-14$ |
3584.7-b3 |
3584.7-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3584.7 |
\( 2^{9} \cdot 7 \) |
\( 2^{25} \cdot 7 \) |
$1.82928$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$2.261235310$ |
1.709333224 |
\( \frac{59930}{7} a + \frac{286932}{7} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 2 a + 17\) , \( 29 a - 18\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(2a+17\right){x}+29a-18$ |
3584.7-b4 |
3584.7-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3584.7 |
\( 2^{9} \cdot 7 \) |
\( 2^{28} \cdot 7^{4} \) |
$1.82928$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.130617655$ |
1.709333224 |
\( \frac{3543122}{49} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 40 a + 40\) , \( 84 a - 252\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(40a+40\right){x}+84a-252$ |
3584.7-c1 |
3584.7-c |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3584.7 |
\( 2^{9} \cdot 7 \) |
\( 2^{25} \cdot 7^{4} \) |
$1.82928$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.611837523$ |
$1.538008342$ |
2.845350462 |
\( \frac{91484}{49} a - \frac{488028}{49} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 20 a - 24\) , \( -44 a + 4\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(20a-24\right){x}-44a+4$ |
3584.7-c2 |
3584.7-c |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3584.7 |
\( 2^{9} \cdot 7 \) |
\( 2^{10} \cdot 7 \) |
$1.82928$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.611837523$ |
$6.152033368$ |
2.845350462 |
\( -\frac{21696}{7} a - \frac{9088}{7} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+{x}$ |
3584.7-c3 |
3584.7-c |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3584.7 |
\( 2^{9} \cdot 7 \) |
\( 2^{20} \cdot 7^{2} \) |
$1.82928$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.305918761$ |
$3.076016684$ |
2.845350462 |
\( \frac{3408}{7} a - 1360 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -4\) , \( -4 a - 4\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}-4{x}-4a-4$ |
3584.7-c4 |
3584.7-c |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3584.7 |
\( 2^{9} \cdot 7 \) |
\( 2^{25} \cdot 7 \) |
$1.82928$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.611837523$ |
$1.538008342$ |
2.845350462 |
\( -\frac{12673028}{7} a + \frac{25007348}{7} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -20 a - 64\) , \( -140 a - 188\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-20a-64\right){x}-140a-188$ |
3584.7-d1 |
3584.7-d |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3584.7 |
\( 2^{9} \cdot 7 \) |
\( 2^{26} \cdot 7 \) |
$1.82928$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$1.347763164$ |
2.037626376 |
\( \frac{39051258}{7} a - \frac{25340662}{7} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 86 a - 43\) , \( -261 a - 150\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(86a-43\right){x}-261a-150$ |
3584.7-d2 |
3584.7-d |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3584.7 |
\( 2^{9} \cdot 7 \) |
\( 2^{17} \cdot 7^{4} \) |
$1.82928$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.695526328$ |
2.037626376 |
\( -\frac{24238}{49} a + \frac{44442}{49} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( a - 6\) , \( -6 a + 4\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(a-6\right){x}-6a+4$ |
3584.7-d3 |
3584.7-d |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3584.7 |
\( 2^{9} \cdot 7 \) |
\( 2^{22} \cdot 7^{2} \) |
$1.82928$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$2.695526328$ |
2.037626376 |
\( \frac{10452}{7} a + \frac{13028}{7} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 6 a - 3\) , \( -5 a + 2\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(6a-3\right){x}-5a+2$ |
3584.7-d4 |
3584.7-d |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3584.7 |
\( 2^{9} \cdot 7 \) |
\( 2^{23} \cdot 7 \) |
$1.82928$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.695526328$ |
2.037626376 |
\( -\frac{88712}{7} a + \frac{116960}{7} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 4 a - 12\) , \( -4 a + 12\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(4a-12\right){x}-4a+12$ |
3584.7-e1 |
3584.7-e |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3584.7 |
\( 2^{9} \cdot 7 \) |
\( 2^{22} \cdot 7^{2} \) |
$1.82928$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$2.839949937$ |
2.146800363 |
\( \frac{432}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -a - 1\) , \( -2 a + 6\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}-2a+6$ |
3584.7-e2 |
3584.7-e |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3584.7 |
\( 2^{9} \cdot 7 \) |
\( 2^{28} \cdot 7^{8} \) |
$1.82928$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.709987484$ |
2.146800363 |
\( \frac{11090466}{2401} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 59 a + 59\) , \( 138 a - 414\bigr] \) |
${y}^2={x}^{3}+\left(59a+59\right){x}+138a-414$ |
3584.7-e3 |
3584.7-e |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3584.7 |
\( 2^{9} \cdot 7 \) |
\( 2^{26} \cdot 7^{4} \) |
$1.82928$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.419974968$ |
2.146800363 |
\( \frac{740772}{49} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 19 a + 19\) , \( -30 a + 90\bigr] \) |
${y}^2={x}^{3}+\left(19a+19\right){x}-30a+90$ |
3584.7-e4 |
3584.7-e |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3584.7 |
\( 2^{9} \cdot 7 \) |
\( 2^{20} \cdot 7 \) |
$1.82928$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.839949937$ |
2.146800363 |
\( -\frac{516132}{7} a + \frac{464076}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -a - 13\) , \( 2 a + 18\bigr] \) |
${y}^2={x}^{3}+\left(-a-13\right){x}+2a+18$ |
3584.7-e5 |
3584.7-e |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3584.7 |
\( 2^{9} \cdot 7 \) |
\( 2^{20} \cdot 7 \) |
$1.82928$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.839949937$ |
2.146800363 |
\( \frac{516132}{7} a - \frac{52056}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -10 a + 2\) , \( -13 a + 15\bigr] \) |
${y}^2={x}^{3}+\left(-10a+2\right){x}-13a+15$ |
3584.7-e6 |
3584.7-e |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3584.7 |
\( 2^{9} \cdot 7 \) |
\( 2^{28} \cdot 7^{2} \) |
$1.82928$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$0.709987484$ |
2.146800363 |
\( \frac{1443468546}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 299 a + 299\) , \( -1990 a + 5970\bigr] \) |
${y}^2={x}^{3}+\left(299a+299\right){x}-1990a+5970$ |
*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.