| 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 |
| 3872.5-a1 |
3872.5-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3872.5 |
\( 2^{5} \cdot 11^{2} \) |
\( 2^{16} \cdot 11^{4} \) |
$1.86497$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.292255878$ |
$2.457844850$ |
2.171994331 |
\( \frac{704969}{484} \) |
\( \bigl[a\) , \( -a\) , \( 0\) , \( 6 a - 4\) , \( 0\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(6a-4\right){x}$ |
| 3872.5-a2 |
3872.5-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3872.5 |
\( 2^{5} \cdot 11^{2} \) |
\( 2^{14} \cdot 11^{8} \) |
$1.86497$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.146127939$ |
$1.228922425$ |
2.171994331 |
\( \frac{59776471}{29282} \) |
\( \bigl[a\) , \( -a\) , \( 0\) , \( -24 a + 16\) , \( 18 a - 44\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(-24a+16\right){x}+18a-44$ |
| 3872.5-a3 |
3872.5-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3872.5 |
\( 2^{5} \cdot 11^{2} \) |
\( 2^{17} \cdot 11^{2} \) |
$1.86497$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.584511757$ |
$2.457844850$ |
2.171994331 |
\( -\frac{34643161}{176} a + \frac{13683239}{88} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 22\) , \( -27 a + 13\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+22{x}-27a+13$ |
| 3872.5-a4 |
3872.5-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3872.5 |
\( 2^{5} \cdot 11^{2} \) |
\( 2^{17} \cdot 11^{2} \) |
$1.86497$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.584511757$ |
$2.457844850$ |
2.171994331 |
\( \frac{34643161}{176} a - \frac{7276683}{176} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( -3 a - 19\) , \( -a + 31\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-3a-19\right){x}-a+31$ |
| 3872.5-b1 |
3872.5-b |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3872.5 |
\( 2^{5} \cdot 11^{2} \) |
\( 2^{18} \cdot 11^{6} \) |
$1.86497$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$1$ |
$1.461921226$ |
2.210217144 |
\( -\frac{46830231}{234256} a + \frac{212077575}{117128} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -9 a + 23\) , \( 0\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-9a+23\right){x}$ |
| 3872.5-b2 |
3872.5-b |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3872.5 |
\( 2^{5} \cdot 11^{2} \) |
\( 2^{18} \cdot 11^{6} \) |
$1.86497$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.461921226$ |
2.210217144 |
\( \frac{46830231}{234256} a + \frac{377324919}{234256} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -12 a - 7\) , \( a + 10\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-12a-7\right){x}+a+10$ |
| 3872.5-b3 |
3872.5-b |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3872.5 |
\( 2^{5} \cdot 11^{2} \) |
\( 2^{15} \cdot 11^{9} \) |
$1.86497$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$0.730960613$ |
2.210217144 |
\( -\frac{56046918875913}{857435524} a + \frac{93327675428637}{857435524} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -102 a - 107\) , \( 867 a + 190\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-102a-107\right){x}+867a+190$ |
| 3872.5-b4 |
3872.5-b |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3872.5 |
\( 2^{5} \cdot 11^{2} \) |
\( 2^{15} \cdot 11^{9} \) |
$1.86497$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.730960613$ |
2.210217144 |
\( \frac{56046918875913}{857435524} a + \frac{9320189138181}{214358881} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -69 a + 223\) , \( -684 a - 536\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-69a+223\right){x}-684a-536$ |
| 3872.5-b5 |
3872.5-b |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3872.5 |
\( 2^{5} \cdot 11^{2} \) |
\( 2^{21} \cdot 11^{3} \) |
$1.86497$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$1.461921226$ |
2.210217144 |
\( -\frac{14003310699}{30976} a + \frac{9620888049}{15488} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -42 a - 19\) , \( 205 a - 62\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-42a-19\right){x}+205a-62$ |
| 3872.5-b6 |
3872.5-b |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3872.5 |
\( 2^{5} \cdot 11^{2} \) |
\( 2^{21} \cdot 11^{3} \) |
$1.86497$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.461921226$ |
2.210217144 |
\( \frac{14003310699}{30976} a + \frac{5238465399}{30976} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -33 a + 71\) , \( -78 a - 204\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-33a+71\right){x}-78a-204$ |
| 3872.5-c1 |
3872.5-c |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3872.5 |
\( 2^{5} \cdot 11^{2} \) |
\( 2^{17} \cdot 11^{2} \) |
$1.86497$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.619709498$ |
2.810738089 |
\( \frac{32518499729401}{704} a - \frac{15898155671547}{352} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 469 a - 1407\) , \( 9386 a - 18877\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(469a-1407\right){x}+9386a-18877$ |
| 3872.5-c2 |
3872.5-c |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3872.5 |
\( 2^{5} \cdot 11^{2} \) |
\( 2^{35} \cdot 11^{2} \) |
$1.86497$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$1.239418997$ |
2.810738089 |
\( -\frac{16131562657}{184549376} a + \frac{3800221619}{92274688} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 9 a - 3\) , \( -6 a - 67\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(9a-3\right){x}-6a-67$ |
| 3872.5-c3 |
3872.5-c |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3872.5 |
\( 2^{5} \cdot 11^{2} \) |
\( 2^{14} \cdot 11^{8} \) |
$1.86497$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$1.239418997$ |
2.810738089 |
\( -\frac{16280859}{937024} a + \frac{747699265}{468512} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -17 a - 13\) , \( 0\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-17a-13\right){x}$ |
| 3872.5-c4 |
3872.5-c |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3872.5 |
\( 2^{5} \cdot 11^{2} \) |
\( 2^{7} \cdot 11^{10} \) |
$1.86497$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$1.239418997$ |
2.810738089 |
\( \frac{34401807041}{1714871048} a + \frac{1602489013229}{857435524} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( 18 a - 29\) , \( 6 a - 23\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(18a-29\right){x}+6a-23$ |
| 3872.5-c5 |
3872.5-c |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3872.5 |
\( 2^{5} \cdot 11^{2} \) |
\( 2^{22} \cdot 11^{4} \) |
$1.86497$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \cdot 3 \) |
$1$ |
$1.239418997$ |
2.810738089 |
\( \frac{78156424101}{495616} a + \frac{16938341377}{247808} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 29 a - 87\) , \( 146 a - 309\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(29a-87\right){x}+146a-309$ |
| 3872.5-c6 |
3872.5-c |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3872.5 |
\( 2^{5} \cdot 11^{2} \) |
\( 2^{13} \cdot 11^{10} \) |
$1.86497$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.619709498$ |
2.810738089 |
\( -\frac{320710739562017}{1714871048} a + \frac{225827695068387}{857435524} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -157 a - 193\) , \( -1580 a - 372\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-157a-193\right){x}-1580a-372$ |
| 3872.5-d1 |
3872.5-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3872.5 |
\( 2^{5} \cdot 11^{2} \) |
\( 2^{48} \cdot 11^{3} \) |
$1.86497$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.478347664$ |
2.892774765 |
\( -\frac{31504873455125}{519691042816} a + \frac{132554493440375}{519691042816} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -48 a - 65\) , \( 352 a - 1185\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-48a-65\right){x}+352a-1185$ |
| 3872.5-d2 |
3872.5-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3872.5 |
\( 2^{5} \cdot 11^{2} \) |
\( 2^{48} \cdot 11^{3} \) |
$1.86497$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$1$ |
$0.478347664$ |
2.892774765 |
\( \frac{31504873455125}{519691042816} a + \frac{50524809992625}{259845521408} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -30 a + 117\) , \( 617 a - 1138\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-30a+117\right){x}+617a-1138$ |
| 3872.5-d3 |
3872.5-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3872.5 |
\( 2^{5} \cdot 11^{2} \) |
\( 2^{36} \cdot 11^{6} \) |
$1.86497$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{9} \) |
$1$ |
$0.478347664$ |
2.892774765 |
\( -\frac{1133731711875}{959512576} a + \frac{4028870229625}{479756288} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( -178 a - 86\) , \( 1188 a - 129\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-178a-86\right){x}+1188a-129$ |
| 3872.5-d4 |
3872.5-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3872.5 |
\( 2^{5} \cdot 11^{2} \) |
\( 2^{36} \cdot 11^{6} \) |
$1.86497$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$1$ |
$0.478347664$ |
2.892774765 |
\( \frac{1133731711875}{959512576} a + \frac{6924008747375}{959512576} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -140 a + 299\) , \( -624 a - 1207\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-140a+299\right){x}-624a-1207$ |
| 3872.5-d5 |
3872.5-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3872.5 |
\( 2^{5} \cdot 11^{2} \) |
\( 2^{24} \cdot 11^{9} \) |
$1.86497$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{8} \) |
$1$ |
$0.239173832$ |
2.892774765 |
\( -\frac{915988506230265125}{54875873536} a + \frac{1519749586080622375}{27437936768} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( -2738 a - 1366\) , \( 86180 a - 19585\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-2738a-1366\right){x}+86180a-19585$ |
| 3872.5-d6 |
3872.5-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3872.5 |
\( 2^{5} \cdot 11^{2} \) |
\( 2^{24} \cdot 11^{9} \) |
$1.86497$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$1$ |
$0.239173832$ |
2.892774765 |
\( \frac{915988506230265125}{54875873536} a + \frac{2123510665930979625}{54875873536} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -2140 a + 4619\) , \( -46032 a - 77943\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-2140a+4619\right){x}-46032a-77943$ |
*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.
