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 |
225.5-a1 |
225.5-a |
$8$ |
$16$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
225.5 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{32} \cdot 5^{2} \) |
$1.14784$ |
$(-a), (a-1), (-a-1), (a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.666073956$ |
$0.558925428$ |
1.123082843 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -110\) , \( -880\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-110{x}-880$ |
225.5-a2 |
225.5-a |
$8$ |
$16$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
225.5 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{2} \cdot 5^{2} \) |
$1.14784$ |
$(-a), (a-1), (-a-1), (a-2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1.666073956$ |
$8.942806850$ |
1.123082843 |
\( -\frac{1}{15} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}$ |
225.5-a3 |
225.5-a |
$8$ |
$16$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
225.5 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{4} \cdot 5^{16} \) |
$1.14784$ |
$(-a), (a-1), (-a-1), (a-2)$ |
$1$ |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{8} \) |
$0.208259244$ |
$1.117850856$ |
1.123082843 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 35\) , \( -28\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+35{x}-28$ |
225.5-a4 |
225.5-a |
$8$ |
$16$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
225.5 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{8} \cdot 5^{8} \) |
$1.14784$ |
$(-a), (a-1), (-a-1), (a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$0.416518489$ |
$2.235701712$ |
1.123082843 |
\( \frac{111284641}{50625} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -10\) , \( -10\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-10{x}-10$ |
225.5-a5 |
225.5-a |
$8$ |
$16$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
225.5 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{4} \cdot 5^{4} \) |
$1.14784$ |
$(-a), (a-1), (-a-1), (a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.833036978$ |
$4.471403425$ |
1.123082843 |
\( \frac{13997521}{225} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -5\) , \( 2\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-5{x}+2$ |
225.5-a6 |
225.5-a |
$8$ |
$16$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
225.5 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{16} \cdot 5^{4} \) |
$1.14784$ |
$(-a), (a-1), (-a-1), (a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.833036978$ |
$1.117850856$ |
1.123082843 |
\( \frac{272223782641}{164025} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -135\) , \( -660\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-135{x}-660$ |
225.5-a7 |
225.5-a |
$8$ |
$16$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
225.5 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{2} \cdot 5^{2} \) |
$1.14784$ |
$(-a), (a-1), (-a-1), (a-2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1.666073956$ |
$2.235701712$ |
1.123082843 |
\( \frac{56667352321}{15} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -80\) , \( 242\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-80{x}+242$ |
225.5-a8 |
225.5-a |
$8$ |
$16$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
225.5 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{8} \cdot 5^{2} \) |
$1.14784$ |
$(-a), (a-1), (-a-1), (a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.666073956$ |
$0.558925428$ |
1.123082843 |
\( \frac{1114544804970241}{405} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -2160\) , \( -39540\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-2160{x}-39540$ |
225.5-b1 |
225.5-b |
$8$ |
$16$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
225.5 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{6} \cdot 5^{10} \) |
$1.14784$ |
$(-a), (a-1), (-a-1), (a-2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.676292688$ |
1.631279343 |
\( \frac{5020579657727137}{31640625} a - \frac{15548725694657158}{31640625} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -385 a - 144\) , \( -4471 a + 3234\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-385a-144\right){x}-4471a+3234$ |
225.5-b2 |
225.5-b |
$8$ |
$16$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
225.5 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{9} \cdot 5^{17} \) |
$1.14784$ |
$(-a), (a-1), (-a-1), (a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.338146344$ |
1.631279343 |
\( \frac{785995287207294187003}{1001129150390625} a - \frac{4434281600575826892151}{1001129150390625} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -980 a + 901\) , \( 6920 a - 26670\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-980a+901\right){x}+6920a-26670$ |
225.5-b3 |
225.5-b |
$8$ |
$16$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
225.5 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{12} \cdot 5^{8} \) |
$1.14784$ |
$(-a), (a-1), (-a-1), (a-2)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$1$ |
$1.352585377$ |
1.631279343 |
\( -\frac{10492718831}{820125} a + \frac{3853977841}{4100625} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -25 a - 9\) , \( -70 a + 75\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-25a-9\right){x}-70a+75$ |
225.5-b4 |
225.5-b |
$8$ |
$16$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
225.5 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{12} \cdot 5^{4} \) |
$1.14784$ |
$(-a), (a-1), (-a-1), (a-2)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$2.705170755$ |
1.631279343 |
\( -\frac{2328193}{32805} a - \frac{9002158}{54675} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -4\) , \( -5 a + 7\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}-4{x}-5a+7$ |
225.5-b5 |
225.5-b |
$8$ |
$16$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
225.5 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{33} \cdot 5^{5} \) |
$1.14784$ |
$(-a), (a-1), (-a-1), (a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$0.338146344$ |
1.631279343 |
\( -\frac{1003477310557125250603}{1158137618032400625} a + \frac{1313609484592825399351}{1158137618032400625} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 210 a + 71\) , \( 826 a - 3542\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(210a+71\right){x}+826a-3542$ |
225.5-b6 |
225.5-b |
$8$ |
$16$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
225.5 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{18} \cdot 5^{10} \) |
$1.14784$ |
$(-a), (a-1), (-a-1), (a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$0.676292688$ |
1.631279343 |
\( \frac{19658857399239023}{16815125390625} a + \frac{8228798640710134}{16815125390625} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -65 a + 46\) , \( 71 a - 372\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-65a+46\right){x}+71a-372$ |
225.5-b7 |
225.5-b |
$8$ |
$16$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
225.5 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{6} \cdot 5^{2} \) |
$1.14784$ |
$(-a), (a-1), (-a-1), (a-2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$5.410341510$ |
1.631279343 |
\( \frac{3229921}{405} a - \frac{210241}{135} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+{x}$ |
225.5-b8 |
225.5-b |
$8$ |
$16$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
225.5 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{18} \cdot 5^{2} \) |
$1.14784$ |
$(-a), (a-1), (-a-1), (a-2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$1.352585377$ |
1.631279343 |
\( \frac{29881004028839}{215233605} a + \frac{30104948010361}{71744535} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 25 a - 79\) , \( -160 a + 247\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(25a-79\right){x}-160a+247$ |
225.5-c1 |
225.5-c |
$8$ |
$16$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
225.5 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{6} \cdot 5^{10} \) |
$1.14784$ |
$(-a), (a-1), (-a-1), (a-2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.676292688$ |
1.631279343 |
\( -\frac{5020579657727137}{31640625} a - \frac{3509382012310007}{10546875} \) |
\( \bigl[a + 1\) , \( a\) , \( 1\) , \( 384 a - 531\) , \( 4327 a - 2390\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(384a-531\right){x}+4327a-2390$ |
225.5-c2 |
225.5-c |
$8$ |
$16$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
225.5 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{9} \cdot 5^{17} \) |
$1.14784$ |
$(-a), (a-1), (-a-1), (a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.338146344$ |
1.631279343 |
\( -\frac{785995287207294187003}{1001129150390625} a - \frac{1216095437789510901716}{333709716796875} \) |
\( \bigl[a + 1\) , \( a\) , \( 1\) , \( 979 a - 81\) , \( -6019 a - 22688\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(979a-81\right){x}-6019a-22688$ |
225.5-c3 |
225.5-c |
$8$ |
$16$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
225.5 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{12} \cdot 5^{8} \) |
$1.14784$ |
$(-a), (a-1), (-a-1), (a-2)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$1$ |
$1.352585377$ |
1.631279343 |
\( \frac{10492718831}{820125} a - \frac{16203205438}{1366875} \) |
\( \bigl[a + 1\) , \( a\) , \( 1\) , \( 24 a - 36\) , \( 61 a - 68\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(24a-36\right){x}+61a-68$ |
225.5-c4 |
225.5-c |
$8$ |
$16$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
225.5 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{12} \cdot 5^{4} \) |
$1.14784$ |
$(-a), (a-1), (-a-1), (a-2)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$2.705170755$ |
1.631279343 |
\( \frac{2328193}{32805} a - \frac{38647439}{164025} \) |
\( \bigl[a + 1\) , \( a\) , \( 1\) , \( -a - 6\) , \( a + 4\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-a-6\right){x}+a+4$ |
225.5-c5 |
225.5-c |
$8$ |
$16$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
225.5 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{33} \cdot 5^{5} \) |
$1.14784$ |
$(-a), (a-1), (-a-1), (a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$0.338146344$ |
1.631279343 |
\( \frac{1003477310557125250603}{1158137618032400625} a + \frac{103377391345233382916}{386045872677466875} \) |
\( \bigl[a + 1\) , \( a\) , \( 1\) , \( -211 a + 279\) , \( -755 a - 2084\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-211a+279\right){x}-755a-2084$ |
225.5-c6 |
225.5-c |
$8$ |
$16$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
225.5 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{18} \cdot 5^{10} \) |
$1.14784$ |
$(-a), (a-1), (-a-1), (a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$0.676292688$ |
1.631279343 |
\( -\frac{19658857399239023}{16815125390625} a + \frac{9295885346649719}{5605041796875} \) |
\( \bigl[a + 1\) , \( a\) , \( 1\) , \( 64 a - 21\) , \( -25 a - 494\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(64a-21\right){x}-25a-494$ |
225.5-c7 |
225.5-c |
$8$ |
$16$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
225.5 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{6} \cdot 5^{2} \) |
$1.14784$ |
$(-a), (a-1), (-a-1), (a-2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$5.410341510$ |
1.631279343 |
\( -\frac{3229921}{405} a + \frac{2599198}{405} \) |
\( \bigl[a + 1\) , \( a\) , \( 1\) , \( -a - 1\) , \( a + 2\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-a-1\right){x}+a+2$ |
225.5-c8 |
225.5-c |
$8$ |
$16$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
225.5 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{18} \cdot 5^{2} \) |
$1.14784$ |
$(-a), (a-1), (-a-1), (a-2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$1.352585377$ |
1.631279343 |
\( -\frac{29881004028839}{215233605} a + \frac{120195848059922}{215233605} \) |
\( \bigl[a + 1\) , \( a\) , \( 1\) , \( -26 a - 56\) , \( 81 a + 164\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-26a-56\right){x}+81a+164$ |
*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.