| 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 |
| 27225.6-a1 |
27225.6-a |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
27225.6 |
\( 3^{2} \cdot 5^{2} \cdot 11^{2} \) |
\( 3^{7} \cdot 5^{8} \cdot 11^{3} \) |
$3.80695$ |
$(-a), (a-1), (a-2), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.763924145$ |
$1.384648879$ |
5.102858613 |
\( \frac{9137}{2025} a - \frac{27961}{675} \) |
\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( -3 a - 2\) , \( -27 a + 11\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-3a-2\right){x}-27a+11$ |
| 27225.6-a2 |
27225.6-a |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
27225.6 |
\( 3^{2} \cdot 5^{2} \cdot 11^{2} \) |
\( 3^{14} \cdot 5^{7} \cdot 11^{3} \) |
$3.80695$ |
$(-a), (a-1), (a-2), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.527848290$ |
$0.692324439$ |
5.102858613 |
\( \frac{507753467}{32805} a + \frac{96307804}{10935} \) |
\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( 87 a - 157\) , \( -583 a + 663\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(87a-157\right){x}-583a+663$ |
| 27225.6-b1 |
27225.6-b |
$2$ |
$3$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
27225.6 |
\( 3^{2} \cdot 5^{2} \cdot 11^{2} \) |
\( 3^{5} \cdot 5^{8} \cdot 11^{9} \) |
$3.80695$ |
$(-a), (a-1), (a-2), (-2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.437242627$ |
$0.485407095$ |
6.143325203 |
\( \frac{2854912}{3267} a + \frac{643072}{1089} \) |
\( \bigl[0\) , \( -1\) , \( a\) , \( -33 a - 172\) , \( -487 a - 275\bigr] \) |
${y}^2+a{y}={x}^{3}-{x}^{2}+\left(-33a-172\right){x}-487a-275$ |
| 27225.6-b2 |
27225.6-b |
$2$ |
$3$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
27225.6 |
\( 3^{2} \cdot 5^{2} \cdot 11^{2} \) |
\( 3^{7} \cdot 5^{8} \cdot 11^{7} \) |
$3.80695$ |
$(-a), (a-1), (a-2), (-2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{3} \) |
$1.311727881$ |
$0.485407095$ |
6.143325203 |
\( \frac{305475584}{8019} a + \frac{105951232}{8019} \) |
\( \bigl[0\) , \( -1\) , \( a\) , \( 187 a + 213\) , \( 701 a - 3696\bigr] \) |
${y}^2+a{y}={x}^{3}-{x}^{2}+\left(187a+213\right){x}+701a-3696$ |
| 27225.6-c1 |
27225.6-c |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
27225.6 |
\( 3^{2} \cdot 5^{2} \cdot 11^{2} \) |
\( 3^{12} \cdot 5^{6} \cdot 11^{6} \) |
$3.80695$ |
$(-a), (a-1), (a-2), (-2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2Cs, 5B |
$1$ |
\( 2^{6} \) |
$1.422113402$ |
$0.534743389$ |
3.668624767 |
\( \frac{349209575}{59049} a - \frac{1245002978}{59049} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -171 a + 85\) , \( 750 a - 1899\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-171a+85\right){x}+750a-1899$ |
| 27225.6-c2 |
27225.6-c |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
27225.6 |
\( 3^{2} \cdot 5^{2} \cdot 11^{2} \) |
\( 3^{12} \cdot 5^{6} \cdot 11^{6} \) |
$3.80695$ |
$(-a), (a-1), (a-2), (-2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2Cs, 5B |
$1$ |
\( 2^{6} \cdot 5 \) |
$0.284422680$ |
$0.534743389$ |
3.668624767 |
\( -\frac{349209575}{59049} a - \frac{298597801}{19683} \) |
\( \bigl[a\) , \( a - 1\) , \( a + 1\) , \( -169 a + 28\) , \( -984 a + 1556\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-169a+28\right){x}-984a+1556$ |
| 27225.6-c3 |
27225.6-c |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
27225.6 |
\( 3^{2} \cdot 5^{2} \cdot 11^{2} \) |
\( 3^{6} \cdot 5^{6} \cdot 11^{6} \) |
$3.80695$ |
$(-a), (a-1), (a-2), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{2} \) |
$2.844226804$ |
$1.069486778$ |
3.668624767 |
\( \frac{77935}{243} a - \frac{112717}{243} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -6 a + 30\) , \( 57 a - 18\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-6a+30\right){x}+57a-18$ |
| 27225.6-c4 |
27225.6-c |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
27225.6 |
\( 3^{2} \cdot 5^{2} \cdot 11^{2} \) |
\( 3^{21} \cdot 5^{6} \cdot 11^{6} \) |
$3.80695$ |
$(-a), (a-1), (a-2), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{4} \cdot 5 \) |
$0.568845360$ |
$0.267371694$ |
3.668624767 |
\( \frac{2927543402641}{3486784401} a - \frac{430814699872}{1162261467} \) |
\( \bigl[a\) , \( a - 1\) , \( a + 1\) , \( -279 a + 523\) , \( -2524 a - 3889\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-279a+523\right){x}-2524a-3889$ |
| 27225.6-c5 |
27225.6-c |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
27225.6 |
\( 3^{2} \cdot 5^{2} \cdot 11^{2} \) |
\( 3^{6} \cdot 5^{6} \cdot 11^{6} \) |
$3.80695$ |
$(-a), (a-1), (a-2), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{2} \cdot 5 \) |
$0.568845360$ |
$1.069486778$ |
3.668624767 |
\( -\frac{77935}{243} a - \frac{11594}{81} \) |
\( \bigl[a\) , \( a - 1\) , \( a + 1\) , \( -4 a - 27\) , \( -27 a + 137\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-4a-27\right){x}-27a+137$ |
| 27225.6-c6 |
27225.6-c |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
27225.6 |
\( 3^{2} \cdot 5^{2} \cdot 11^{2} \) |
\( 3^{21} \cdot 5^{6} \cdot 11^{6} \) |
$3.80695$ |
$(-a), (a-1), (a-2), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{4} \) |
$2.844226804$ |
$0.267371694$ |
3.668624767 |
\( -\frac{2927543402641}{3486784401} a + \frac{1635099303025}{3486784401} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -226 a - 355\) , \( -2143 a - 5243\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-226a-355\right){x}-2143a-5243$ |
| 27225.6-c7 |
27225.6-c |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
27225.6 |
\( 3^{2} \cdot 5^{2} \cdot 11^{2} \) |
\( 3^{9} \cdot 5^{6} \cdot 11^{6} \) |
$3.80695$ |
$(-a), (a-1), (a-2), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{4} \cdot 5 \) |
$0.568845360$ |
$0.267371694$ |
3.668624767 |
\( \frac{54238838797}{243} a + \frac{1331574640}{9} \) |
\( \bigl[a\) , \( a - 1\) , \( a + 1\) , \( -2699 a + 413\) , \( -63112 a + 89457\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-2699a+413\right){x}-63112a+89457$ |
| 27225.6-c8 |
27225.6-c |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
27225.6 |
\( 3^{2} \cdot 5^{2} \cdot 11^{2} \) |
\( 3^{9} \cdot 5^{6} \cdot 11^{6} \) |
$3.80695$ |
$(-a), (a-1), (a-2), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{4} \) |
$2.844226804$ |
$0.267371694$ |
3.668624767 |
\( -\frac{54238838797}{243} a + \frac{90191354077}{243} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -2756 a + 1405\) , \( 49535 a - 112119\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2756a+1405\right){x}+49535a-112119$ |
| 27225.6-d1 |
27225.6-d |
$2$ |
$3$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
27225.6 |
\( 3^{2} \cdot 5^{2} \cdot 11^{2} \) |
\( 3^{5} \cdot 5^{2} \cdot 11^{9} \) |
$3.80695$ |
$(-a), (a-1), (a-2), (-2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$0.545155217$ |
$1.085403261$ |
2.854532127 |
\( \frac{2854912}{3267} a + \frac{643072}{1089} \) |
\( \bigl[0\) , \( a + 1\) , \( a\) , \( -21 a + 25\) , \( 11 a + 108\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-21a+25\right){x}+11a+108$ |
| 27225.6-d2 |
27225.6-d |
$2$ |
$3$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
27225.6 |
\( 3^{2} \cdot 5^{2} \cdot 11^{2} \) |
\( 3^{7} \cdot 5^{2} \cdot 11^{7} \) |
$3.80695$ |
$(-a), (a-1), (a-2), (-2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.181718405$ |
$1.085403261$ |
2.854532127 |
\( \frac{305475584}{8019} a + \frac{105951232}{8019} \) |
\( \bigl[0\) , \( a + 1\) , \( a\) , \( 34 a - 85\) , \( -165 a + 185\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(34a-85\right){x}-165a+185$ |
| 27225.6-e1 |
27225.6-e |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
27225.6 |
\( 3^{2} \cdot 5^{2} \cdot 11^{2} \) |
\( 3^{6} \cdot 5^{6} \cdot 11^{4} \) |
$3.80695$ |
$(-a), (a-1), (a-2), (-2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
|
$1$ |
\( 2 \cdot 3^{2} \) |
$0.107600940$ |
$1.596960189$ |
3.730321925 |
\( \frac{45056}{27} \) |
\( \bigl[0\) , \( a + 1\) , \( 1\) , \( -10 a + 3\) , \( -8 a + 8\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-10a+3\right){x}-8a+8$ |
| 27225.6-f1 |
27225.6-f |
$2$ |
$3$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
27225.6 |
\( 3^{2} \cdot 5^{2} \cdot 11^{2} \) |
\( 3^{8} \cdot 5^{6} \cdot 11^{2} \) |
$3.80695$ |
$(-a), (a-1), (a-2), (-2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.287254929$ |
$1.917754005$ |
7.972697452 |
\( \frac{1068415}{729} a + \frac{709403}{729} \) |
\( \bigl[1\) , \( a\) , \( a\) , \( -3 a - 13\) , \( 3 a + 11\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-3a-13\right){x}+3a+11$ |
| 27225.6-f2 |
27225.6-f |
$2$ |
$3$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
27225.6 |
\( 3^{2} \cdot 5^{2} \cdot 11^{2} \) |
\( 3^{8} \cdot 5^{6} \cdot 11^{2} \) |
$3.80695$ |
$(-a), (a-1), (a-2), (-2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$0.861764789$ |
$1.917754005$ |
7.972697452 |
\( -\frac{1068415}{729} a + \frac{592606}{243} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -5 a + 16\) , \( 5 a + 18\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-5a+16\right){x}+5a+18$ |
| 27225.6-g1 |
27225.6-g |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
27225.6 |
\( 3^{2} \cdot 5^{2} \cdot 11^{2} \) |
\( 3^{6} \cdot 5^{8} \cdot 11^{8} \) |
$3.80695$ |
$(-a), (a-1), (a-2), (-2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$0.548674873$ |
3.308633975 |
\( \frac{2449408}{6075} a + \frac{4272128}{6075} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -55 a - 73\) , \( -341 a + 391\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}+\left(-55a-73\right){x}-341a+391$ |
*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.
