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 |
2500.3-a1 |
2500.3-a |
$4$ |
$15$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
2500.3 |
\( 2^{2} \cdot 5^{4} \) |
\( 2^{6} \cdot 5^{20} \) |
$2.09566$ |
$(-a-1), (a-2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 5$ |
3B, 5B.1.2 |
$1$ |
\( 3 \) |
$1$ |
$0.284833349$ |
0.515282916 |
\( -\frac{349938025}{8} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -3138\) , \( -68969\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-3138{x}-68969$ |
2500.3-a2 |
2500.3-a |
$4$ |
$15$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
2500.3 |
\( 2^{2} \cdot 5^{4} \) |
\( 2^{10} \cdot 5^{4} \) |
$2.09566$ |
$(-a-1), (a-2), (2)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 5$ |
3B, 5B.1.1 |
$1$ |
\( 5 \) |
$1$ |
$4.272500240$ |
0.515282916 |
\( -\frac{121945}{32} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -3\) , \( 1\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-3{x}+1$ |
2500.3-a3 |
2500.3-a |
$4$ |
$15$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
2500.3 |
\( 2^{2} \cdot 5^{4} \) |
\( 2^{2} \cdot 5^{20} \) |
$2.09566$ |
$(-a-1), (a-2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 5$ |
3B, 5B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$0.854500048$ |
0.515282916 |
\( -\frac{25}{2} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -13\) , \( -219\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-13{x}-219$ |
2500.3-a4 |
2500.3-a |
$4$ |
$15$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
2500.3 |
\( 2^{2} \cdot 5^{4} \) |
\( 2^{30} \cdot 5^{4} \) |
$2.09566$ |
$(-a-1), (a-2), (2)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 5$ |
3B, 5B.1.1 |
$1$ |
\( 3 \cdot 5 \) |
$1$ |
$1.424166746$ |
0.515282916 |
\( \frac{46969655}{32768} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 22\) , \( -9\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+22{x}-9$ |
2500.3-b1 |
2500.3-b |
$4$ |
$15$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
2500.3 |
\( 2^{2} \cdot 5^{4} \) |
\( 2^{6} \cdot 5^{14} \) |
$2.09566$ |
$(-a-1), (a-2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 5$ |
3B, 5B.4.2 |
$1$ |
\( 3 \) |
$1$ |
$0.636906731$ |
1.152207629 |
\( -\frac{349938025}{8} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 1\) , \( 376 a - 126\) , \( 2207 a + 3862\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(376a-126\right){x}+2207a+3862$ |
2500.3-b2 |
2500.3-b |
$4$ |
$15$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
2500.3 |
\( 2^{2} \cdot 5^{4} \) |
\( 2^{10} \cdot 5^{10} \) |
$2.09566$ |
$(-a-1), (a-2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 5$ |
3B, 5B.4.1 |
$1$ |
\( 1 \) |
$1$ |
$1.910720194$ |
1.152207629 |
\( -\frac{121945}{32} \) |
\( \bigl[a\) , \( a - 1\) , \( a + 1\) , \( -11 a + 7\) , \( 13 a - 18\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-11a+7\right){x}+13a-18$ |
2500.3-b3 |
2500.3-b |
$4$ |
$15$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
2500.3 |
\( 2^{2} \cdot 5^{4} \) |
\( 2^{2} \cdot 5^{14} \) |
$2.09566$ |
$(-a-1), (a-2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 5$ |
3B, 5B.4.2 |
$1$ |
\( 1 \) |
$1$ |
$1.910720194$ |
1.152207629 |
\( -\frac{25}{2} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 1\) , \( a - 1\) , \( 7 a + 12\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(a-1\right){x}+7a+12$ |
2500.3-b4 |
2500.3-b |
$4$ |
$15$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
2500.3 |
\( 2^{2} \cdot 5^{4} \) |
\( 2^{30} \cdot 5^{10} \) |
$2.09566$ |
$(-a-1), (a-2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 5$ |
3B, 5B.4.1 |
$1$ |
\( 3 \) |
$1$ |
$0.636906731$ |
1.152207629 |
\( \frac{46969655}{32768} \) |
\( \bigl[a\) , \( a - 1\) , \( a + 1\) , \( 64 a - 43\) , \( -102 a + 142\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(64a-43\right){x}-102a+142$ |
2500.3-c1 |
2500.3-c |
$2$ |
$5$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
2500.3 |
\( 2^{2} \cdot 5^{4} \) |
\( 2^{2} \cdot 5^{14} \) |
$2.09566$ |
$(-a-1), (a-2), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.4.1 |
$1$ |
\( 2^{3} \) |
$0.187131889$ |
$1.873441976$ |
3.382530227 |
\( -\frac{2632683}{6250} a + \frac{1560961}{6250} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a\) , \( -7 a + 6\) , \( -12 a + 13\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-7a+6\right){x}-12a+13$ |
2500.3-c2 |
2500.3-c |
$2$ |
$5$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
2500.3 |
\( 2^{2} \cdot 5^{4} \) |
\( 2^{10} \cdot 5^{10} \) |
$2.09566$ |
$(-a-1), (a-2), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.4.2 |
$1$ |
\( 2^{3} \cdot 5 \) |
$0.037426377$ |
$1.873441976$ |
3.382530227 |
\( -\frac{344373}{160} a + \frac{580523}{80} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -10 a - 7\) , \( 15 a + 14\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-10a-7\right){x}+15a+14$ |
2500.3-d1 |
2500.3-d |
$4$ |
$15$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
2500.3 |
\( 2^{2} \cdot 5^{4} \) |
\( 2^{6} \cdot 5^{14} \) |
$2.09566$ |
$(-a-1), (a-2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 5$ |
3B, 5B.4.2 |
$1$ |
\( 3 \) |
$1$ |
$0.636906731$ |
1.152207629 |
\( -\frac{349938025}{8} \) |
\( \bigl[a\) , \( 1\) , \( 1\) , \( -377 a + 251\) , \( -2207 a + 6069\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-377a+251\right){x}-2207a+6069$ |
2500.3-d2 |
2500.3-d |
$4$ |
$15$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
2500.3 |
\( 2^{2} \cdot 5^{4} \) |
\( 2^{10} \cdot 5^{10} \) |
$2.09566$ |
$(-a-1), (a-2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 5$ |
3B, 5B.4.1 |
$1$ |
\( 1 \) |
$1$ |
$1.910720194$ |
1.152207629 |
\( -\frac{121945}{32} \) |
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 8 a - 5\) , \( -9 a - 32\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(8a-5\right){x}-9a-32$ |
2500.3-d3 |
2500.3-d |
$4$ |
$15$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
2500.3 |
\( 2^{2} \cdot 5^{4} \) |
\( 2^{2} \cdot 5^{14} \) |
$2.09566$ |
$(-a-1), (a-2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 5$ |
3B, 5B.4.2 |
$1$ |
\( 1 \) |
$1$ |
$1.910720194$ |
1.152207629 |
\( -\frac{25}{2} \) |
\( \bigl[a\) , \( 1\) , \( 1\) , \( -2 a + 1\) , \( -7 a + 19\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-2a+1\right){x}-7a+19$ |
2500.3-d4 |
2500.3-d |
$4$ |
$15$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
2500.3 |
\( 2^{2} \cdot 5^{4} \) |
\( 2^{30} \cdot 5^{10} \) |
$2.09566$ |
$(-a-1), (a-2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 5$ |
3B, 5B.4.1 |
$1$ |
\( 3 \) |
$1$ |
$0.636906731$ |
1.152207629 |
\( \frac{46969655}{32768} \) |
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( -67 a + 20\) , \( 56 a + 238\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-67a+20\right){x}+56a+238$ |
2500.3-e1 |
2500.3-e |
$2$ |
$5$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
2500.3 |
\( 2^{2} \cdot 5^{4} \) |
\( 2^{2} \cdot 5^{14} \) |
$2.09566$ |
$(-a-1), (a-2), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.4.1 |
$1$ |
\( 2^{3} \) |
$0.187131889$ |
$1.873441976$ |
3.382530227 |
\( \frac{2632683}{6250} a - \frac{535861}{3125} \) |
\( \bigl[a\) , \( 1\) , \( a + 1\) , \( 5 a\) , \( 11 a + 1\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+5a{x}+11a+1$ |
2500.3-e2 |
2500.3-e |
$2$ |
$5$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
2500.3 |
\( 2^{2} \cdot 5^{4} \) |
\( 2^{10} \cdot 5^{10} \) |
$2.09566$ |
$(-a-1), (a-2), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.4.2 |
$1$ |
\( 2^{3} \cdot 5 \) |
$0.037426377$ |
$1.873441976$ |
3.382530227 |
\( \frac{344373}{160} a + \frac{816673}{160} \) |
\( \bigl[a + 1\) , \( a\) , \( 1\) , \( 9 a - 19\) , \( -22 a + 1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(9a-19\right){x}-22a+1$ |
2500.3-f1 |
2500.3-f |
$2$ |
$5$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
2500.3 |
\( 2^{2} \cdot 5^{4} \) |
\( 2^{2} \cdot 5^{20} \) |
$2.09566$ |
$(-a-1), (a-2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.1.4 |
$1$ |
\( 2^{2} \) |
$1$ |
$0.837828722$ |
2.020918916 |
\( \frac{2632683}{6250} a - \frac{535861}{3125} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -50\) , \( -81 a - 146\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-50{x}-81a-146$ |
2500.3-f2 |
2500.3-f |
$2$ |
$5$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
2500.3 |
\( 2^{2} \cdot 5^{4} \) |
\( 2^{10} \cdot 5^{16} \) |
$2.09566$ |
$(-a-1), (a-2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.1.3 |
$1$ |
\( 2^{2} \) |
$1$ |
$0.837828722$ |
2.020918916 |
\( \frac{344373}{160} a + \frac{816673}{160} \) |
\( \bigl[1\) , \( 0\) , \( a + 1\) , \( -38 a - 51\) , \( 168 a + 30\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-38a-51\right){x}+168a+30$ |
2500.3-g1 |
2500.3-g |
$2$ |
$5$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
2500.3 |
\( 2^{2} \cdot 5^{4} \) |
\( 2^{2} \cdot 5^{20} \) |
$2.09566$ |
$(-a-1), (a-2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.1.4 |
$1$ |
\( 2^{2} \) |
$1$ |
$0.837828722$ |
2.020918916 |
\( -\frac{2632683}{6250} a + \frac{1560961}{6250} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -2 a - 48\) , \( 80 a - 226\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2a-48\right){x}+80a-226$ |
2500.3-g2 |
2500.3-g |
$2$ |
$5$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
2500.3 |
\( 2^{2} \cdot 5^{4} \) |
\( 2^{10} \cdot 5^{16} \) |
$2.09566$ |
$(-a-1), (a-2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.1.3 |
$1$ |
\( 2^{2} \) |
$1$ |
$0.837828722$ |
2.020918916 |
\( -\frac{344373}{160} a + \frac{580523}{80} \) |
\( \bigl[1\) , \( 0\) , \( a\) , \( 37 a - 88\) , \( -169 a + 199\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(37a-88\right){x}-169a+199$ |
2500.3-h1 |
2500.3-h |
$4$ |
$15$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
2500.3 |
\( 2^{2} \cdot 5^{4} \) |
\( 2^{6} \cdot 5^{8} \) |
$2.09566$ |
$(-a-1), (a-2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 5$ |
3B.1.2, 5B.1.3 |
$1$ |
\( 3 \) |
$1$ |
$1.424166746$ |
2.576414584 |
\( -\frac{349938025}{8} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -126\) , \( -552\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-126{x}-552$ |
2500.3-h2 |
2500.3-h |
$4$ |
$15$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
2500.3 |
\( 2^{2} \cdot 5^{4} \) |
\( 2^{10} \cdot 5^{16} \) |
$2.09566$ |
$(-a-1), (a-2), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 5$ |
3B.1.1, 5B.1.4 |
$1$ |
\( 3^{2} \cdot 5 \) |
$1$ |
$0.854500048$ |
2.576414584 |
\( -\frac{121945}{32} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -76\) , \( 298\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-76{x}+298$ |
2500.3-h3 |
2500.3-h |
$4$ |
$15$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
2500.3 |
\( 2^{2} \cdot 5^{4} \) |
\( 2^{2} \cdot 5^{8} \) |
$2.09566$ |
$(-a-1), (a-2), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 5$ |
3B.1.1, 5B.1.3 |
$1$ |
\( 3^{2} \) |
$1$ |
$4.272500240$ |
2.576414584 |
\( -\frac{25}{2} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( -2\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}-2$ |
2500.3-h4 |
2500.3-h |
$4$ |
$15$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
2500.3 |
\( 2^{2} \cdot 5^{4} \) |
\( 2^{30} \cdot 5^{16} \) |
$2.09566$ |
$(-a-1), (a-2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 5$ |
3B.1.2, 5B.1.4 |
$1$ |
\( 3 \cdot 5 \) |
$1$ |
$0.284833349$ |
2.576414584 |
\( \frac{46969655}{32768} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 549\) , \( -2202\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+549{x}-2202$ |
*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.