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 |
28812.3-a1 |
28812.3-a |
$2$ |
$7$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28812.3 |
\( 2^{2} \cdot 3 \cdot 7^{4} \) |
\( 2^{14} \cdot 3^{14} \cdot 7^{16} \) |
$2.01647$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$7$ |
7B.1.6 |
$1$ |
\( 2 \cdot 7 \) |
$1$ |
$0.109168439$ |
1.764795976 |
\( -\frac{6329617441}{279936} \) |
\( \bigl[a\) , \( a - 1\) , \( 1\) , \( 6909 a\) , \( -232261\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+6909a{x}-232261$ |
28812.3-a2 |
28812.3-a |
$2$ |
$7$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28812.3 |
\( 2^{2} \cdot 3 \cdot 7^{4} \) |
\( 2^{2} \cdot 3^{2} \cdot 7^{16} \) |
$2.01647$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$7$ |
7B.1.4 |
$1$ |
\( 2 \) |
$1$ |
$0.764179074$ |
1.764795976 |
\( -\frac{2401}{6} \) |
\( \bigl[a\) , \( a - 1\) , \( 1\) , \( 49 a\) , \( 293\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+49a{x}+293$ |
28812.3-b1 |
28812.3-b |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28812.3 |
\( 2^{2} \cdot 3 \cdot 7^{4} \) |
\( 2^{30} \cdot 3^{2} \cdot 7^{20} \) |
$2.01647$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B[2] |
$1$ |
\( 2 \cdot 3 \cdot 5 \) |
$1$ |
$0.058440408$ |
2.024435147 |
\( -\frac{16591834777}{98304} \) |
\( \bigl[a + 1\) , \( a\) , \( 1\) , \( -34864 a + 34863\) , \( 2538800\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-34864a+34863\right){x}+2538800$ |
28812.3-b2 |
28812.3-b |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28812.3 |
\( 2^{2} \cdot 3 \cdot 7^{4} \) |
\( 2^{10} \cdot 3^{6} \cdot 7^{20} \) |
$2.01647$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B[2] |
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$0.175321226$ |
2.024435147 |
\( \frac{596183}{864} \) |
\( \bigl[a + 1\) , \( a\) , \( 1\) , \( 1151 a - 1152\) , \( 17750\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(1151a-1152\right){x}+17750$ |
28812.3-c1 |
28812.3-c |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28812.3 |
\( 2^{2} \cdot 3 \cdot 7^{4} \) |
\( 2^{8} \cdot 3^{8} \cdot 7^{18} \) |
$2.01647$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.229529190$ |
2.120299834 |
\( \frac{4913}{1296} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( 122\) , \( -10940\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+122{x}-10940$ |
28812.3-c2 |
28812.3-c |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28812.3 |
\( 2^{2} \cdot 3 \cdot 7^{4} \) |
\( 2^{4} \cdot 3^{16} \cdot 7^{18} \) |
$2.01647$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$1$ |
$0.114764595$ |
2.120299834 |
\( \frac{838561807}{26244} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -6738\) , \( -209880\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-6738{x}-209880$ |
28812.3-d1 |
28812.3-d |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28812.3 |
\( 2^{2} \cdot 3 \cdot 7^{4} \) |
\( 2^{2} \cdot 3^{4} \cdot 7^{21} \) |
$2.01647$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.245324381$ |
2.266209564 |
\( \frac{28037148049}{2117682} a - \frac{2552218955}{117649} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( -1109 a - 351\) , \( -21852 a + 4784\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-1109a-351\right){x}-21852a+4784$ |
28812.3-d2 |
28812.3-d |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28812.3 |
\( 2^{2} \cdot 3 \cdot 7^{4} \) |
\( 2^{4} \cdot 3^{2} \cdot 7^{18} \) |
$2.01647$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.490648763$ |
2.266209564 |
\( \frac{2016793}{4116} a - \frac{2483137}{4116} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( -129 a + 139\) , \( -586 a - 704\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-129a+139\right){x}-586a-704$ |
28812.3-e1 |
28812.3-e |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28812.3 |
\( 2^{2} \cdot 3 \cdot 7^{4} \) |
\( 2^{2} \cdot 3^{4} \cdot 7^{21} \) |
$2.01647$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.245324381$ |
2.266209564 |
\( -\frac{28037148049}{2117682} a - \frac{17902793141}{2117682} \) |
\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( -1461 a + 352\) , \( 21851 a - 17068\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-1461a+352\right){x}+21851a-17068$ |
28812.3-e2 |
28812.3-e |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28812.3 |
\( 2^{2} \cdot 3 \cdot 7^{4} \) |
\( 2^{4} \cdot 3^{2} \cdot 7^{18} \) |
$2.01647$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.490648763$ |
2.266209564 |
\( -\frac{2016793}{4116} a - \frac{38862}{343} \) |
\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( 9 a - 138\) , \( 585 a - 1290\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(9a-138\right){x}+585a-1290$ |
28812.3-f1 |
28812.3-f |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28812.3 |
\( 2^{2} \cdot 3 \cdot 7^{4} \) |
\( 2^{16} \cdot 3^{4} \cdot 7^{14} \) |
$2.01647$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{9} \) |
$0.138307751$ |
$0.391481047$ |
4.001350588 |
\( -\frac{7189057}{16128} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -197 a + 197\) , \( -2367\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-197a+197\right){x}-2367$ |
28812.3-f2 |
28812.3-f |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28812.3 |
\( 2^{2} \cdot 3 \cdot 7^{4} \) |
\( 2^{2} \cdot 3^{32} \cdot 7^{16} \) |
$2.01647$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$1.106462011$ |
$0.048935130$ |
4.001350588 |
\( \frac{6359387729183}{4218578658} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 18913 a - 18913\) , \( -381333\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(18913a-18913\right){x}-381333$ |
28812.3-f3 |
28812.3-f |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28812.3 |
\( 2^{2} \cdot 3 \cdot 7^{4} \) |
\( 2^{4} \cdot 3^{16} \cdot 7^{20} \) |
$2.01647$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{9} \) |
$0.553231005$ |
$0.097870261$ |
4.001350588 |
\( \frac{124475734657}{63011844} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -5097 a + 5097\) , \( -49995\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-5097a+5097\right){x}-49995$ |
28812.3-f4 |
28812.3-f |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28812.3 |
\( 2^{2} \cdot 3 \cdot 7^{4} \) |
\( 2^{2} \cdot 3^{8} \cdot 7^{28} \) |
$2.01647$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$1.106462011$ |
$0.048935130$ |
4.001350588 |
\( \frac{84448510979617}{933897762} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -44787 a + 44787\) , \( 3609423\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-44787a+44787\right){x}+3609423$ |
28812.3-f5 |
28812.3-f |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28812.3 |
\( 2^{2} \cdot 3 \cdot 7^{4} \) |
\( 2^{8} \cdot 3^{8} \cdot 7^{16} \) |
$2.01647$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{9} \) |
$0.276615502$ |
$0.195740523$ |
4.001350588 |
\( \frac{65597103937}{63504} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -4117 a + 4117\) , \( -101935\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-4117a+4117\right){x}-101935$ |
28812.3-f6 |
28812.3-f |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28812.3 |
\( 2^{2} \cdot 3 \cdot 7^{4} \) |
\( 2^{4} \cdot 3^{4} \cdot 7^{14} \) |
$2.01647$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{5} \) |
$0.553231005$ |
$0.097870261$ |
4.001350588 |
\( \frac{268498407453697}{252} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -65857 a + 65857\) , \( -6510547\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-65857a+65857\right){x}-6510547$ |
28812.3-g1 |
28812.3-g |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28812.3 |
\( 2^{2} \cdot 3 \cdot 7^{4} \) |
\( 2^{30} \cdot 3^{2} \cdot 7^{8} \) |
$2.01647$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.1[2] |
$1$ |
\( 2 \cdot 3^{3} \cdot 5 \) |
$0.141160516$ |
$0.409082862$ |
4.000784346 |
\( -\frac{16591834777}{98304} \) |
\( \bigl[a\) , \( 0\) , \( 1\) , \( 711 a\) , \( -7402\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+711a{x}-7402$ |
28812.3-g2 |
28812.3-g |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28812.3 |
\( 2^{2} \cdot 3 \cdot 7^{4} \) |
\( 2^{10} \cdot 3^{6} \cdot 7^{8} \) |
$2.01647$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.1[2] |
$1$ |
\( 2 \cdot 3^{3} \cdot 5 \) |
$0.047053505$ |
$1.227248586$ |
4.000784346 |
\( \frac{596183}{864} \) |
\( \bigl[a\) , \( 0\) , \( 1\) , \( -24 a\) , \( -52\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-24a{x}-52$ |
28812.3-h1 |
28812.3-h |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28812.3 |
\( 2^{2} \cdot 3 \cdot 7^{4} \) |
\( 2^{8} \cdot 3^{8} \cdot 7^{6} \) |
$2.01647$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$0.033626968$ |
$1.606704330$ |
3.992758292 |
\( \frac{4913}{1296} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 2\) , \( 32\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+2{x}+32$ |
28812.3-h2 |
28812.3-h |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28812.3 |
\( 2^{2} \cdot 3 \cdot 7^{4} \) |
\( 2^{4} \cdot 3^{16} \cdot 7^{6} \) |
$2.01647$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$0.067253936$ |
$0.803352165$ |
3.992758292 |
\( \frac{838561807}{26244} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -138\) , \( 592\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-138{x}+592$ |
28812.3-i1 |
28812.3-i |
$2$ |
$7$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28812.3 |
\( 2^{2} \cdot 3 \cdot 7^{4} \) |
\( 2^{14} \cdot 3^{14} \cdot 7^{4} \) |
$2.01647$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$7$ |
7B.1.1 |
$1$ |
\( 2 \cdot 7^{2} \) |
$1.160660403$ |
$0.764179074$ |
4.096657620 |
\( -\frac{6329617441}{279936} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 141 a\) , \( 657\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+141a{x}+657$ |
28812.3-i2 |
28812.3-i |
$2$ |
$7$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28812.3 |
\( 2^{2} \cdot 3 \cdot 7^{4} \) |
\( 2^{2} \cdot 3^{2} \cdot 7^{4} \) |
$2.01647$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$7$ |
7B.1.3 |
$1$ |
\( 2 \) |
$0.165808629$ |
$5.349253519$ |
4.096657620 |
\( -\frac{2401}{6} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( a\) , \( -1\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}-1$ |
*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.