| 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 |
| 86436.3-a1 |
86436.3-a |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
86436.3 |
\( 2^{2} \cdot 3^{2} \cdot 7^{4} \) |
\( 2^{30} \cdot 3^{8} \cdot 7^{14} \) |
$2.65383$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B[2] |
$1$ |
\( 2 \) |
$9.010310084$ |
$0.089269199$ |
3.715101942 |
\( -\frac{16591834777}{98304} \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 17076 a - 6404\) , \( 444105 a + 377489\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(17076a-6404\right){x}+444105a+377489$ |
| 86436.3-a2 |
86436.3-a |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
86436.3 |
\( 2^{2} \cdot 3^{2} \cdot 7^{4} \) |
\( 2^{10} \cdot 3^{12} \cdot 7^{14} \) |
$2.65383$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B[2] |
$1$ |
\( 2 \) |
$3.003436694$ |
$0.267807597$ |
3.715101942 |
\( \frac{596183}{864} \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -564 a + 211\) , \( 3105 a + 2639\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-564a+211\right){x}+3105a+2639$ |
| 86436.3-b1 |
86436.3-b |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
86436.3 |
\( 2^{2} \cdot 3^{2} \cdot 7^{4} \) |
\( 2^{8} \cdot 3^{14} \cdot 7^{12} \) |
$2.65383$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.350611629$ |
1.619405748 |
\( \frac{4913}{1296} \) |
\( \bigl[a\) , \( a\) , \( 1\) , \( 37 a - 60\) , \( -1935 a - 1645\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(37a-60\right){x}-1935a-1645$ |
| 86436.3-b2 |
86436.3-b |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
86436.3 |
\( 2^{2} \cdot 3^{2} \cdot 7^{4} \) |
\( 2^{4} \cdot 3^{22} \cdot 7^{12} \) |
$2.65383$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.175305814$ |
1.619405748 |
\( \frac{838561807}{26244} \) |
\( \bigl[a\) , \( a\) , \( 1\) , \( -2063 a + 3300\) , \( -35535 a - 30205\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-2063a+3300\right){x}-35535a-30205$ |
| 86436.3-c1 |
86436.3-c |
$2$ |
$7$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
86436.3 |
\( 2^{2} \cdot 3^{2} \cdot 7^{4} \) |
\( 2^{14} \cdot 3^{20} \cdot 7^{10} \) |
$2.65383$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$7$ |
7B.6.1 |
$1$ |
\( 2 \cdot 3 \) |
$1.586594667$ |
$0.166757545$ |
3.666081354 |
\( -\frac{6329617441}{279936} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( -3384 a + 2115\) , \( 39420 a - 72927\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(-3384a+2115\right){x}+39420a-72927$ |
| 86436.3-c2 |
86436.3-c |
$2$ |
$7$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
86436.3 |
\( 2^{2} \cdot 3^{2} \cdot 7^{4} \) |
\( 2^{2} \cdot 3^{8} \cdot 7^{10} \) |
$2.65383$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$7$ |
7B.6.3 |
$1$ |
\( 2 \cdot 3 \) |
$0.226656381$ |
$1.167302817$ |
3.666081354 |
\( -\frac{2401}{6} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( -24 a + 15\) , \( -60 a + 111\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(-24a+15\right){x}-60a+111$ |
| 86436.3-d1 |
86436.3-d |
$2$ |
$7$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
86436.3 |
\( 2^{2} \cdot 3^{2} \cdot 7^{4} \) |
\( 2^{14} \cdot 3^{20} \cdot 7^{10} \) |
$2.65383$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$7$ |
7B.6.1 |
$1$ |
\( 2 \cdot 3 \) |
$1.586594667$ |
$0.166757545$ |
3.666081354 |
\( -\frac{6329617441}{279936} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -1269 a - 2115\) , \( -39420 a - 33507\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-1269a-2115\right){x}-39420a-33507$ |
| 86436.3-d2 |
86436.3-d |
$2$ |
$7$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
86436.3 |
\( 2^{2} \cdot 3^{2} \cdot 7^{4} \) |
\( 2^{2} \cdot 3^{8} \cdot 7^{10} \) |
$2.65383$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$7$ |
7B.6.3 |
$1$ |
\( 2 \cdot 3 \) |
$0.226656381$ |
$1.167302817$ |
3.666081354 |
\( -\frac{2401}{6} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -9 a - 15\) , \( 60 a + 51\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-9a-15\right){x}+60a+51$ |
| 86436.3-e1 |
86436.3-e |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
86436.3 |
\( 2^{2} \cdot 3^{2} \cdot 7^{4} \) |
\( 2^{30} \cdot 3^{8} \cdot 7^{14} \) |
$2.65383$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B[2] |
$1$ |
\( 2 \) |
$9.010310084$ |
$0.089269199$ |
3.715101942 |
\( -\frac{16591834777}{98304} \) |
\( \bigl[1\) , \( a\) , \( 1\) , \( -17076 a + 10672\) , \( -444105 a + 821594\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-17076a+10672\right){x}-444105a+821594$ |
| 86436.3-e2 |
86436.3-e |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
86436.3 |
\( 2^{2} \cdot 3^{2} \cdot 7^{4} \) |
\( 2^{10} \cdot 3^{12} \cdot 7^{14} \) |
$2.65383$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B[2] |
$1$ |
\( 2 \) |
$3.003436694$ |
$0.267807597$ |
3.715101942 |
\( \frac{596183}{864} \) |
\( \bigl[1\) , \( a\) , \( 1\) , \( 564 a - 353\) , \( -3105 a + 5744\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(564a-353\right){x}-3105a+5744$ |
| 86436.3-f1 |
86436.3-f |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
86436.3 |
\( 2^{2} \cdot 3^{2} \cdot 7^{4} \) |
\( 2^{8} \cdot 3^{14} \cdot 7^{12} \) |
$2.65383$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.350611629$ |
1.619405748 |
\( \frac{4913}{1296} \) |
\( \bigl[a\) , \( -1\) , \( 1\) , \( -23 a + 60\) , \( 1935 a - 3580\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-23a+60\right){x}+1935a-3580$ |
| 86436.3-f2 |
86436.3-f |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
86436.3 |
\( 2^{2} \cdot 3^{2} \cdot 7^{4} \) |
\( 2^{4} \cdot 3^{22} \cdot 7^{12} \) |
$2.65383$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.175305814$ |
1.619405748 |
\( \frac{838561807}{26244} \) |
\( \bigl[a\) , \( -1\) , \( 1\) , \( 1237 a - 3300\) , \( 35535 a - 65740\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(1237a-3300\right){x}+35535a-65740$ |
| 86436.3-g1 |
86436.3-g |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
86436.3 |
\( 2^{2} \cdot 3^{2} \cdot 7^{4} \) |
\( 2^{2} \cdot 3^{10} \cdot 7^{15} \) |
$2.65383$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.662245288$ |
$0.374739182$ |
4.584978817 |
\( -\frac{28037148049}{2117682} a - \frac{17902793141}{2117682} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( 377 a + 275\) , \( 4394 a - 6257\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(377a+275\right){x}+4394a-6257$ |
| 86436.3-g2 |
86436.3-g |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
86436.3 |
\( 2^{2} \cdot 3^{2} \cdot 7^{4} \) |
\( 2^{4} \cdot 3^{8} \cdot 7^{12} \) |
$2.65383$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.331122644$ |
$0.749478365$ |
4.584978817 |
\( -\frac{2016793}{4116} a - \frac{38862}{343} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( -43 a + 65\) , \( -58 a - 251\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-43a+65\right){x}-58a-251$ |
| 86436.3-h1 |
86436.3-h |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
86436.3 |
\( 2^{2} \cdot 3^{2} \cdot 7^{4} \) |
\( 2^{6} \cdot 3^{6} \cdot 7^{4} \) |
$2.65383$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B[2] |
$1$ |
\( 2 \cdot 3 \) |
$0.213735627$ |
$1.498465456$ |
4.437866884 |
\( -\frac{67645179}{8} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -93\) , \( -323\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-93{x}-323$ |
| 86436.3-h2 |
86436.3-h |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
86436.3 |
\( 2^{2} \cdot 3^{2} \cdot 7^{4} \) |
\( 2^{18} \cdot 3^{6} \cdot 7^{4} \) |
$2.65383$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B[2] |
$1$ |
\( 2 \cdot 3^{2} \) |
$0.071245209$ |
$1.498465456$ |
4.437866884 |
\( \frac{189}{512} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 1\) , \( 39\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+{x}+39$ |
| 86436.3-i1 |
86436.3-i |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
86436.3 |
\( 2^{2} \cdot 3^{2} \cdot 7^{4} \) |
\( 2^{2} \cdot 3^{10} \cdot 7^{15} \) |
$2.65383$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.662245288$ |
$0.374739182$ |
4.584978817 |
\( \frac{28037148049}{2117682} a - \frac{2552218955}{117649} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( 650 a - 275\) , \( -3743 a - 2138\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(650a-275\right){x}-3743a-2138$ |
| 86436.3-i2 |
86436.3-i |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
86436.3 |
\( 2^{2} \cdot 3^{2} \cdot 7^{4} \) |
\( 2^{4} \cdot 3^{8} \cdot 7^{12} \) |
$2.65383$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.331122644$ |
$0.749478365$ |
4.584978817 |
\( \frac{2016793}{4116} a - \frac{2483137}{4116} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( 20 a - 65\) , \( 79 a - 374\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(20a-65\right){x}+79a-374$ |
| 86436.3-j1 |
86436.3-j |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
86436.3 |
\( 2^{2} \cdot 3^{2} \cdot 7^{4} \) |
\( 2^{6} \cdot 3^{6} \cdot 7^{16} \) |
$2.65383$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.1[2] |
$1$ |
\( 2 \cdot 3^{3} \) |
$1.646058679$ |
$0.214066493$ |
4.882526660 |
\( -\frac{67645179}{8} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -4566 a + 4566\) , \( 119916\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-4566a+4566\right){x}+119916$ |
| 86436.3-j2 |
86436.3-j |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
86436.3 |
\( 2^{2} \cdot 3^{2} \cdot 7^{4} \) |
\( 2^{18} \cdot 3^{6} \cdot 7^{16} \) |
$2.65383$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.1[2] |
$1$ |
\( 2 \cdot 3^{4} \) |
$0.548686226$ |
$0.214066493$ |
4.882526660 |
\( \frac{189}{512} \) |
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 64 a - 65\) , \( -13597\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(64a-65\right){x}-13597$ |
*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.
