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 |
1.1-a1 |
1.1-a |
$4$ |
$14$ |
\(\Q(\sqrt{301}) \) |
$2$ |
$[2, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$1.55032$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-7$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
$43$ |
43Ns.9.1 |
$1$ |
\( 1 \) |
$1$ |
$26.16385905$ |
0.377014941 |
\( -3375 \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( 400 a - 3665\) , \( -12979 a + 119119\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(400a-3665\right){x}-12979a+119119$ |
1.1-a2 |
1.1-a |
$4$ |
$14$ |
\(\Q(\sqrt{301}) \) |
$2$ |
$[2, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$1.55032$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-7$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
$43$ |
43Ns.9.1 |
$1$ |
\( 1 \) |
$1$ |
$26.16385905$ |
0.377014941 |
\( -3375 \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -402 a - 3265\) , \( 12978 a + 106140\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-402a-3265\right){x}+12978a+106140$ |
1.1-a3 |
1.1-a |
$4$ |
$14$ |
\(\Q(\sqrt{301}) \) |
$2$ |
$[2, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$1.55032$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-28$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
$43$ |
43Ns.9.1 |
$1$ |
\( 1 \) |
$1$ |
$26.16385905$ |
0.377014941 |
\( 16581375 \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( 6955 a - 63805\) , \( -874060 a + 8019258\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(6955a-63805\right){x}-874060a+8019258$ |
1.1-a4 |
1.1-a |
$4$ |
$14$ |
\(\Q(\sqrt{301}) \) |
$2$ |
$[2, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$1.55032$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-28$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
$43$ |
43Ns.9.1 |
$1$ |
\( 1 \) |
$1$ |
$26.16385905$ |
0.377014941 |
\( 16581375 \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -6957 a - 56850\) , \( 874059 a + 7145198\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-6957a-56850\right){x}+874059a+7145198$ |
3.1-a1 |
3.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{301}) \) |
$2$ |
$[2, 0]$ |
3.1 |
\( 3 \) |
\( - 3^{3} \) |
$2.04034$ |
$(-a+9)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 3 \) |
$0.554611758$ |
$20.97578440$ |
4.023233935 |
\( \frac{5404}{27} a + \frac{22925}{27} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -76 a - 398\) , \( 200 a + 2277\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-76a-398\right){x}+200a+2277$ |
3.1-b1 |
3.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{301}) \) |
$2$ |
$[2, 0]$ |
3.1 |
\( 3 \) |
\( - 3^{3} \) |
$2.04034$ |
$(-a+9)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 1 \) |
$0.221630154$ |
$40.46933302$ |
2.067910033 |
\( \frac{5404}{27} a + \frac{22925}{27} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( 4331 a - 39735\) , \( -815041 a + 7477737\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(4331a-39735\right){x}-815041a+7477737$ |
3.2-a1 |
3.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{301}) \) |
$2$ |
$[2, 0]$ |
3.2 |
\( 3 \) |
\( - 3^{3} \) |
$2.04034$ |
$(-a-8)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 3 \) |
$0.554611758$ |
$20.97578440$ |
4.023233935 |
\( -\frac{5404}{27} a + \frac{9443}{9} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 76 a - 474\) , \( -200 a + 2477\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(76a-474\right){x}-200a+2477$ |
3.2-b1 |
3.2-b |
$1$ |
$1$ |
\(\Q(\sqrt{301}) \) |
$2$ |
$[2, 0]$ |
3.2 |
\( 3 \) |
\( - 3^{3} \) |
$2.04034$ |
$(-a-8)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 1 \) |
$0.221630154$ |
$40.46933302$ |
2.067910033 |
\( -\frac{5404}{27} a + \frac{9443}{9} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -4331 a - 35404\) , \( 815041 a + 6662696\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(-4331a-35404\right){x}+815041a+6662696$ |
9.2-a1 |
9.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{301}) \) |
$2$ |
$[2, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{9} \) |
$2.68524$ |
$(-a+9)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Ns |
$1$ |
\( 2^{2} \) |
$1.152714218$ |
$10.13145612$ |
5.385180412 |
\( \frac{5404}{27} a + \frac{22925}{27} \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( 1277529 a - 11720610\) , \( 4141777236 a - 37999462298\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(1277529a-11720610\right){x}+4141777236a-37999462298$ |
9.2-b1 |
9.2-b |
$1$ |
$1$ |
\(\Q(\sqrt{301}) \) |
$2$ |
$[2, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{9} \) |
$2.68524$ |
$(-a+9)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Ns |
$1$ |
\( 2 \) |
$0.870390261$ |
$27.92872660$ |
5.604564885 |
\( \frac{5404}{27} a + \frac{22925}{27} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 20 a + 168\) , \( 64 a + 525\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(20a+168\right){x}+64a+525$ |
9.2-c1 |
9.2-c |
$4$ |
$14$ |
\(\Q(\sqrt{301}) \) |
$2$ |
$[2, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{6} \) |
$2.68524$ |
$(-a+9)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-7$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$43$ |
43Ns.3.1 |
$1$ |
\( 2 \) |
$2.358552390$ |
$39.96595486$ |
5.433159735 |
\( -3375 \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( -13 a - 102\) , \( 90 a + 719\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-13a-102\right){x}+90a+719$ |
9.2-c2 |
9.2-c |
$4$ |
$14$ |
\(\Q(\sqrt{301}) \) |
$2$ |
$[2, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{6} \) |
$2.68524$ |
$(-a+9)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-7$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$43$ |
43Ns.3.1 |
$1$ |
\( 2 \) |
$16.50986673$ |
$5.709422123$ |
5.433159735 |
\( -3375 \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 120854 a - 1108595\) , \( 83293389 a - 764189269\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(120854a-1108595\right){x}+83293389a-764189269$ |
9.2-c3 |
9.2-c |
$4$ |
$14$ |
\(\Q(\sqrt{301}) \) |
$2$ |
$[2, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{6} \) |
$2.68524$ |
$(-a+9)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-28$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$43$ |
43Ns.3.1 |
$1$ |
\( 2^{2} \) |
$1.179276195$ |
$39.96595486$ |
5.433159735 |
\( 16581375 \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( -213 a - 1737\) , \( 5019 a + 41012\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-213a-1737\right){x}+5019a+41012$ |
9.2-c4 |
9.2-c |
$4$ |
$14$ |
\(\Q(\sqrt{301}) \) |
$2$ |
$[2, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{6} \) |
$2.68524$ |
$(-a+9)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-28$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$43$ |
43Ns.3.1 |
$1$ |
\( 2^{2} \) |
$8.254933368$ |
$5.709422123$ |
5.433159735 |
\( 16581375 \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 2054379 a - 18848060\) , \( 4728597369 a - 43383347215\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(2054379a-18848060\right){x}+4728597369a-43383347215$ |
9.3-a1 |
9.3-a |
$1$ |
$1$ |
\(\Q(\sqrt{301}) \) |
$2$ |
$[2, 0]$ |
9.3 |
\( 3^{2} \) |
\( - 3^{9} \) |
$2.68524$ |
$(-a-8)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Ns |
$1$ |
\( 2^{2} \) |
$1.152714218$ |
$10.13145612$ |
5.385180412 |
\( -\frac{5404}{27} a + \frac{9443}{9} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( -1277489 a - 10443044\) , \( -4153497845 a - 33953498256\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-1277489a-10443044\right){x}-4153497845a-33953498256$ |
9.3-b1 |
9.3-b |
$1$ |
$1$ |
\(\Q(\sqrt{301}) \) |
$2$ |
$[2, 0]$ |
9.3 |
\( 3^{2} \) |
\( - 3^{9} \) |
$2.68524$ |
$(-a-8)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Ns |
$1$ |
\( 2 \) |
$0.870390261$ |
$27.92872660$ |
5.604564885 |
\( -\frac{5404}{27} a + \frac{9443}{9} \) |
\( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( 18 a + 113\) , \( 66 a + 495\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(18a+113\right){x}+66a+495$ |
9.3-c1 |
9.3-c |
$4$ |
$14$ |
\(\Q(\sqrt{301}) \) |
$2$ |
$[2, 0]$ |
9.3 |
\( 3^{2} \) |
\( 3^{6} \) |
$2.68524$ |
$(-a-8)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-7$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$43$ |
43Ns.3.1 |
$1$ |
\( 2 \) |
$16.50986673$ |
$5.709422123$ |
5.433159735 |
\( -3375 \) |
\( \bigl[a\) , \( -a\) , \( 1\) , \( -120855 a - 987740\) , \( -83293389 a - 680895880\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-120855a-987740\right){x}-83293389a-680895880$ |
9.3-c2 |
9.3-c |
$4$ |
$14$ |
\(\Q(\sqrt{301}) \) |
$2$ |
$[2, 0]$ |
9.3 |
\( 3^{2} \) |
\( 3^{6} \) |
$2.68524$ |
$(-a-8)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-7$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$43$ |
43Ns.3.1 |
$1$ |
\( 2 \) |
$2.358552390$ |
$39.96595486$ |
5.433159735 |
\( -3375 \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 12 a - 115\) , \( -91 a + 809\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(12a-115\right){x}-91a+809$ |
9.3-c3 |
9.3-c |
$4$ |
$14$ |
\(\Q(\sqrt{301}) \) |
$2$ |
$[2, 0]$ |
9.3 |
\( 3^{2} \) |
\( 3^{6} \) |
$2.68524$ |
$(-a-8)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-28$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$43$ |
43Ns.3.1 |
$1$ |
\( 2^{2} \) |
$8.254933368$ |
$5.709422123$ |
5.433159735 |
\( 16581375 \) |
\( \bigl[a\) , \( -a\) , \( 1\) , \( -2054380 a - 16793680\) , \( -4728597369 a - 38654749846\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-2054380a-16793680\right){x}-4728597369a-38654749846$ |
9.3-c4 |
9.3-c |
$4$ |
$14$ |
\(\Q(\sqrt{301}) \) |
$2$ |
$[2, 0]$ |
9.3 |
\( 3^{2} \) |
\( 3^{6} \) |
$2.68524$ |
$(-a-8)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-28$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$43$ |
43Ns.3.1 |
$1$ |
\( 2^{2} \) |
$1.179276195$ |
$39.96595486$ |
5.433159735 |
\( 16581375 \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 212 a - 1950\) , \( -5020 a + 46031\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(212a-1950\right){x}-5020a+46031$ |
15.1-a1 |
15.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{301}) \) |
$2$ |
$[2, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{6} \cdot 5^{2} \) |
$3.05102$ |
$(-a+9), (-6a+55)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$1$ |
$18.93354958$ |
4.365246621 |
\( -\frac{403177472}{18225} a - \frac{3273392128}{18225} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -1910572 a + 17528879\) , \( 2687078497 a - 24653074023\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}+\left(-1910572a+17528879\right){x}+2687078497a-24653074023$ |
15.1-a2 |
15.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{301}) \) |
$2$ |
$[2, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{2} \cdot 5^{6} \) |
$3.05102$ |
$(-a+9), (-6a+55)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$1$ |
$18.93354958$ |
4.365246621 |
\( \frac{24051712}{140625} a - \frac{169050112}{140625} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( 90938 a + 743389\) , \( 84627209 a + 691799996\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}+\left(90938a+743389\right){x}+84627209a+691799996$ |
15.1-b1 |
15.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{301}) \) |
$2$ |
$[2, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{6} \cdot 5^{2} \) |
$3.05102$ |
$(-a+9), (-6a+55)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$5.384850921$ |
3.724531766 |
\( -\frac{403177472}{18225} a - \frac{3273392128}{18225} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -8 a - 65\) , \( -39 a - 319\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}+\left(-8a-65\right){x}-39a-319$ |
15.1-b2 |
15.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{301}) \) |
$2$ |
$[2, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{2} \cdot 5^{6} \) |
$3.05102$ |
$(-a+9), (-6a+55)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$5.384850921$ |
3.724531766 |
\( \frac{24051712}{140625} a - \frac{169050112}{140625} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( 42 a - 385\) , \( 577 a - 5294\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}+\left(42a-385\right){x}+577a-5294$ |
15.2-a1 |
15.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{301}) \) |
$2$ |
$[2, 0]$ |
15.2 |
\( 3 \cdot 5 \) |
\( 3^{3} \cdot 5^{9} \) |
$3.05102$ |
$(-a-8), (-6a+55)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 3^{2} \) |
$0.742329761$ |
$6.799969143$ |
5.237126591 |
\( \frac{3565416510442094}{52734375} a - \frac{10903846831184923}{17578125} \) |
\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( 249169 a - 2286010\) , \( -197430230 a + 1811358398\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(249169a-2286010\right){x}-197430230a+1811358398$ |
15.2-b1 |
15.2-b |
$1$ |
$1$ |
\(\Q(\sqrt{301}) \) |
$2$ |
$[2, 0]$ |
15.2 |
\( 3 \cdot 5 \) |
\( 3 \cdot 5 \) |
$3.05102$ |
$(-a-8), (-6a+55)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$54.53642909$ |
3.143427514 |
\( -\frac{3368038}{15} a - \frac{9182149}{5} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( 16 a + 106\) , \( 45 a + 353\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(16a+106\right){x}+45a+353$ |
15.2-c1 |
15.2-c |
$1$ |
$1$ |
\(\Q(\sqrt{301}) \) |
$2$ |
$[2, 0]$ |
15.2 |
\( 3 \cdot 5 \) |
\( 3 \cdot 5 \) |
$3.05102$ |
$(-a-8), (-6a+55)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$4.829291155$ |
0.278355714 |
\( -\frac{3368038}{15} a - \frac{9182149}{5} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( 561064 a - 5147318\) , \( 1143855488 a - 10494502248\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(561064a-5147318\right){x}+1143855488a-10494502248$ |
15.2-d1 |
15.2-d |
$1$ |
$1$ |
\(\Q(\sqrt{301}) \) |
$2$ |
$[2, 0]$ |
15.2 |
\( 3 \cdot 5 \) |
\( 3^{3} \cdot 5^{9} \) |
$3.05102$ |
$(-a-8), (-6a+55)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 3 \) |
$2.476069346$ |
$1.723394042$ |
1.475758840 |
\( \frac{3565416510442094}{52734375} a - \frac{10903846831184923}{17578125} \) |
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 1026 a + 8446\) , \( 2723356 a + 22262631\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(1026a+8446\right){x}+2723356a+22262631$ |
15.3-a1 |
15.3-a |
$1$ |
$1$ |
\(\Q(\sqrt{301}) \) |
$2$ |
$[2, 0]$ |
15.3 |
\( 3 \cdot 5 \) |
\( 3^{3} \cdot 5^{9} \) |
$3.05102$ |
$(-a+9), (6a+49)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 3^{2} \) |
$0.742329761$ |
$6.799969143$ |
5.237126591 |
\( -\frac{3565416510442094}{52734375} a - \frac{1165844959324507}{2109375} \) |
\( \bigl[a + 1\) , \( 1\) , \( a\) , \( -249169 a - 2036841\) , \( 197181061 a + 1611891327\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-249169a-2036841\right){x}+197181061a+1611891327$ |
15.3-b1 |
15.3-b |
$1$ |
$1$ |
\(\Q(\sqrt{301}) \) |
$2$ |
$[2, 0]$ |
15.3 |
\( 3 \cdot 5 \) |
\( 3 \cdot 5 \) |
$3.05102$ |
$(-a+9), (6a+49)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$54.53642909$ |
3.143427514 |
\( \frac{3368038}{15} a - \frac{6182897}{3} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 22 a + 123\) , \( 61 a + 567\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(22a+123\right){x}+61a+567$ |
15.3-c1 |
15.3-c |
$1$ |
$1$ |
\(\Q(\sqrt{301}) \) |
$2$ |
$[2, 0]$ |
15.3 |
\( 3 \cdot 5 \) |
\( 3 \cdot 5 \) |
$3.05102$ |
$(-a+9), (6a+49)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$4.829291155$ |
0.278355714 |
\( \frac{3368038}{15} a - \frac{6182897}{3} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( -561025 a - 4586216\) , \( -1149002768 a - 9392725116\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-561025a-4586216\right){x}-1149002768a-9392725116$ |
15.3-d1 |
15.3-d |
$1$ |
$1$ |
\(\Q(\sqrt{301}) \) |
$2$ |
$[2, 0]$ |
15.3 |
\( 3 \cdot 5 \) |
\( 3^{3} \cdot 5^{9} \) |
$3.05102$ |
$(-a+9), (6a+49)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 3 \) |
$2.476069346$ |
$1.723394042$ |
1.475758840 |
\( -\frac{3565416510442094}{52734375} a - \frac{1165844959324507}{2109375} \) |
\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -1027 a + 9473\) , \( -2723356 a + 24985987\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-1027a+9473\right){x}-2723356a+24985987$ |
15.4-a1 |
15.4-a |
$2$ |
$3$ |
\(\Q(\sqrt{301}) \) |
$2$ |
$[2, 0]$ |
15.4 |
\( 3 \cdot 5 \) |
\( 3^{2} \cdot 5^{6} \) |
$3.05102$ |
$(-a-8), (6a+49)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$1$ |
$18.93354958$ |
4.365246621 |
\( -\frac{24051712}{140625} a - \frac{1933312}{1875} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -90938 a + 834327\) , \( -84627209 a + 776427205\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}+\left(-90938a+834327\right){x}-84627209a+776427205$ |
15.4-a2 |
15.4-a |
$2$ |
$3$ |
\(\Q(\sqrt{301}) \) |
$2$ |
$[2, 0]$ |
15.4 |
\( 3 \cdot 5 \) |
\( 3^{6} \cdot 5^{2} \) |
$3.05102$ |
$(-a-8), (6a+49)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$1$ |
$18.93354958$ |
4.365246621 |
\( \frac{403177472}{18225} a - \frac{49020928}{243} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( 1910572 a + 15618307\) , \( -2687078497 a - 21965995526\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}+\left(1910572a+15618307\right){x}-2687078497a-21965995526$ |
15.4-b1 |
15.4-b |
$2$ |
$3$ |
\(\Q(\sqrt{301}) \) |
$2$ |
$[2, 0]$ |
15.4 |
\( 3 \cdot 5 \) |
\( 3^{2} \cdot 5^{6} \) |
$3.05102$ |
$(-a-8), (6a+49)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$5.384850921$ |
3.724531766 |
\( -\frac{24051712}{140625} a - \frac{1933312}{1875} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -42 a - 343\) , \( -577 a - 4717\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}+\left(-42a-343\right){x}-577a-4717$ |
15.4-b2 |
15.4-b |
$2$ |
$3$ |
\(\Q(\sqrt{301}) \) |
$2$ |
$[2, 0]$ |
15.4 |
\( 3 \cdot 5 \) |
\( 3^{6} \cdot 5^{2} \) |
$3.05102$ |
$(-a-8), (6a+49)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$5.384850921$ |
3.724531766 |
\( \frac{403177472}{18225} a - \frac{49020928}{243} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( 8 a - 73\) , \( 39 a - 358\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}+\left(8a-73\right){x}+39a-358$ |
20.1-a1 |
20.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{301}) \) |
$2$ |
$[2, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( - 2^{6} \cdot 5 \) |
$3.27853$ |
$(-6a+55), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$4$ |
\( 1 \) |
$1$ |
$22.28759743$ |
5.138543038 |
\( -\frac{102081}{20} a + \frac{1870817}{40} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 11440 a - 104961\) , \( 2035889 a - 18678595\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(11440a-104961\right){x}+2035889a-18678595$ |
20.1-a2 |
20.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{301}) \) |
$2$ |
$[2, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( - 2^{2} \cdot 5^{3} \) |
$3.27853$ |
$(-6a+55), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$4$ |
\( 1 \) |
$1$ |
$22.28759743$ |
5.138543038 |
\( -\frac{486003}{250} a + \frac{2236489}{125} \) |
\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( 4082737 a + 33375119\) , \( -72075964995 a - 589197645731\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(4082737a+33375119\right){x}-72075964995a-589197645731$ |
20.1-b1 |
20.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{301}) \) |
$2$ |
$[2, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( - 2^{6} \cdot 5 \) |
$3.27853$ |
$(-6a+55), (2)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
|
\( 1 \) |
$1$ |
$5.049999803$ |
6.703766758 |
\( -\frac{5031337703}{40} a - \frac{41129472787}{40} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( -20678976 a - 169043910\) , \( -151007863785 a - 1234440327640\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-20678976a-169043910\right){x}-151007863785a-1234440327640$ |
20.1-c1 |
20.1-c |
$1$ |
$1$ |
\(\Q(\sqrt{301}) \) |
$2$ |
$[2, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( - 2^{6} \cdot 5 \) |
$3.27853$ |
$(-6a+55), (2)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.552386710$ |
$31.00673775$ |
3.948899142 |
\( -\frac{5031337703}{40} a - \frac{41129472787}{40} \) |
\( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( 20 a + 94\) , \( 80 a + 360\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(20a+94\right){x}+80a+360$ |
20.1-d1 |
20.1-d |
$2$ |
$3$ |
\(\Q(\sqrt{301}) \) |
$2$ |
$[2, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( - 2^{6} \cdot 5 \) |
$3.27853$ |
$(-6a+55), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.734562548$ |
$20.58488197$ |
1.743106455 |
\( -\frac{102081}{20} a + \frac{1870817}{40} \) |
\( \bigl[a + 1\) , \( 0\) , \( a\) , \( -68 a - 530\) , \( -6625 a - 54095\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-68a-530\right){x}-6625a-54095$ |
20.1-d2 |
20.1-d |
$2$ |
$3$ |
\(\Q(\sqrt{301}) \) |
$2$ |
$[2, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( - 2^{2} \cdot 5^{3} \) |
$3.27853$ |
$(-6a+55), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \) |
$0.244854182$ |
$20.58488197$ |
1.743106455 |
\( -\frac{486003}{250} a + \frac{2236489}{125} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -10 a + 105\) , \( -31 a + 343\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-10a+105\right){x}-31a+343$ |
20.2-a1 |
20.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{301}) \) |
$2$ |
$[2, 0]$ |
20.2 |
\( 2^{2} \cdot 5 \) |
\( - 2^{2} \cdot 5^{3} \) |
$3.27853$ |
$(6a+49), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$4$ |
\( 1 \) |
$1$ |
$22.28759743$ |
5.138543038 |
\( \frac{486003}{250} a + \frac{159479}{10} \) |
\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( -4082737 a + 37457781\) , \( 72080047731 a - 661311068582\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-4082737a+37457781\right){x}+72080047731a-661311068582$ |
20.2-a2 |
20.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{301}) \) |
$2$ |
$[2, 0]$ |
20.2 |
\( 2^{2} \cdot 5 \) |
\( - 2^{6} \cdot 5 \) |
$3.27853$ |
$(6a+49), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$4$ |
\( 1 \) |
$1$ |
$22.28759743$ |
5.138543038 |
\( \frac{102081}{20} a + \frac{333331}{8} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -11439 a - 93446\) , \( -2047329 a - 16736152\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-11439a-93446\right){x}-2047329a-16736152$ |
20.2-b1 |
20.2-b |
$1$ |
$1$ |
\(\Q(\sqrt{301}) \) |
$2$ |
$[2, 0]$ |
20.2 |
\( 2^{2} \cdot 5 \) |
\( - 2^{6} \cdot 5 \) |
$3.27853$ |
$(6a+49), (2)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
|
\( 1 \) |
$1$ |
$5.049999803$ |
6.703766758 |
\( \frac{5031337703}{40} a - \frac{4616081049}{4} \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( 20679016 a - 189722963\) , \( 150818140823 a - 1383707543744\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(20679016a-189722963\right){x}+150818140823a-1383707543744$ |
20.2-c1 |
20.2-c |
$1$ |
$1$ |
\(\Q(\sqrt{301}) \) |
$2$ |
$[2, 0]$ |
20.2 |
\( 2^{2} \cdot 5 \) |
\( - 2^{6} \cdot 5 \) |
$3.27853$ |
$(6a+49), (2)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.552386710$ |
$31.00673775$ |
3.948899142 |
\( \frac{5031337703}{40} a - \frac{4616081049}{4} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 18 a + 151\) , \( 33 a + 271\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(18a+151\right){x}+33a+271$ |
20.2-d1 |
20.2-d |
$2$ |
$3$ |
\(\Q(\sqrt{301}) \) |
$2$ |
$[2, 0]$ |
20.2 |
\( 2^{2} \cdot 5 \) |
\( - 2^{2} \cdot 5^{3} \) |
$3.27853$ |
$(6a+49), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \) |
$0.244854182$ |
$20.58488197$ |
1.743106455 |
\( \frac{486003}{250} a + \frac{159479}{10} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 8 a + 95\) , \( 30 a + 312\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(8a+95\right){x}+30a+312$ |
20.2-d2 |
20.2-d |
$2$ |
$3$ |
\(\Q(\sqrt{301}) \) |
$2$ |
$[2, 0]$ |
20.2 |
\( 2^{2} \cdot 5 \) |
\( - 2^{6} \cdot 5 \) |
$3.27853$ |
$(6a+49), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.734562548$ |
$20.58488197$ |
1.743106455 |
\( \frac{102081}{20} a + \frac{333331}{8} \) |
\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( 66 a - 597\) , \( 6624 a - 60720\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(66a-597\right){x}+6624a-60720$ |
25.1-a1 |
25.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{301}) \) |
$2$ |
$[2, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{6} \) |
$3.46662$ |
$(-6a+55), (6a+49)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$3$ |
3Nn |
$1$ |
\( 3 \) |
$1.199506422$ |
$12.17791294$ |
5.051768556 |
\( -\frac{110592}{125} \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -1311 a - 10717\) , \( -130778 a - 1069068\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-1311a-10717\right){x}-130778a-1069068$ |
25.1-b1 |
25.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{301}) \) |
$2$ |
$[2, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{6} \) |
$3.46662$ |
$(-6a+55), (6a+49)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$3$ |
3Nn |
$1$ |
\( 3 \) |
$1.199506422$ |
$12.17791294$ |
5.051768556 |
\( -\frac{110592}{125} \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 1311 a - 12028\) , \( 130778 a - 1199846\bigr] \) |
${y}^2+{y}={x}^{3}+\left(1311a-12028\right){x}+130778a-1199846$ |
*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.