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 |
375.2-a1 |
375.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
375.2 |
\( 3 \cdot 5^{3} \) |
\( - 3 \cdot 5^{11} \) |
$1.92642$ |
$(a+3), (-a-1), (-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.040625144$ |
$10.53250423$ |
4.474559968 |
\( -\frac{208058}{75} a + \frac{33551}{25} \) |
\( \bigl[a + 1\) , \( a\) , \( 1\) , \( a - 4\) , \( a - 1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(a-4\right){x}+a-1$ |
375.2-a2 |
375.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
375.2 |
\( 3 \cdot 5^{3} \) |
\( - 3^{2} \cdot 5^{13} \) |
$1.92642$ |
$(a+3), (-a-1), (-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.520312572$ |
$5.266252119$ |
4.474559968 |
\( \frac{14550280309}{1875} a + \frac{35641186181}{1875} \) |
\( \bigl[a + 1\) , \( a\) , \( 1\) , \( -34 a - 69\) , \( 112 a + 223\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-34a-69\right){x}+112a+223$ |
375.2-b1 |
375.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
375.2 |
\( 3 \cdot 5^{3} \) |
\( - 3 \cdot 5^{11} \) |
$1.92642$ |
$(a+3), (-a-1), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$5.373592794$ |
1.096880035 |
\( -\frac{208058}{75} a + \frac{33551}{25} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( 168 a - 410\) , \( -1498 a + 3669\bigr] \) |
${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(168a-410\right){x}-1498a+3669$ |
375.2-b2 |
375.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
375.2 |
\( 3 \cdot 5^{3} \) |
\( - 3^{2} \cdot 5^{13} \) |
$1.92642$ |
$(a+3), (-a-1), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.686796397$ |
1.096880035 |
\( \frac{14550280309}{1875} a + \frac{35641186181}{1875} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( -247 a + 605\) , \( -8721 a + 21362\bigr] \) |
${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(-247a+605\right){x}-8721a+21362$ |
375.2-c1 |
375.2-c |
$4$ |
$10$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
375.2 |
\( 3 \cdot 5^{3} \) |
\( - 3 \cdot 5^{5} \) |
$1.92642$ |
$(a+3), (-a-1), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B.4.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$20.38989080$ |
4.162069031 |
\( -\frac{81720253739776}{75} a + \frac{66724211524672}{25} \) |
\( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( 1241 a - 3040\) , \( -37209 a + 91141\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(1241a-3040\right){x}-37209a+91141$ |
375.2-c2 |
375.2-c |
$4$ |
$10$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
375.2 |
\( 3 \cdot 5^{3} \) |
\( - 3^{5} \cdot 5^{13} \) |
$1.92642$ |
$(a+3), (-a-1), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$4.077978161$ |
4.162069031 |
\( -\frac{8297016064}{263671875} a + \frac{155957523008}{87890625} \) |
\( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( 356 a + 870\) , \( -179 a - 439\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(356a+870\right){x}-179a-439$ |
375.2-c3 |
375.2-c |
$4$ |
$10$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
375.2 |
\( 3 \cdot 5^{3} \) |
\( 3^{10} \cdot 5^{8} \) |
$1.92642$ |
$(a+3), (-a-1), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$4.077978161$ |
4.162069031 |
\( -\frac{109693837568}{759375} a + \frac{270029745088}{759375} \) |
\( \bigl[a\) , \( 1\) , \( 1\) , \( 11 a - 44\) , \( 59 a - 163\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(11a-44\right){x}+59a-163$ |
375.2-c4 |
375.2-c |
$4$ |
$10$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
375.2 |
\( 3 \cdot 5^{3} \) |
\( 3^{2} \cdot 5^{4} \) |
$1.92642$ |
$(a+3), (-a-1), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B.4.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$20.38989080$ |
4.162069031 |
\( \frac{45398592012032}{15} a + \frac{111203420137408}{15} \) |
\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -329 a - 812\) , \( 5101 a + 12497\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-329a-812\right){x}+5101a+12497$ |
375.2-d1 |
375.2-d |
$4$ |
$10$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
375.2 |
\( 3 \cdot 5^{3} \) |
\( - 3 \cdot 5^{5} \) |
$1.92642$ |
$(a+3), (-a-1), (-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B.1.2 |
$1$ |
\( 2^{2} \) |
$5.517065719$ |
$0.905698896$ |
2.039935193 |
\( -\frac{81720253739776}{75} a + \frac{66724211524672}{25} \) |
\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( -72 a - 232\) , \( -582 a - 1712\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-72a-232\right){x}-582a-1712$ |
375.2-d2 |
375.2-d |
$4$ |
$10$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
375.2 |
\( 3 \cdot 5^{3} \) |
\( - 3^{5} \cdot 5^{13} \) |
$1.92642$ |
$(a+3), (-a-1), (-a+1)$ |
$1$ |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 2^{2} \cdot 5^{2} \) |
$1.103413143$ |
$4.528494481$ |
2.039935193 |
\( -\frac{8297016064}{263671875} a + \frac{155957523008}{87890625} \) |
\( \bigl[a\) , \( 1\) , \( a + 1\) , \( 8 a - 4\) , \( 5 a + 4\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(8a-4\right){x}+5a+4$ |
375.2-d3 |
375.2-d |
$4$ |
$10$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
375.2 |
\( 3 \cdot 5^{3} \) |
\( 3^{10} \cdot 5^{8} \) |
$1.92642$ |
$(a+3), (-a-1), (-a+1)$ |
$1$ |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 2^{2} \cdot 5^{2} \) |
$0.551706571$ |
$9.056988962$ |
2.039935193 |
\( -\frac{109693837568}{759375} a + \frac{270029745088}{759375} \) |
\( \bigl[a\) , \( a + 1\) , \( 1\) , \( -357 a - 874\) , \( 178 a + 436\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-357a-874\right){x}+178a+436$ |
375.2-d4 |
375.2-d |
$4$ |
$10$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
375.2 |
\( 3 \cdot 5^{3} \) |
\( 3^{2} \cdot 5^{4} \) |
$1.92642$ |
$(a+3), (-a-1), (-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B.1.2 |
$1$ |
\( 2^{2} \) |
$2.758532859$ |
$1.811397792$ |
2.039935193 |
\( \frac{45398592012032}{15} a + \frac{111203420137408}{15} \) |
\( \bigl[a\) , \( a + 1\) , \( 1\) , \( 308 a - 764\) , \( 4648 a - 11434\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(308a-764\right){x}+4648a-11434$ |
375.2-e1 |
375.2-e |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
375.2 |
\( 3 \cdot 5^{3} \) |
\( - 3 \cdot 5^{5} \) |
$1.92642$ |
$(a+3), (-a-1), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$15.83482297$ |
3.232269705 |
\( -\frac{1075456}{75} a + \frac{877632}{25} \) |
\( \bigl[a\) , \( -1\) , \( a + 1\) , \( 13 a - 36\) , \( -40 a + 95\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(13a-36\right){x}-40a+95$ |
375.2-e2 |
375.2-e |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
375.2 |
\( 3 \cdot 5^{3} \) |
\( 3^{2} \cdot 5^{4} \) |
$1.92642$ |
$(a+3), (-a-1), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$15.83482297$ |
3.232269705 |
\( \frac{143104}{5} a + \frac{1083328}{15} \) |
\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( -4 a - 6\) , \( -3 a - 7\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-4a-6\right){x}-3a-7$ |
375.2-f1 |
375.2-f |
$4$ |
$4$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
375.2 |
\( 3 \cdot 5^{3} \) |
\( - 3^{12} \cdot 5^{7} \) |
$1.92642$ |
$(a+3), (-a-1), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$1.127613823$ |
2.762078493 |
\( -\frac{346213168567}{3645} a + \frac{848044778507}{3645} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -154 a - 387\) , \( -4879 a - 11963\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-154a-387\right){x}-4879a-11963$ |
375.2-f2 |
375.2-f |
$4$ |
$4$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
375.2 |
\( 3 \cdot 5^{3} \) |
\( - 3^{3} \cdot 5^{7} \) |
$1.92642$ |
$(a+3), (-a-1), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$9.020910584$ |
2.762078493 |
\( \frac{16292}{45} a + \frac{13591}{15} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -19 a - 47\) , \( -15 a - 37\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-19a-47\right){x}-15a-37$ |
375.2-f3 |
375.2-f |
$4$ |
$4$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
375.2 |
\( 3 \cdot 5^{3} \) |
\( 3^{6} \cdot 5^{8} \) |
$1.92642$ |
$(a+3), (-a-1), (-a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$4.510455292$ |
2.762078493 |
\( \frac{73011154}{675} a + \frac{193909061}{675} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -229 a - 562\) , \( -2969 a - 7273\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-229a-562\right){x}-2969a-7273$ |
375.2-f4 |
375.2-f |
$4$ |
$4$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
375.2 |
\( 3 \cdot 5^{3} \) |
\( 3^{3} \cdot 5^{10} \) |
$1.92642$ |
$(a+3), (-a-1), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$2.255227646$ |
2.762078493 |
\( \frac{349197440831723}{5625} a + \frac{285118523163019}{1875} \) |
\( \bigl[1\) , \( a\) , \( 1\) , \( 3117 a - 7635\) , \( -108499 a + 265765\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(3117a-7635\right){x}-108499a+265765$ |
375.2-g1 |
375.2-g |
$4$ |
$4$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
375.2 |
\( 3 \cdot 5^{3} \) |
\( - 3^{12} \cdot 5^{7} \) |
$1.92642$ |
$(a+3), (-a-1), (-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.060493764$ |
$7.536433371$ |
2.233480139 |
\( -\frac{346213168567}{3645} a + \frac{848044778507}{3645} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 185 a - 458\) , \( -2125 a + 5223\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(185a-458\right){x}-2125a+5223$ |
375.2-g2 |
375.2-g |
$4$ |
$4$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
375.2 |
\( 3 \cdot 5^{3} \) |
\( - 3^{3} \cdot 5^{7} \) |
$1.92642$ |
$(a+3), (-a-1), (-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.241975057$ |
$15.07286674$ |
2.233480139 |
\( \frac{16292}{45} a + \frac{13591}{15} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 2\) , \( -2 a + 5\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+2{x}-2a+5$ |
375.2-g3 |
375.2-g |
$4$ |
$4$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
375.2 |
\( 3 \cdot 5^{3} \) |
\( 3^{6} \cdot 5^{8} \) |
$1.92642$ |
$(a+3), (-a-1), (-a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.120987528$ |
$15.07286674$ |
2.233480139 |
\( \frac{73011154}{675} a + \frac{193909061}{675} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 10 a - 33\) , \( -30 a + 78\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(10a-33\right){x}-30a+78$ |
375.2-g4 |
375.2-g |
$4$ |
$4$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
375.2 |
\( 3 \cdot 5^{3} \) |
\( 3^{3} \cdot 5^{10} \) |
$1.92642$ |
$(a+3), (-a-1), (-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.241975057$ |
$7.536433371$ |
2.233480139 |
\( \frac{349197440831723}{5625} a + \frac{285118523163019}{1875} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -5 a - 168\) , \( 273 a + 105\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-5a-168\right){x}+273a+105$ |
375.2-h1 |
375.2-h |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
375.2 |
\( 3 \cdot 5^{3} \) |
\( - 3 \cdot 5^{5} \) |
$1.92642$ |
$(a+3), (-a-1), (-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.188797424$ |
$16.84581154$ |
1.298411572 |
\( -\frac{1075456}{75} a + \frac{877632}{25} \) |
\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( -a - 2\) , \( a + 2\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-a-2\right){x}+a+2$ |
375.2-h2 |
375.2-h |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
375.2 |
\( 3 \cdot 5^{3} \) |
\( 3^{2} \cdot 5^{4} \) |
$1.92642$ |
$(a+3), (-a-1), (-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.094398712$ |
$33.69162308$ |
1.298411572 |
\( \frac{143104}{5} a + \frac{1083328}{15} \) |
\( \bigl[a\) , \( -1\) , \( 1\) , \( 6 a - 16\) , \( -5 a + 12\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(6a-16\right){x}-5a+12$ |
*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.