| 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 |
| 48384.2-a1 |
48384.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
48384.2 |
\( 2^{8} \cdot 3^{3} \cdot 7 \) |
\( 2^{22} \cdot 3^{5} \cdot 7 \) |
$2.29549$ |
$(-2a+1), (3a-2), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$0.173851334$ |
$2.018313476$ |
3.241350559 |
\( -\frac{13096}{7} a + \frac{23186}{7} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 16 a - 8\) , \( -16 a\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(16a-8\right){x}-16a$ |
| 48384.2-b1 |
48384.2-b |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
48384.2 |
\( 2^{8} \cdot 3^{3} \cdot 7 \) |
\( 2^{22} \cdot 3^{9} \cdot 7^{5} \) |
$2.29549$ |
$(-2a+1), (3a-2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$0.751118604$ |
1.734634114 |
\( -\frac{15182142}{16807} a + \frac{20850726}{16807} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 81 a - 57\) , \( -84 a - 194\bigr] \) |
${y}^2={x}^{3}+\left(81a-57\right){x}-84a-194$ |
| 48384.2-c1 |
48384.2-c |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
48384.2 |
\( 2^{8} \cdot 3^{3} \cdot 7 \) |
\( 2^{26} \cdot 3^{5} \cdot 7 \) |
$2.29549$ |
$(-2a+1), (3a-2), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B[2] |
$1$ |
\( 2^{2} \) |
$1.019258308$ |
$0.368682494$ |
3.471331850 |
\( -\frac{94629827885}{14} a - \frac{42409905046}{7} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 3729 a - 2103\) , \( -65721 a - 10368\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(3729a-2103\right){x}-65721a-10368$ |
| 48384.2-c2 |
48384.2-c |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
48384.2 |
\( 2^{8} \cdot 3^{3} \cdot 7 \) |
\( 2^{42} \cdot 3^{5} \cdot 7 \) |
$2.29549$ |
$(-2a+1), (3a-2), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B[2] |
$1$ |
\( 2^{2} \) |
$1.019258308$ |
$0.368682494$ |
3.471331850 |
\( -\frac{2250281123}{896} a - \frac{3901494743}{3584} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 1329 a + 57\) , \( -2121 a + 20256\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(1329a+57\right){x}-2121a+20256$ |
| 48384.2-c3 |
48384.2-c |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
48384.2 |
\( 2^{8} \cdot 3^{3} \cdot 7 \) |
\( 2^{30} \cdot 3^{3} \cdot 7^{3} \) |
$2.29549$ |
$(-2a+1), (3a-2), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs[2] |
$1$ |
\( 2^{2} \) |
$0.339752769$ |
$1.106047484$ |
3.471331850 |
\( \frac{1598955}{686} a + \frac{947913}{2744} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 49 a - 23\) , \( -121 a + 32\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(49a-23\right){x}-121a+32$ |
| 48384.2-c4 |
48384.2-c |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
48384.2 |
\( 2^{8} \cdot 3^{3} \cdot 7 \) |
\( 2^{26} \cdot 3^{9} \cdot 7 \) |
$2.29549$ |
$(-2a+1), (3a-2), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B[2] |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.113250923$ |
$1.106047484$ |
3.471331850 |
\( -\frac{40743}{14} a + \frac{37395}{14} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -48 a + 33\) , \( -84 a + 114\bigr] \) |
${y}^2={x}^{3}+\left(-48a+33\right){x}-84a+114$ |
| 48384.2-c5 |
48384.2-c |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
48384.2 |
\( 2^{8} \cdot 3^{3} \cdot 7 \) |
\( 2^{26} \cdot 3^{5} \cdot 7^{9} \) |
$2.29549$ |
$(-2a+1), (3a-2), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B[2] |
$1$ |
\( 2^{2} \) |
$1.019258308$ |
$0.368682494$ |
3.471331850 |
\( \frac{1490704436330}{40353607} a + \frac{1297954794313}{80707214} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -591 a - 183\) , \( -7257 a + 1440\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-591a-183\right){x}-7257a+1440$ |
| 48384.2-d1 |
48384.2-d |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
48384.2 |
\( 2^{8} \cdot 3^{3} \cdot 7 \) |
\( 2^{22} \cdot 3^{3} \cdot 7^{5} \) |
$2.29549$ |
$(-2a+1), (3a-2), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \cdot 5 \) |
$0.061116933$ |
$1.300975585$ |
3.672485281 |
\( -\frac{15182142}{16807} a + \frac{20850726}{16807} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -26 a + 19\) , \( -41 a + 25\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-26a+19\right){x}-41a+25$ |
| 48384.2-e1 |
48384.2-e |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
48384.2 |
\( 2^{8} \cdot 3^{3} \cdot 7 \) |
\( 2^{26} \cdot 3^{11} \cdot 7 \) |
$2.29549$ |
$(-2a+1), (3a-2), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B[2] |
$1$ |
\( 2^{2} \) |
$1.917579323$ |
$0.212858937$ |
3.770548955 |
\( -\frac{94629827885}{14} a - \frac{42409905046}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -11184 a + 6309\) , \( -265680 a + 420554\bigr] \) |
${y}^2={x}^{3}+\left(-11184a+6309\right){x}-265680a+420554$ |
| 48384.2-e2 |
48384.2-e |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
48384.2 |
\( 2^{8} \cdot 3^{3} \cdot 7 \) |
\( 2^{42} \cdot 3^{11} \cdot 7 \) |
$2.29549$ |
$(-2a+1), (3a-2), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B[2] |
$1$ |
\( 2^{2} \) |
$1.917579323$ |
$0.212858937$ |
3.770548955 |
\( -\frac{2250281123}{896} a - \frac{3901494743}{3584} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -3984 a - 171\) , \( 115344 a - 52198\bigr] \) |
${y}^2={x}^{3}+\left(-3984a-171\right){x}+115344a-52198$ |
| 48384.2-e3 |
48384.2-e |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
48384.2 |
\( 2^{8} \cdot 3^{3} \cdot 7 \) |
\( 2^{30} \cdot 3^{9} \cdot 7^{3} \) |
$2.29549$ |
$(-2a+1), (3a-2), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs[2] |
$1$ |
\( 2^{2} \) |
$0.639193107$ |
$0.638576813$ |
3.770548955 |
\( \frac{1598955}{686} a + \frac{947913}{2744} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -144 a + 69\) , \( -240 a + 554\bigr] \) |
${y}^2={x}^{3}+\left(-144a+69\right){x}-240a+554$ |
| 48384.2-e4 |
48384.2-e |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
48384.2 |
\( 2^{8} \cdot 3^{3} \cdot 7 \) |
\( 2^{26} \cdot 3^{3} \cdot 7 \) |
$2.29549$ |
$(-2a+1), (3a-2), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B[2] |
$1$ |
\( 2^{2} \) |
$0.213064369$ |
$1.915730439$ |
3.770548955 |
\( -\frac{40743}{14} a + \frac{37395}{14} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 16 a - 11\) , \( -16 a - 6\bigr] \) |
${y}^2={x}^{3}+\left(16a-11\right){x}-16a-6$ |
| 48384.2-e5 |
48384.2-e |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
48384.2 |
\( 2^{8} \cdot 3^{3} \cdot 7 \) |
\( 2^{26} \cdot 3^{11} \cdot 7^{9} \) |
$2.29549$ |
$(-2a+1), (3a-2), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B[2] |
$1$ |
\( 2^{2} \) |
$1.917579323$ |
$0.212858937$ |
3.770548955 |
\( \frac{1490704436330}{40353607} a + \frac{1297954794313}{80707214} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 1776 a + 549\) , \( -13680 a + 41546\bigr] \) |
${y}^2={x}^{3}+\left(1776a+549\right){x}-13680a+41546$ |
| 48384.2-f1 |
48384.2-f |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
48384.2 |
\( 2^{8} \cdot 3^{3} \cdot 7 \) |
\( 2^{22} \cdot 3^{9} \cdot 7^{5} \) |
$2.29549$ |
$(-2a+1), (3a-2), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \cdot 3 \cdot 5 \) |
$0.036906548$ |
$0.751118604$ |
3.841161469 |
\( -\frac{15182142}{16807} a + \frac{20850726}{16807} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -24 a + 81\) , \( 84 a + 194\bigr] \) |
${y}^2={x}^{3}+\left(-24a+81\right){x}+84a+194$ |
| 48384.2-g1 |
48384.2-g |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
48384.2 |
\( 2^{8} \cdot 3^{3} \cdot 7 \) |
\( 2^{26} \cdot 3^{5} \cdot 7 \) |
$2.29549$ |
$(-2a+1), (3a-2), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B[2] |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.376189967$ |
$0.368682494$ |
3.843619050 |
\( -\frac{94629827885}{14} a - \frac{42409905046}{7} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -2102 a - 1625\) , \( 61993 a + 12471\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-2102a-1625\right){x}+61993a+12471$ |
| 48384.2-g2 |
48384.2-g |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
48384.2 |
\( 2^{8} \cdot 3^{3} \cdot 7 \) |
\( 2^{42} \cdot 3^{5} \cdot 7 \) |
$2.29549$ |
$(-2a+1), (3a-2), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B[2] |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.376189967$ |
$0.368682494$ |
3.843619050 |
\( -\frac{2250281123}{896} a - \frac{3901494743}{3584} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 58 a - 1385\) , \( 793 a - 20313\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(58a-1385\right){x}+793a-20313$ |
| 48384.2-g3 |
48384.2-g |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
48384.2 |
\( 2^{8} \cdot 3^{3} \cdot 7 \) |
\( 2^{30} \cdot 3^{3} \cdot 7^{3} \) |
$2.29549$ |
$(-2a+1), (3a-2), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs[2] |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.125396655$ |
$1.106047484$ |
3.843619050 |
\( \frac{1598955}{686} a + \frac{947913}{2744} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -22 a - 25\) , \( 73 a - 9\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-22a-25\right){x}+73a-9$ |
| 48384.2-g4 |
48384.2-g |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
48384.2 |
\( 2^{8} \cdot 3^{3} \cdot 7 \) |
\( 2^{26} \cdot 3^{9} \cdot 7 \) |
$2.29549$ |
$(-2a+1), (3a-2), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B[2] |
$1$ |
\( 2^{2} \) |
$0.376189967$ |
$1.106047484$ |
3.843619050 |
\( -\frac{40743}{14} a + \frac{37395}{14} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 33 a + 15\) , \( 84 a - 114\bigr] \) |
${y}^2={x}^{3}+\left(33a+15\right){x}+84a-114$ |
| 48384.2-g5 |
48384.2-g |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
48384.2 |
\( 2^{8} \cdot 3^{3} \cdot 7 \) |
\( 2^{26} \cdot 3^{5} \cdot 7^{9} \) |
$2.29549$ |
$(-2a+1), (3a-2), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B[2] |
$1$ |
\( 2^{2} \cdot 3^{3} \) |
$0.041798885$ |
$0.368682494$ |
3.843619050 |
\( \frac{1490704436330}{40353607} a + \frac{1297954794313}{80707214} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -182 a + 775\) , \( 7849 a - 1257\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-182a+775\right){x}+7849a-1257$ |
| 48384.2-h1 |
48384.2-h |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
48384.2 |
\( 2^{8} \cdot 3^{3} \cdot 7 \) |
\( 2^{22} \cdot 3^{5} \cdot 7 \) |
$2.29549$ |
$(-2a+1), (3a-2), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \cdot 3 \) |
$0.066556414$ |
$2.018313476$ |
3.722709501 |
\( -\frac{13096}{7} a + \frac{23186}{7} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -6 a + 15\) , \( 9 a + 15\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-6a+15\right){x}+9a+15$ |
| 48384.2-i1 |
48384.2-i |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
48384.2 |
\( 2^{8} \cdot 3^{3} \cdot 7 \) |
\( 2^{22} \cdot 3^{11} \cdot 7 \) |
$2.29549$ |
$(-2a+1), (3a-2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$1.165273828$ |
2.691084634 |
\( -\frac{13096}{7} a + \frac{23186}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 21 a - 45\) , \( -72 a + 74\bigr] \) |
${y}^2={x}^{3}+\left(21a-45\right){x}-72a+74$ |
*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.
