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 |
3072.1-a1 |
3072.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{18} \cdot 3^{4} \) |
$1.15227$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.208930895$ |
$2.876942816$ |
1.388139971 |
\( \frac{188632}{9} a - \frac{255448}{9} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 10 a - 11\) , \( -15 a + 6\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(10a-11\right){x}-15a+6$ |
3072.1-a2 |
3072.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{12} \cdot 3^{2} \) |
$1.15227$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.417861791$ |
$5.753885633$ |
1.388139971 |
\( \frac{1216}{3} a - 384 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -1\) , \( -a\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}-{x}-a$ |
3072.1-a3 |
3072.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{24} \cdot 3 \) |
$1.15227$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.835723582$ |
$2.876942816$ |
1.388139971 |
\( -\frac{27712}{3} a + \frac{20672}{3} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -5 a + 9\) , \( -4 a - 3\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-5a+9\right){x}-4a-3$ |
3072.1-a4 |
3072.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{18} \cdot 3 \) |
$1.15227$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.835723582$ |
$2.876942816$ |
1.388139971 |
\( -\frac{2285576}{3} a + \frac{2214136}{3} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -10 a - 11\) , \( -31 a - 6\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-10a-11\right){x}-31a-6$ |
3072.1-b1 |
3072.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{18} \cdot 3^{4} \) |
$1.15227$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.208930895$ |
$2.876942816$ |
1.388139971 |
\( -\frac{188632}{9} a - 7424 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -10 a - 1\) , \( 15 a - 9\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-10a-1\right){x}+15a-9$ |
3072.1-b2 |
3072.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{12} \cdot 3^{2} \) |
$1.15227$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.417861791$ |
$5.753885633$ |
1.388139971 |
\( -\frac{1216}{3} a + \frac{64}{3} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -1\) , \( a - 1\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}-{x}+a-1$ |
3072.1-b3 |
3072.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{24} \cdot 3 \) |
$1.15227$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.835723582$ |
$2.876942816$ |
1.388139971 |
\( \frac{27712}{3} a - \frac{7040}{3} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 5 a + 4\) , \( 4 a - 7\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(5a+4\right){x}+4a-7$ |
3072.1-b4 |
3072.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{18} \cdot 3 \) |
$1.15227$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.835723582$ |
$2.876942816$ |
1.388139971 |
\( \frac{2285576}{3} a - \frac{71440}{3} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 10 a - 21\) , \( 31 a - 37\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(10a-21\right){x}+31a-37$ |
3072.1-c1 |
3072.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{18} \cdot 3^{8} \) |
$1.15227$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$2.345364298$ |
1.354096709 |
\( \frac{97336}{81} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 8 a - 8\) , \( -8\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(8a-8\right){x}-8$ |
3072.1-c2 |
3072.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{12} \cdot 3^{4} \) |
$1.15227$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$4.690728597$ |
1.354096709 |
\( \frac{21952}{9} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -2 a + 2\) , \( 0\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-2a+2\right){x}$ |
3072.1-c3 |
3072.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{24} \cdot 3^{2} \) |
$1.15227$ |
$(-2a+1), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.345364298$ |
1.354096709 |
\( \frac{140608}{3} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -17 a + 17\) , \( 33\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-17a+17\right){x}+33$ |
3072.1-c4 |
3072.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{18} \cdot 3^{2} \) |
$1.15227$ |
$(-2a+1), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.345364298$ |
1.354096709 |
\( \frac{7301384}{3} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -32 a + 32\) , \( -60\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-32a+32\right){x}-60$ |
3072.1-d1 |
3072.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{18} \cdot 3^{8} \) |
$1.15227$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.155042418$ |
$2.345364298$ |
1.679539426 |
\( \frac{97336}{81} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 8 a - 8\) , \( 8\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(8a-8\right){x}+8$ |
3072.1-d2 |
3072.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{12} \cdot 3^{4} \) |
$1.15227$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.310084836$ |
$4.690728597$ |
1.679539426 |
\( \frac{21952}{9} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -2 a + 2\) , \( 0\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-2a+2\right){x}$ |
3072.1-d3 |
3072.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{24} \cdot 3^{2} \) |
$1.15227$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.620169672$ |
$2.345364298$ |
1.679539426 |
\( \frac{140608}{3} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -17 a + 17\) , \( -33\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-17a+17\right){x}-33$ |
3072.1-d4 |
3072.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{18} \cdot 3^{2} \) |
$1.15227$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.620169672$ |
$2.345364298$ |
1.679539426 |
\( \frac{7301384}{3} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -32 a + 32\) , \( 60\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-32a+32\right){x}+60$ |
3072.1-e1 |
3072.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{18} \cdot 3^{4} \) |
$1.15227$ |
$(-2a+1), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.876942816$ |
1.661003709 |
\( -\frac{188632}{9} a - 7424 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 11 a - 10\) , \( -15 a + 9\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(11a-10\right){x}-15a+9$ |
3072.1-e2 |
3072.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{12} \cdot 3^{2} \) |
$1.15227$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$5.753885633$ |
1.661003709 |
\( -\frac{1216}{3} a + \frac{64}{3} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( a\) , \( -a + 1\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+a{x}-a+1$ |
3072.1-e3 |
3072.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{24} \cdot 3 \) |
$1.15227$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$2.876942816$ |
1.661003709 |
\( \frac{27712}{3} a - \frac{7040}{3} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -9 a + 5\) , \( -4 a + 7\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-9a+5\right){x}-4a+7$ |
3072.1-e4 |
3072.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{18} \cdot 3 \) |
$1.15227$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$2.876942816$ |
1.661003709 |
\( \frac{2285576}{3} a - \frac{71440}{3} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 11 a + 10\) , \( -31 a + 37\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(11a+10\right){x}-31a+37$ |
3072.1-f1 |
3072.1-f |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{18} \cdot 3^{4} \) |
$1.15227$ |
$(-2a+1), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.876942816$ |
1.661003709 |
\( \frac{188632}{9} a - \frac{255448}{9} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -11 a + 1\) , \( 15 a - 6\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-11a+1\right){x}+15a-6$ |
3072.1-f2 |
3072.1-f |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{12} \cdot 3^{2} \) |
$1.15227$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$5.753885633$ |
1.661003709 |
\( \frac{1216}{3} a - 384 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -a + 1\) , \( a\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-a+1\right){x}+a$ |
3072.1-f3 |
3072.1-f |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{24} \cdot 3 \) |
$1.15227$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$2.876942816$ |
1.661003709 |
\( -\frac{27712}{3} a + \frac{20672}{3} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 9 a - 4\) , \( 4 a + 3\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(9a-4\right){x}+4a+3$ |
3072.1-f4 |
3072.1-f |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{18} \cdot 3 \) |
$1.15227$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$2.876942816$ |
1.661003709 |
\( -\frac{2285576}{3} a + \frac{2214136}{3} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -11 a + 21\) , \( 31 a + 6\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-11a+21\right){x}+31a+6$ |
*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.