| 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 |
| 2304.1-a1 |
2304.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( - 2^{16} \cdot 3^{9} \) |
$2.14462$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$4.308039162$ |
2.487247569 |
\( -\frac{14225792}{9} a + \frac{8213248}{3} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 22 a - 39\) , \( 95 a - 146\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(22a-39\right){x}+95a-146$ |
| 2304.1-a2 |
2304.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( - 2^{19} \cdot 3^{18} \) |
$2.14462$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$2.154019581$ |
2.487247569 |
\( \frac{217996}{729} a + \frac{1023628}{729} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -244 a + 420\) , \( 2504 a - 4336\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-244a+420\right){x}+2504a-4336$ |
| 2304.1-a3 |
2304.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{14} \cdot 3^{12} \) |
$2.14462$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$8.616078324$ |
2.487247569 |
\( \frac{770336}{27} a + \frac{1419904}{27} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 86 a - 150\) , \( 440 a - 760\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(86a-150\right){x}+440a-760$ |
| 2304.1-a4 |
2304.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{19} \cdot 3^{9} \) |
$2.14462$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$8.616078324$ |
2.487247569 |
\( \frac{26639622068}{9} a + \frac{15380474156}{3} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 536 a - 960\) , \( -8488 a + 14792\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(536a-960\right){x}-8488a+14792$ |
| 2304.1-b1 |
2304.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( - 2^{21} \cdot 3^{14} \) |
$2.14462$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.510861184$ |
1.449646380 |
\( -\frac{443186854}{81} a + \frac{767608522}{81} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -312 a - 552\) , \( -13308 a - 23040\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-312a-552\right){x}-13308a-23040$ |
| 2304.1-b2 |
2304.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( - 2^{18} \cdot 3^{7} \) |
$2.14462$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.510861184$ |
1.449646380 |
\( -\frac{132636728}{3} a + 76579552 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 43288 a - 74976\) , \( 6476960 a - 11218424\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(43288a-74976\right){x}+6476960a-11218424$ |
| 2304.1-b3 |
2304.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{8} \) |
$2.14462$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$10.04344473$ |
1.449646380 |
\( -\frac{9856}{3} a + \frac{22336}{3} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 2758 a - 4776\) , \( 98288 a - 170240\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(2758a-4776\right){x}+98288a-170240$ |
| 2304.1-b4 |
2304.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( - 2^{12} \cdot 3^{7} \) |
$2.14462$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$10.04344473$ |
1.449646380 |
\( \frac{166016}{3} a + 95936 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -9304 a + 16116\) , \( 2793284 a - 4838110\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-9304a+16116\right){x}+2793284a-4838110$ |
| 2304.1-b5 |
2304.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{18} \cdot 3^{10} \) |
$2.14462$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$5.021722368$ |
1.449646380 |
\( \frac{1122088}{9} a + \frac{1989808}{9} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 44 a - 84\) , \( -160 a + 272\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(44a-84\right){x}-160a+272$ |
| 2304.1-b6 |
2304.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( - 2^{21} \cdot 3^{8} \) |
$2.14462$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$1.255430592$ |
1.449646380 |
\( \frac{164847992914}{3} a + \frac{285525100658}{3} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -136 a + 96\) , \( -1312 a + 1712\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-136a+96\right){x}-1312a+1712$ |
| 2304.1-c1 |
2304.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{6} \) |
$2.14462$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$7.938780765$ |
2.291728606 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -12 a + 21\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-12a+21\right){x}$ |
| 2304.1-c2 |
2304.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{6} \) |
$2.14462$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$15.87756153$ |
2.291728606 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -3\) , \( 0\bigr] \) |
${y}^2={x}^{3}-3{x}$ |
| 2304.1-c3 |
2304.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{18} \cdot 3^{6} \) |
$2.14462$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$7.938780765$ |
2.291728606 |
\( 287496 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -33\) , \( -42 a\bigr] \) |
${y}^2={x}^{3}-33{x}-42a$ |
| 2304.1-c4 |
2304.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{18} \cdot 3^{6} \) |
$2.14462$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$7.938780765$ |
2.291728606 |
\( 287496 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -33\) , \( 42 a\bigr] \) |
${y}^2={x}^{3}-33{x}+42a$ |
| 2304.1-d1 |
2304.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( - 2^{16} \cdot 3^{9} \) |
$2.14462$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$5.617501307$ |
1.621632946 |
\( -2688 a + 4608 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 90 a - 156\) , \( -552 a + 956\bigr] \) |
${y}^2={x}^{3}+\left(90a-156\right){x}-552a+956$ |
| 2304.1-d2 |
2304.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( - 2^{14} \cdot 3^{9} \) |
$2.14462$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$5.617501307$ |
1.621632946 |
\( 59424 a + 103104 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -6 a - 3\) , \( -12 a + 2\bigr] \) |
${y}^2={x}^{3}+\left(-6a-3\right){x}-12a+2$ |
| 2304.1-e1 |
2304.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( - 2^{21} \cdot 3^{14} \) |
$2.14462$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.945772875$ |
2.246784987 |
\( -\frac{443186854}{81} a + \frac{767608522}{81} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -312 a - 552\) , \( 13308 a + 23040\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-312a-552\right){x}+13308a+23040$ |
| 2304.1-e2 |
2304.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( - 2^{18} \cdot 3^{7} \) |
$2.14462$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$7.783091503$ |
2.246784987 |
\( -\frac{132636728}{3} a + 76579552 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 43288 a - 74976\) , \( -6476960 a + 11218424\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(43288a-74976\right){x}-6476960a+11218424$ |
| 2304.1-e3 |
2304.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{8} \) |
$2.14462$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$15.56618300$ |
2.246784987 |
\( -\frac{9856}{3} a + \frac{22336}{3} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 2758 a - 4776\) , \( -98288 a + 170240\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(2758a-4776\right){x}-98288a+170240$ |
| 2304.1-e4 |
2304.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( - 2^{12} \cdot 3^{7} \) |
$2.14462$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$7.783091503$ |
2.246784987 |
\( \frac{166016}{3} a + 95936 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -9304 a + 16116\) , \( -2793284 a + 4838110\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-9304a+16116\right){x}-2793284a+4838110$ |
| 2304.1-e5 |
2304.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{18} \cdot 3^{10} \) |
$2.14462$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$7.783091503$ |
2.246784987 |
\( \frac{1122088}{9} a + \frac{1989808}{9} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 44 a - 84\) , \( 160 a - 272\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(44a-84\right){x}+160a-272$ |
| 2304.1-e6 |
2304.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( - 2^{21} \cdot 3^{8} \) |
$2.14462$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$3.891545751$ |
2.246784987 |
\( \frac{164847992914}{3} a + \frac{285525100658}{3} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -136 a + 96\) , \( 1312 a - 1712\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-136a+96\right){x}+1312a-1712$ |
| 2304.1-f1 |
2304.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{6} \) |
$2.14462$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$13.93454908$ |
2.011278916 |
\( 512 a + 512 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( a\) , \( -a + 1\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+a{x}-a+1$ |
| 2304.1-f2 |
2304.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{6} \) |
$2.14462$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$13.93454908$ |
2.011278916 |
\( -249872 a + 434912 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 16 a - 30\) , \( -40 a + 70\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(16a-30\right){x}-40a+70$ |
| 2304.1-g1 |
2304.1-g |
$6$ |
$18$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( - 2^{12} \cdot 3^{9} \) |
$2.14462$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-36$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$9$ |
\( 2 \) |
$1$ |
$1.641748434$ |
2.132693776 |
\( -44330496 a + 76771008 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 102 a - 183\) , \( 756 a - 1316\bigr] \) |
${y}^2={x}^{3}+\left(102a-183\right){x}+756a-1316$ |
| 2304.1-g2 |
2304.1-g |
$6$ |
$18$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( - 2^{12} \cdot 3^{9} \) |
$2.14462$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-36$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$14.77573591$ |
2.132693776 |
\( -44330496 a + 76771008 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 102 a - 183\) , \( -756 a + 1316\bigr] \) |
${y}^2={x}^{3}+\left(102a-183\right){x}-756a+1316$ |
| 2304.1-g3 |
2304.1-g |
$6$ |
$18$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( - 2^{12} \cdot 3^{3} \) |
$2.14462$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3$ |
3Cs |
$1$ |
\( 2 \) |
$1$ |
$14.77573591$ |
2.132693776 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -2 a - 3\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-2a-3\right){x}$ |
| 2304.1-g4 |
2304.1-g |
$6$ |
$18$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( - 2^{12} \cdot 3^{3} \) |
$2.14462$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3$ |
3Cs |
$1$ |
\( 2 \) |
$1$ |
$14.77573591$ |
2.132693776 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 2 a - 3\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(2a-3\right){x}$ |
| 2304.1-g5 |
2304.1-g |
$6$ |
$18$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( - 2^{12} \cdot 3^{9} \) |
$2.14462$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-36$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$9$ |
\( 2 \) |
$1$ |
$1.641748434$ |
2.132693776 |
\( 44330496 a + 76771008 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -102 a - 183\) , \( -756 a - 1316\bigr] \) |
${y}^2={x}^{3}+\left(-102a-183\right){x}-756a-1316$ |
| 2304.1-g6 |
2304.1-g |
$6$ |
$18$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( - 2^{12} \cdot 3^{9} \) |
$2.14462$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-36$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$14.77573591$ |
2.132693776 |
\( 44330496 a + 76771008 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -102 a - 183\) , \( 756 a + 1316\bigr] \) |
${y}^2={x}^{3}+\left(-102a-183\right){x}+756a+1316$ |
| 2304.1-h1 |
2304.1-h |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( - 2^{16} \cdot 3^{9} \) |
$2.14462$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$5.799519847$ |
1.674177172 |
\( -\frac{14225792}{9} a + \frac{8213248}{3} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 22 a - 39\) , \( -95 a + 146\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(22a-39\right){x}-95a+146$ |
| 2304.1-h2 |
2304.1-h |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( - 2^{19} \cdot 3^{18} \) |
$2.14462$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.899759923$ |
1.674177172 |
\( \frac{217996}{729} a + \frac{1023628}{729} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -244 a + 420\) , \( -2504 a + 4336\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-244a+420\right){x}-2504a+4336$ |
| 2304.1-h3 |
2304.1-h |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{14} \cdot 3^{12} \) |
$2.14462$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$5.799519847$ |
1.674177172 |
\( \frac{770336}{27} a + \frac{1419904}{27} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 86 a - 150\) , \( -440 a + 760\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(86a-150\right){x}-440a+760$ |
| 2304.1-h4 |
2304.1-h |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{19} \cdot 3^{9} \) |
$2.14462$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.449879961$ |
1.674177172 |
\( \frac{26639622068}{9} a + \frac{15380474156}{3} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 536 a - 960\) , \( 8488 a - 14792\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(536a-960\right){x}+8488a-14792$ |
| 2304.1-i1 |
2304.1-i |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( - 2^{19} \cdot 3^{10} \) |
$2.14462$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.926892945$ |
$3.073336964$ |
3.289342713 |
\( -\frac{2695276}{3} a + \frac{14006500}{9} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 20 a + 12\) , \( 124 a + 184\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(20a+12\right){x}+124a+184$ |
| 2304.1-i2 |
2304.1-i |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( - 2^{16} \cdot 3^{7} \) |
$2.14462$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.231723236$ |
$6.146673929$ |
3.289342713 |
\( \frac{4736}{3} a + 3840 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -6 a + 9\) , \( 9 a - 18\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-6a+9\right){x}+9a-18$ |
| 2304.1-i3 |
2304.1-i |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{14} \cdot 3^{8} \) |
$2.14462$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.463446472$ |
$12.29334785$ |
3.289342713 |
\( 2080 a + \frac{18688}{3} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -10 a - 18\) , \( 16 a + 28\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-10a-18\right){x}+16a+28$ |
| 2304.1-i4 |
2304.1-i |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{19} \cdot 3^{7} \) |
$2.14462$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.231723236$ |
$12.29334785$ |
3.289342713 |
\( \frac{71147500}{3} a + 41116428 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -160 a - 288\) , \( 1396 a + 2440\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-160a-288\right){x}+1396a+2440$ |
| 2304.1-j1 |
2304.1-j |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( - 2^{14} \cdot 3^{9} \) |
$2.14462$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$7.594916975$ |
2.192463680 |
\( -59424 a + 103104 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 6 a - 3\) , \( -12 a - 2\bigr] \) |
${y}^2={x}^{3}+\left(6a-3\right){x}-12a-2$ |
| 2304.1-j2 |
2304.1-j |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( - 2^{16} \cdot 3^{9} \) |
$2.14462$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$7.594916975$ |
2.192463680 |
\( 2688 a + 4608 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 6 a - 12\) , \( -72 a + 124\bigr] \) |
${y}^2={x}^{3}+\left(6a-12\right){x}-72a+124$ |
| 2304.1-k1 |
2304.1-k |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( - 2^{19} \cdot 3^{18} \) |
$2.14462$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.899759923$ |
1.674177172 |
\( -\frac{217996}{729} a + \frac{1023628}{729} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 204 a - 348\) , \( -540 a + 936\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(204a-348\right){x}-540a+936$ |
| 2304.1-k2 |
2304.1-k |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{14} \cdot 3^{12} \) |
$2.14462$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$5.799519847$ |
1.674177172 |
\( -\frac{770336}{27} a + \frac{1419904}{27} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 114 a - 198\) , \( 936 a - 1620\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(114a-198\right){x}+936a-1620$ |
| 2304.1-k3 |
2304.1-k |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{19} \cdot 3^{9} \) |
$2.14462$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.449879961$ |
1.674177172 |
\( -\frac{26639622068}{9} a + \frac{15380474156}{3} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 1824 a - 3168\) , \( 56988 a - 98712\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(1824a-3168\right){x}+56988a-98712$ |
| 2304.1-k4 |
2304.1-k |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( - 2^{16} \cdot 3^{9} \) |
$2.14462$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$5.799519847$ |
1.674177172 |
\( \frac{14225792}{9} a + \frac{8213248}{3} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -22 a - 39\) , \( 95 a + 146\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-22a-39\right){x}+95a+146$ |
| 2304.1-l1 |
2304.1-l |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( - 2^{16} \cdot 3^{9} \) |
$2.14462$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$7.594916975$ |
2.192463680 |
\( -2688 a + 4608 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 90 a - 156\) , \( 552 a - 956\bigr] \) |
${y}^2={x}^{3}+\left(90a-156\right){x}+552a-956$ |
| 2304.1-l2 |
2304.1-l |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( - 2^{14} \cdot 3^{9} \) |
$2.14462$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$7.594916975$ |
2.192463680 |
\( 59424 a + 103104 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -6 a - 3\) , \( 12 a - 2\bigr] \) |
${y}^2={x}^{3}+\left(-6a-3\right){x}+12a-2$ |
| 2304.1-m1 |
2304.1-m |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( - 2^{19} \cdot 3^{18} \) |
$2.14462$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$2.154019581$ |
2.487247569 |
\( -\frac{217996}{729} a + \frac{1023628}{729} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 204 a - 348\) , \( 540 a - 936\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(204a-348\right){x}+540a-936$ |
| 2304.1-m2 |
2304.1-m |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{14} \cdot 3^{12} \) |
$2.14462$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$8.616078324$ |
2.487247569 |
\( -\frac{770336}{27} a + \frac{1419904}{27} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 114 a - 198\) , \( -936 a + 1620\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(114a-198\right){x}-936a+1620$ |
| 2304.1-m3 |
2304.1-m |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{19} \cdot 3^{9} \) |
$2.14462$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$8.616078324$ |
2.487247569 |
\( -\frac{26639622068}{9} a + \frac{15380474156}{3} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 1824 a - 3168\) , \( -56988 a + 98712\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(1824a-3168\right){x}-56988a+98712$ |
| 2304.1-m4 |
2304.1-m |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( - 2^{16} \cdot 3^{9} \) |
$2.14462$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$4.308039162$ |
2.487247569 |
\( \frac{14225792}{9} a + \frac{8213248}{3} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -22 a - 39\) , \( -95 a - 146\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-22a-39\right){x}-95a-146$ |
*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.
