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 |
49152.1-a1 |
49152.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
49152.1 |
\( 2^{14} \cdot 3 \) |
\( 2^{26} \cdot 3^{2} \) |
$2.30454$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.263184633$ |
$2.454726994$ |
2.983960614 |
\( \frac{10336}{3} a - 1344 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( a + 8\) , \( 8 a - 7\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(a+8\right){x}+8a-7$ |
49152.1-a2 |
49152.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
49152.1 |
\( 2^{14} \cdot 3 \) |
\( 2^{16} \cdot 3 \) |
$2.30454$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.526369266$ |
$4.909453989$ |
2.983960614 |
\( -\frac{4736}{3} a + \frac{2176}{3} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( a - 2\) , \( 2 a - 1\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(a-2\right){x}+2a-1$ |
49152.1-b1 |
49152.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
49152.1 |
\( 2^{14} \cdot 3 \) |
\( 2^{26} \cdot 3^{4} \) |
$2.30454$ |
$(-2a+1), (2)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.193042724$ |
$2.146294034$ |
3.827383780 |
\( \frac{4000}{9} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -7 a\) , \( 9\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}-7a{x}+9$ |
49152.1-b2 |
49152.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
49152.1 |
\( 2^{14} \cdot 3 \) |
\( 2^{16} \cdot 3^{2} \) |
$2.30454$ |
$(-2a+1), (2)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.193042724$ |
$4.292588069$ |
3.827383780 |
\( \frac{16000}{3} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 3 a\) , \( 3\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+3a{x}+3$ |
49152.1-c1 |
49152.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
49152.1 |
\( 2^{14} \cdot 3 \) |
\( 2^{14} \cdot 3^{12} \) |
$2.30454$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$2.054849002$ |
1.186367624 |
\( -\frac{219488}{729} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 6 a\) , \( 18\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+6a{x}+18$ |
49152.1-c2 |
49152.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
49152.1 |
\( 2^{14} \cdot 3 \) |
\( 2^{28} \cdot 3^{6} \) |
$2.30454$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.027424501$ |
1.186367624 |
\( \frac{19056256}{27} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 141 a\) , \( 693\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+141a{x}+693$ |
49152.1-d1 |
49152.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
49152.1 |
\( 2^{14} \cdot 3 \) |
\( 2^{14} \cdot 3^{6} \) |
$2.30454$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.702555855$ |
$3.467222156$ |
2.812754934 |
\( -\frac{32224}{27} a + \frac{76576}{27} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( a + 4\) , \( -3 a\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(a+4\right){x}-3a$ |
49152.1-d2 |
49152.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
49152.1 |
\( 2^{14} \cdot 3 \) |
\( 2^{28} \cdot 3^{3} \) |
$2.30454$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.405111710$ |
$1.733611078$ |
2.812754934 |
\( \frac{290176}{9} a + \frac{48640}{9} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 16 a + 19\) , \( 48 a - 75\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(16a+19\right){x}+48a-75$ |
49152.1-e1 |
49152.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
49152.1 |
\( 2^{14} \cdot 3 \) |
\( 2^{28} \cdot 3 \) |
$2.30454$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.142615817$ |
$2.454726994$ |
3.238715492 |
\( \frac{4736}{3} a - \frac{2560}{3} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -3 a + 8\) , \( 8 a - 3\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-3a+8\right){x}+8a-3$ |
49152.1-e2 |
49152.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
49152.1 |
\( 2^{14} \cdot 3 \) |
\( 2^{14} \cdot 3^{2} \) |
$2.30454$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.571307908$ |
$4.909453989$ |
3.238715492 |
\( -\frac{10336}{3} a + \frac{6304}{3} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 2 a - 2\) , \( 2 a\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(2a-2\right){x}+2a$ |
49152.1-f1 |
49152.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
49152.1 |
\( 2^{14} \cdot 3 \) |
\( 2^{14} \cdot 3^{6} \) |
$2.30454$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.702555855$ |
$3.467222156$ |
2.812754934 |
\( \frac{32224}{27} a + \frac{4928}{3} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 5 a - 4\) , \( 3 a - 3\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(5a-4\right){x}+3a-3$ |
49152.1-f2 |
49152.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
49152.1 |
\( 2^{14} \cdot 3 \) |
\( 2^{28} \cdot 3^{3} \) |
$2.30454$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.405111710$ |
$1.733611078$ |
2.812754934 |
\( -\frac{290176}{9} a + \frac{338816}{9} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 35 a - 19\) , \( -48 a - 27\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(35a-19\right){x}-48a-27$ |
49152.1-g1 |
49152.1-g |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
49152.1 |
\( 2^{14} \cdot 3 \) |
\( 2^{26} \cdot 3^{6} \) |
$2.30454$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.733611078$ |
2.001801645 |
\( \frac{32224}{27} a + \frac{4928}{3} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -15 a - 4\) , \( -20 a + 5\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-15a-4\right){x}-20a+5$ |
49152.1-g2 |
49152.1-g |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
49152.1 |
\( 2^{14} \cdot 3 \) |
\( 2^{16} \cdot 3^{3} \) |
$2.30454$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$3.467222156$ |
2.001801645 |
\( -\frac{290176}{9} a + \frac{338816}{9} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -5 a - 4\) , \( 8 a - 1\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-5a-4\right){x}+8a-1$ |
49152.1-h1 |
49152.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
49152.1 |
\( 2^{14} \cdot 3 \) |
\( 2^{16} \cdot 3 \) |
$2.30454$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.526369266$ |
$4.909453989$ |
2.983960614 |
\( \frac{4736}{3} a - \frac{2560}{3} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -a + 2\) , \( -2 a + 1\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-a+2\right){x}-2a+1$ |
49152.1-h2 |
49152.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
49152.1 |
\( 2^{14} \cdot 3 \) |
\( 2^{26} \cdot 3^{2} \) |
$2.30454$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.263184633$ |
$2.454726994$ |
2.983960614 |
\( -\frac{10336}{3} a + \frac{6304}{3} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 9 a - 8\) , \( -8 a + 1\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(9a-8\right){x}-8a+1$ |
49152.1-i1 |
49152.1-i |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
49152.1 |
\( 2^{14} \cdot 3 \) |
\( 2^{26} \cdot 3^{6} \) |
$2.30454$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.733611078$ |
2.001801645 |
\( -\frac{32224}{27} a + \frac{76576}{27} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 4 a + 15\) , \( 20 a - 15\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(4a+15\right){x}+20a-15$ |
49152.1-i2 |
49152.1-i |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
49152.1 |
\( 2^{14} \cdot 3 \) |
\( 2^{16} \cdot 3^{3} \) |
$2.30454$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$3.467222156$ |
2.001801645 |
\( \frac{290176}{9} a + \frac{48640}{9} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 4 a + 5\) , \( -8 a + 7\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(4a+5\right){x}-8a+7$ |
49152.1-j1 |
49152.1-j |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
49152.1 |
\( 2^{14} \cdot 3 \) |
\( 2^{26} \cdot 3^{12} \) |
$2.30454$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.027424501$ |
2.372735248 |
\( -\frac{219488}{729} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -25 a + 25\) , \( -119\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-25a+25\right){x}-119$ |
49152.1-j2 |
49152.1-j |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
49152.1 |
\( 2^{14} \cdot 3 \) |
\( 2^{16} \cdot 3^{6} \) |
$2.30454$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.054849002$ |
2.372735248 |
\( \frac{19056256}{27} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -35 a + 35\) , \( -69\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-35a+35\right){x}-69$ |
49152.1-k1 |
49152.1-k |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
49152.1 |
\( 2^{14} \cdot 3 \) |
\( 2^{14} \cdot 3^{4} \) |
$2.30454$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$4.292588069$ |
2.478326877 |
\( \frac{4000}{9} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 2 a - 2\) , \( -2\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(2a-2\right){x}-2$ |
49152.1-k2 |
49152.1-k |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
49152.1 |
\( 2^{14} \cdot 3 \) |
\( 2^{28} \cdot 3^{2} \) |
$2.30454$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.146294034$ |
2.478326877 |
\( \frac{16000}{3} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -13 a + 13\) , \( -11\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-13a+13\right){x}-11$ |
49152.1-l1 |
49152.1-l |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
49152.1 |
\( 2^{14} \cdot 3 \) |
\( 2^{14} \cdot 3^{2} \) |
$2.30454$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.571307908$ |
$4.909453989$ |
3.238715492 |
\( \frac{10336}{3} a - 1344 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 2 a - 2\) , \( -2 a + 2\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(2a-2\right){x}-2a+2$ |
49152.1-l2 |
49152.1-l |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
49152.1 |
\( 2^{14} \cdot 3 \) |
\( 2^{28} \cdot 3 \) |
$2.30454$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.142615817$ |
$2.454726994$ |
3.238715492 |
\( -\frac{4736}{3} a + \frac{2176}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -8 a + 3\) , \( -8 a + 5\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-8a+3\right){x}-8a+5$ |
49152.1-m1 |
49152.1-m |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
49152.1 |
\( 2^{14} \cdot 3 \) |
\( 2^{14} \cdot 3^{2} \) |
$2.30454$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.708778614$ |
$4.909453989$ |
4.018029934 |
\( \frac{10336}{3} a - 1344 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -2 a\) , \( 2 a - 2\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}-2a{x}+2a-2$ |
49152.1-m2 |
49152.1-m |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
49152.1 |
\( 2^{14} \cdot 3 \) |
\( 2^{28} \cdot 3 \) |
$2.30454$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.417557229$ |
$2.454726994$ |
4.018029934 |
\( -\frac{4736}{3} a + \frac{2176}{3} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 3 a + 5\) , \( 8 a - 5\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(3a+5\right){x}+8a-5$ |
49152.1-n1 |
49152.1-n |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
49152.1 |
\( 2^{14} \cdot 3 \) |
\( 2^{26} \cdot 3^{12} \) |
$2.30454$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.135844784$ |
$1.027424501$ |
3.867884495 |
\( -\frac{219488}{729} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -25\) , \( 119\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-25{x}+119$ |
49152.1-n2 |
49152.1-n |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
49152.1 |
\( 2^{14} \cdot 3 \) |
\( 2^{16} \cdot 3^{6} \) |
$2.30454$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.271689568$ |
$2.054849002$ |
3.867884495 |
\( \frac{19056256}{27} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -35\) , \( 69\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-35{x}+69$ |
49152.1-o1 |
49152.1-o |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
49152.1 |
\( 2^{14} \cdot 3 \) |
\( 2^{14} \cdot 3^{4} \) |
$2.30454$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.424185996$ |
$4.292588069$ |
4.205086228 |
\( \frac{4000}{9} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 2\) , \( 2\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+2{x}+2$ |
49152.1-o2 |
49152.1-o |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
49152.1 |
\( 2^{14} \cdot 3 \) |
\( 2^{28} \cdot 3^{2} \) |
$2.30454$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.848371993$ |
$2.146294034$ |
4.205086228 |
\( \frac{16000}{3} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -13\) , \( 11\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-13{x}+11$ |
49152.1-p1 |
49152.1-p |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
49152.1 |
\( 2^{14} \cdot 3 \) |
\( 2^{26} \cdot 3^{6} \) |
$2.30454$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.174863789$ |
$1.733611078$ |
4.200511455 |
\( -\frac{32224}{27} a + \frac{76576}{27} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 4 a + 15\) , \( -20 a + 15\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(4a+15\right){x}-20a+15$ |
49152.1-p2 |
49152.1-p |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
49152.1 |
\( 2^{14} \cdot 3 \) |
\( 2^{16} \cdot 3^{3} \) |
$2.30454$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.349727578$ |
$3.467222156$ |
4.200511455 |
\( \frac{290176}{9} a + \frac{48640}{9} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 4 a + 5\) , \( 8 a - 7\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(4a+5\right){x}+8a-7$ |
49152.1-q1 |
49152.1-q |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
49152.1 |
\( 2^{14} \cdot 3 \) |
\( 2^{16} \cdot 3 \) |
$2.30454$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$4.909453989$ |
2.834474582 |
\( \frac{4736}{3} a - \frac{2560}{3} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -a - 1\) , \( 2 a - 1\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-a-1\right){x}+2a-1$ |
49152.1-q2 |
49152.1-q |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
49152.1 |
\( 2^{14} \cdot 3 \) |
\( 2^{26} \cdot 3^{2} \) |
$2.30454$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.454726994$ |
2.834474582 |
\( -\frac{10336}{3} a + \frac{6304}{3} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -a + 9\) , \( 8 a - 1\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-a+9\right){x}+8a-1$ |
49152.1-r1 |
49152.1-r |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
49152.1 |
\( 2^{14} \cdot 3 \) |
\( 2^{26} \cdot 3^{6} \) |
$2.30454$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.174863789$ |
$1.733611078$ |
4.200511455 |
\( \frac{32224}{27} a + \frac{4928}{3} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 19 a - 15\) , \( 20 a - 5\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(19a-15\right){x}+20a-5$ |
49152.1-r2 |
49152.1-r |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
49152.1 |
\( 2^{14} \cdot 3 \) |
\( 2^{16} \cdot 3^{3} \) |
$2.30454$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.349727578$ |
$3.467222156$ |
4.200511455 |
\( -\frac{290176}{9} a + \frac{338816}{9} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 9 a - 5\) , \( -8 a + 1\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(9a-5\right){x}-8a+1$ |
49152.1-s1 |
49152.1-s |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
49152.1 |
\( 2^{14} \cdot 3 \) |
\( 2^{14} \cdot 3^{6} \) |
$2.30454$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.374322969$ |
$3.467222156$ |
4.495922012 |
\( \frac{32224}{27} a + \frac{4928}{3} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 5 a - 4\) , \( -3 a + 3\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(5a-4\right){x}-3a+3$ |
49152.1-s2 |
49152.1-s |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
49152.1 |
\( 2^{14} \cdot 3 \) |
\( 2^{28} \cdot 3^{3} \) |
$2.30454$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.748645938$ |
$1.733611078$ |
4.495922012 |
\( -\frac{290176}{9} a + \frac{338816}{9} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 35 a - 19\) , \( 48 a + 27\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(35a-19\right){x}+48a+27$ |
49152.1-t1 |
49152.1-t |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
49152.1 |
\( 2^{14} \cdot 3 \) |
\( 2^{28} \cdot 3 \) |
$2.30454$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.417557229$ |
$2.454726994$ |
4.018029934 |
\( \frac{4736}{3} a - \frac{2560}{3} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 8 a - 5\) , \( -8 a + 3\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(8a-5\right){x}-8a+3$ |
49152.1-t2 |
49152.1-t |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
49152.1 |
\( 2^{14} \cdot 3 \) |
\( 2^{14} \cdot 3^{2} \) |
$2.30454$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.708778614$ |
$4.909453989$ |
4.018029934 |
\( -\frac{10336}{3} a + \frac{6304}{3} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -2 a\) , \( -2 a\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-2a{x}-2a$ |
49152.1-u1 |
49152.1-u |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
49152.1 |
\( 2^{14} \cdot 3 \) |
\( 2^{14} \cdot 3^{6} \) |
$2.30454$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.374322969$ |
$3.467222156$ |
4.495922012 |
\( -\frac{32224}{27} a + \frac{76576}{27} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( a + 4\) , \( 3 a\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(a+4\right){x}+3a$ |
49152.1-u2 |
49152.1-u |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
49152.1 |
\( 2^{14} \cdot 3 \) |
\( 2^{28} \cdot 3^{3} \) |
$2.30454$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.748645938$ |
$1.733611078$ |
4.495922012 |
\( \frac{290176}{9} a + \frac{48640}{9} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 16 a + 19\) , \( -48 a + 75\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(16a+19\right){x}-48a+75$ |
49152.1-v1 |
49152.1-v |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
49152.1 |
\( 2^{14} \cdot 3 \) |
\( 2^{26} \cdot 3^{4} \) |
$2.30454$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.233061224$ |
$2.146294034$ |
4.620815173 |
\( \frac{4000}{9} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 7\) , \( -9\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+7{x}-9$ |
49152.1-v2 |
49152.1-v |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
49152.1 |
\( 2^{14} \cdot 3 \) |
\( 2^{16} \cdot 3^{2} \) |
$2.30454$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.466122448$ |
$4.292588069$ |
4.620815173 |
\( \frac{16000}{3} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -3\) , \( -3\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-3{x}-3$ |
49152.1-w1 |
49152.1-w |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
49152.1 |
\( 2^{14} \cdot 3 \) |
\( 2^{14} \cdot 3^{12} \) |
$2.30454$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.331892912$ |
$2.054849002$ |
4.724964074 |
\( -\frac{219488}{729} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -6\) , \( -18\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-6{x}-18$ |
49152.1-w2 |
49152.1-w |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
49152.1 |
\( 2^{14} \cdot 3 \) |
\( 2^{28} \cdot 3^{6} \) |
$2.30454$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.663785825$ |
$1.027424501$ |
4.724964074 |
\( \frac{19056256}{27} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -141\) , \( -693\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-141{x}-693$ |
49152.1-x1 |
49152.1-x |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
49152.1 |
\( 2^{14} \cdot 3 \) |
\( 2^{26} \cdot 3^{2} \) |
$2.30454$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.454726994$ |
2.834474582 |
\( \frac{10336}{3} a - 1344 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 8 a - 9\) , \( -8 a + 7\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(8a-9\right){x}-8a+7$ |
49152.1-x2 |
49152.1-x |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
49152.1 |
\( 2^{14} \cdot 3 \) |
\( 2^{16} \cdot 3 \) |
$2.30454$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$4.909453989$ |
2.834474582 |
\( -\frac{4736}{3} a + \frac{2176}{3} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -2 a + 1\) , \( -2 a + 1\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-2a+1\right){x}-2a+1$ |
*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.