| 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 |
| 96.1-a1 |
96.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
96.1 |
\( 2^{5} \cdot 3 \) |
\( - 2^{9} \cdot 3 \) |
$1.37029$ |
$(-a+2), (a+3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$2.703207468$ |
$21.95560021$ |
1.514359844 |
\( -\frac{3625082635210}{3} a + 2959867576296 \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 25 a - 71\) , \( -109 a + 276\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(25a-71\right){x}-109a+276$ |
| 96.1-a2 |
96.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
96.1 |
\( 2^{5} \cdot 3 \) |
\( 2^{6} \cdot 3^{8} \) |
$1.37029$ |
$(-a+2), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.337900933$ |
$10.97780010$ |
1.514359844 |
\( \frac{97336}{81} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 2\) , \( 1\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+2{x}+1$ |
| 96.1-a3 |
96.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
96.1 |
\( 2^{5} \cdot 3 \) |
\( 2^{12} \cdot 3^{4} \) |
$1.37029$ |
$(-a+2), (a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.675801867$ |
$21.95560021$ |
1.514359844 |
\( \frac{21952}{9} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 46 a - 112\) , \( -200 a + 490\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(46a-112\right){x}-200a+490$ |
| 96.1-a4 |
96.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
96.1 |
\( 2^{5} \cdot 3 \) |
\( 2^{12} \cdot 3^{2} \) |
$1.37029$ |
$(-a+2), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.337900933$ |
$10.97780010$ |
1.514359844 |
\( \frac{140608}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -4\) , \( -2\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-4{x}-2$ |
| 96.1-a5 |
96.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
96.1 |
\( 2^{5} \cdot 3 \) |
\( 2^{6} \cdot 3^{2} \) |
$1.37029$ |
$(-a+2), (a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1.351603734$ |
$43.91120043$ |
1.514359844 |
\( \frac{7301384}{3} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -11\) , \( 6\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-11{x}+6$ |
| 96.1-a6 |
96.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
96.1 |
\( 2^{5} \cdot 3 \) |
\( - 2^{9} \cdot 3 \) |
$1.37029$ |
$(-a+2), (a+3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$2.703207468$ |
$21.95560021$ |
1.514359844 |
\( \frac{3625082635210}{3} a + 2959867576296 \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -25 a - 71\) , \( 109 a + 276\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-25a-71\right){x}+109a+276$ |
| 96.1-b1 |
96.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
96.1 |
\( 2^{5} \cdot 3 \) |
\( - 2^{9} \cdot 3 \) |
$1.37029$ |
$(-a+2), (a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$16$ |
\( 1 \) |
$1$ |
$2.004311843$ |
1.636513767 |
\( -\frac{3625082635210}{3} a + 2959867576296 \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -137 a - 334\) , \( -2216 a - 5429\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-137a-334\right){x}-2216a-5429$ |
| 96.1-b2 |
96.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
96.1 |
\( 2^{5} \cdot 3 \) |
\( 2^{6} \cdot 3^{8} \) |
$1.37029$ |
$(-a+2), (a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$8.017247373$ |
1.636513767 |
\( \frac{97336}{81} \) |
\( \bigl[a\) , \( a - 1\) , \( a\) , \( -38 a + 93\) , \( 159 a - 390\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-38a+93\right){x}+159a-390$ |
| 96.1-b3 |
96.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
96.1 |
\( 2^{5} \cdot 3 \) |
\( 2^{12} \cdot 3^{4} \) |
$1.37029$ |
$(-a+2), (a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$16.03449474$ |
1.636513767 |
\( \frac{21952}{9} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -2\) , \( 0\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-2{x}$ |
| 96.1-b4 |
96.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
96.1 |
\( 2^{5} \cdot 3 \) |
\( 2^{12} \cdot 3^{2} \) |
$1.37029$ |
$(-a+2), (a+3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$32.06898949$ |
1.636513767 |
\( \frac{140608}{3} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -86 a - 210\) , \( 774 a + 1896\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-86a-210\right){x}+774a+1896$ |
| 96.1-b5 |
96.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
96.1 |
\( 2^{5} \cdot 3 \) |
\( 2^{6} \cdot 3^{2} \) |
$1.37029$ |
$(-a+2), (a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$8.017247373$ |
1.636513767 |
\( \frac{7301384}{3} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -162 a - 394\) , \( -1646 a - 4031\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-162a-394\right){x}-1646a-4031$ |
| 96.1-b6 |
96.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
96.1 |
\( 2^{5} \cdot 3 \) |
\( - 2^{9} \cdot 3 \) |
$1.37029$ |
$(-a+2), (a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$16$ |
\( 1 \) |
$1$ |
$2.004311843$ |
1.636513767 |
\( \frac{3625082635210}{3} a + 2959867576296 \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 137 a - 334\) , \( 2216 a - 5429\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(137a-334\right){x}+2216a-5429$ |
| 96.1-c1 |
96.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
96.1 |
\( 2^{5} \cdot 3 \) |
\( - 2^{9} \cdot 3 \) |
$1.37029$ |
$(-a+2), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$4.961357382$ |
$2.004311843$ |
2.029832415 |
\( -\frac{3625082635210}{3} a + 2959867576296 \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( 25 a - 66\) , \( 134 a - 345\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(25a-66\right){x}+134a-345$ |
| 96.1-c2 |
96.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
96.1 |
\( 2^{5} \cdot 3 \) |
\( 2^{6} \cdot 3^{8} \) |
$1.37029$ |
$(-a+2), (a+3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.620169672$ |
$8.017247373$ |
2.029832415 |
\( \frac{97336}{81} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 1\) , \( 0\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+{x}$ |
| 96.1-c3 |
96.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
96.1 |
\( 2^{5} \cdot 3 \) |
\( 2^{12} \cdot 3^{4} \) |
$1.37029$ |
$(-a+2), (a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1.240339345$ |
$16.03449474$ |
2.029832415 |
\( \frac{21952}{9} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 46 a - 112\) , \( 200 a - 490\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(46a-112\right){x}+200a-490$ |
| 96.1-c4 |
96.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
96.1 |
\( 2^{5} \cdot 3 \) |
\( 2^{12} \cdot 3^{2} \) |
$1.37029$ |
$(-a+2), (a+3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.620169672$ |
$32.06898949$ |
2.029832415 |
\( \frac{140608}{3} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -4\) , \( 2\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-4{x}+2$ |
| 96.1-c5 |
96.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
96.1 |
\( 2^{5} \cdot 3 \) |
\( 2^{6} \cdot 3^{2} \) |
$1.37029$ |
$(-a+2), (a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$2.480678691$ |
$8.017247373$ |
2.029832415 |
\( \frac{7301384}{3} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -6\) , \( -15\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}-6{x}-15$ |
| 96.1-c6 |
96.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
96.1 |
\( 2^{5} \cdot 3 \) |
\( - 2^{9} \cdot 3 \) |
$1.37029$ |
$(-a+2), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$4.961357382$ |
$2.004311843$ |
2.029832415 |
\( \frac{3625082635210}{3} a + 2959867576296 \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -25 a - 66\) , \( -134 a - 345\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-25a-66\right){x}-134a-345$ |
| 96.1-d1 |
96.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
96.1 |
\( 2^{5} \cdot 3 \) |
\( - 2^{9} \cdot 3 \) |
$1.37029$ |
$(-a+2), (a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$21.95560021$ |
2.240834063 |
\( -\frac{3625082635210}{3} a + 2959867576296 \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( -135 a - 335\) , \( 2080 a + 5094\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-135a-335\right){x}+2080a+5094$ |
| 96.1-d2 |
96.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
96.1 |
\( 2^{5} \cdot 3 \) |
\( 2^{6} \cdot 3^{8} \) |
$1.37029$ |
$(-a+2), (a+3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$10.97780010$ |
2.240834063 |
\( \frac{97336}{81} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -40 a + 98\) , \( -198 a + 485\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-40a+98\right){x}-198a+485$ |
| 96.1-d3 |
96.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
96.1 |
\( 2^{5} \cdot 3 \) |
\( 2^{12} \cdot 3^{4} \) |
$1.37029$ |
$(-a+2), (a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$21.95560021$ |
2.240834063 |
\( \frac{21952}{9} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -2\) , \( 0\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-2{x}$ |
| 96.1-d4 |
96.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
96.1 |
\( 2^{5} \cdot 3 \) |
\( 2^{12} \cdot 3^{2} \) |
$1.37029$ |
$(-a+2), (a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$10.97780010$ |
2.240834063 |
\( \frac{140608}{3} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -86 a - 210\) , \( -774 a - 1896\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-86a-210\right){x}-774a-1896$ |
| 96.1-d5 |
96.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
96.1 |
\( 2^{5} \cdot 3 \) |
\( 2^{6} \cdot 3^{2} \) |
$1.37029$ |
$(-a+2), (a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$43.91120043$ |
2.240834063 |
\( \frac{7301384}{3} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( -160 a - 395\) , \( 1485 a + 3636\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-160a-395\right){x}+1485a+3636$ |
| 96.1-d6 |
96.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
96.1 |
\( 2^{5} \cdot 3 \) |
\( - 2^{9} \cdot 3 \) |
$1.37029$ |
$(-a+2), (a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$21.95560021$ |
2.240834063 |
\( \frac{3625082635210}{3} a + 2959867576296 \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 135 a - 335\) , \( -2080 a + 5094\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(135a-335\right){x}-2080a+5094$ |
*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.
