| 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 |
| 896.2-a1 |
896.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
896.2 |
\( 2^{7} \cdot 7 \) |
\( 2^{19} \cdot 7 \) |
$1.29349$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.691498443$ |
$1.383696732$ |
1.446582121 |
\( \frac{4096655365}{28} a - \frac{2878658051}{14} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( 107 a - 128\) , \( -577 a + 141\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(107a-128\right){x}-577a+141$ |
| 896.2-a2 |
896.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
896.2 |
\( 2^{7} \cdot 7 \) |
\( 2^{11} \cdot 7^{2} \) |
$1.29349$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.345749221$ |
$2.767393464$ |
1.446582121 |
\( -\frac{13647889}{14} a - \frac{40536829}{7} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -10 a + 29\) , \( 32 a + 18\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-10a+29\right){x}+32a+18$ |
| 896.2-a3 |
896.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
896.2 |
\( 2^{7} \cdot 7 \) |
\( 2^{20} \cdot 7^{2} \) |
$1.29349$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.345749221$ |
$2.767393464$ |
1.446582121 |
\( -\frac{1145925}{112} a - \frac{72257}{56} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( 7 a - 8\) , \( -9 a - 3\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(7a-8\right){x}-9a-3$ |
| 896.2-a4 |
896.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
896.2 |
\( 2^{7} \cdot 7 \) |
\( 2^{25} \cdot 7 \) |
$1.29349$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.172874610$ |
$2.767393464$ |
1.446582121 |
\( -\frac{138325}{1792} a - \frac{317937}{896} \) |
\( \bigl[a\) , \( -a\) , \( 0\) , \( -2 a + 3\) , \( 5\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(-2a+3\right){x}+5$ |
| 896.2-a5 |
896.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
896.2 |
\( 2^{7} \cdot 7 \) |
\( 2^{17} \cdot 7^{8} \) |
$1.29349$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.086437305$ |
$1.383696732$ |
1.446582121 |
\( -\frac{5786513}{4802} a + \frac{263001}{343} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 5 a + 20\) , \( 33 a - 15\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(5a+20\right){x}+33a-15$ |
| 896.2-a6 |
896.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
896.2 |
\( 2^{7} \cdot 7 \) |
\( 2^{16} \cdot 7^{4} \) |
$1.29349$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.172874610$ |
$2.767393464$ |
1.446582121 |
\( \frac{361845}{196} a - \frac{43727}{98} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -5 a\) , \( 5 a - 7\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}-5a{x}+5a-7$ |
| 896.2-b1 |
896.2-b |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
896.2 |
\( 2^{7} \cdot 7 \) |
\( 2^{54} \cdot 7^{2} \) |
$1.29349$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$1$ |
$0.309506696$ |
2.105685636 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -853 a - 340\) , \( -14854 a + 5243\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-853a-340\right){x}-14854a+5243$ |
| 896.2-b2 |
896.2-b |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
896.2 |
\( 2^{7} \cdot 7 \) |
\( 2^{33} \cdot 7^{3} \) |
$1.29349$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$0.928520088$ |
2.105685636 |
\( -\frac{10538337875}{200704} a - \frac{13018580375}{100352} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 10 a + 134\) , \( -464 a + 263\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(10a+134\right){x}-464a+263$ |
| 896.2-b3 |
896.2-b |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
896.2 |
\( 2^{7} \cdot 7 \) |
\( 2^{33} \cdot 7^{3} \) |
$1.29349$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$0.928520088$ |
2.105685636 |
\( \frac{10538337875}{200704} a - \frac{36575498625}{200704} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 100 a - 88\) , \( -488 a - 48\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(100a-88\right){x}-488a-48$ |
| 896.2-b4 |
896.2-b |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
896.2 |
\( 2^{7} \cdot 7 \) |
\( 2^{23} \cdot 7 \) |
$1.29349$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.785560266$ |
2.105685636 |
\( -\frac{831875}{112} a - \frac{166375}{112} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 5 a + 2\) , \( -a + 6\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(5a+2\right){x}-a+6$ |
| 896.2-b5 |
896.2-b |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
896.2 |
\( 2^{7} \cdot 7 \) |
\( 2^{23} \cdot 7 \) |
$1.29349$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$2.785560266$ |
2.105685636 |
\( \frac{831875}{112} a - \frac{499125}{56} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 5 a + 4\) , \( -2 a - 13\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(5a+4\right){x}-2a-13$ |
| 896.2-b6 |
896.2-b |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
896.2 |
\( 2^{7} \cdot 7 \) |
\( 2^{22} \cdot 7^{2} \) |
$1.29349$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$2.785560266$ |
2.105685636 |
\( -\frac{15625}{28} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -3 a\) , \( 4 a - 1\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-3a{x}+4a-1$ |
| 896.2-b7 |
896.2-b |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
896.2 |
\( 2^{7} \cdot 7 \) |
\( 2^{30} \cdot 7^{6} \) |
$1.29349$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3Cs |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$0.928520088$ |
2.105685636 |
\( \frac{9938375}{21952} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 22 a + 10\) , \( -98 a + 35\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(22a+10\right){x}-98a+35$ |
| 896.2-b8 |
896.2-b |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
896.2 |
\( 2^{7} \cdot 7 \) |
\( 2^{63} \cdot 7 \) |
$1.29349$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$1$ |
$0.309506696$ |
2.105685636 |
\( -\frac{70135314719125}{481036337152} a + \frac{179276652423375}{240518168576} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 15 a - 376\) , \( -2580 a + 1951\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(15a-376\right){x}-2580a+1951$ |
| 896.2-b9 |
896.2-b |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
896.2 |
\( 2^{7} \cdot 7 \) |
\( 2^{63} \cdot 7 \) |
$1.29349$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$0.309506696$ |
2.105685636 |
\( \frac{70135314719125}{481036337152} a + \frac{288417990127625}{481036337152} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -255 a + 282\) , \( -2259 a + 50\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-255a+282\right){x}-2259a+50$ |
| 896.2-b10 |
896.2-b |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
896.2 |
\( 2^{7} \cdot 7 \) |
\( 2^{24} \cdot 7^{12} \) |
$1.29349$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.464260044$ |
2.105685636 |
\( \frac{4956477625}{941192} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -178 a - 70\) , \( -1186 a + 419\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-178a-70\right){x}-1186a+419$ |
| 896.2-b11 |
896.2-b |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
896.2 |
\( 2^{7} \cdot 7 \) |
\( 2^{20} \cdot 7^{4} \) |
$1.29349$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.392780133$ |
2.105685636 |
\( \frac{128787625}{98} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -53 a - 20\) , \( 208 a - 73\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-53a-20\right){x}+208a-73$ |
| 896.2-b12 |
896.2-b |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
896.2 |
\( 2^{7} \cdot 7 \) |
\( 2^{36} \cdot 7^{4} \) |
$1.29349$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$0.154753348$ |
2.105685636 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -13653 a - 5460\) , \( -937478 a + 330875\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-13653a-5460\right){x}-937478a+330875$ |
*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.
