| 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 |
| 896.7-a1 |
896.7-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
896.7 |
\( 2^{7} \cdot 7 \) |
\( 2^{19} \cdot 7 \) |
$1.29349$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.691498443$ |
$1.383696732$ |
1.446582121 |
\( -\frac{4096655365}{28} a - \frac{1660660737}{28} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -107 a - 23\) , \( 555 a - 201\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-107a-23\right){x}+555a-201$ |
| 896.7-a2 |
896.7-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
896.7 |
\( 2^{7} \cdot 7 \) |
\( 2^{11} \cdot 7^{2} \) |
$1.29349$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.345749221$ |
$2.767393464$ |
1.446582121 |
\( \frac{13647889}{14} a - \frac{94721547}{14} \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 8 a + 19\) , \( -33 a + 50\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(8a+19\right){x}-33a+50$ |
| 896.7-a3 |
896.7-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
896.7 |
\( 2^{7} \cdot 7 \) |
\( 2^{20} \cdot 7^{2} \) |
$1.29349$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.345749221$ |
$2.767393464$ |
1.446582121 |
\( \frac{1145925}{112} a - \frac{1290439}{112} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -7 a - 3\) , \( 7 a + 3\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-7a-3\right){x}+7a+3$ |
| 896.7-a4 |
896.7-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
896.7 |
\( 2^{7} \cdot 7 \) |
\( 2^{25} \cdot 7 \) |
$1.29349$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.172874610$ |
$2.767393464$ |
1.446582121 |
\( \frac{138325}{1792} a - \frac{774199}{1792} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 2 a + 1\) , \( 5\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(2a+1\right){x}+5$ |
| 896.7-a5 |
896.7-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
896.7 |
\( 2^{7} \cdot 7 \) |
\( 2^{17} \cdot 7^{8} \) |
$1.29349$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.086437305$ |
$1.383696732$ |
1.446582121 |
\( \frac{5786513}{4802} a - \frac{2104499}{4802} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -7 a + 25\) , \( -34 a + 18\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-7a+25\right){x}-34a+18$ |
| 896.7-a6 |
896.7-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
896.7 |
\( 2^{7} \cdot 7 \) |
\( 2^{16} \cdot 7^{4} \) |
$1.29349$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.172874610$ |
$2.767393464$ |
1.446582121 |
\( -\frac{361845}{196} a + \frac{274391}{196} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 3 a - 5\) , \( -6 a - 2\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(3a-5\right){x}-6a-2$ |
| 896.7-b1 |
896.7-b |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
896.7 |
\( 2^{7} \cdot 7 \) |
\( 2^{54} \cdot 7^{2} \) |
$1.29349$ |
$(a), (-a+1), (-2a+1)$ |
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 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 851 a - 1193\) , \( 14853 a - 9611\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(851a-1193\right){x}+14853a-9611$ |
| 896.7-b2 |
896.7-b |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
896.7 |
\( 2^{7} \cdot 7 \) |
\( 2^{33} \cdot 7^{3} \) |
$1.29349$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$0.928520088$ |
2.105685636 |
\( -\frac{10538337875}{200704} a - \frac{13018580375}{100352} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -100 a + 11\) , \( 400 a - 335\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(-100a+11\right){x}+400a-335$ |
| 896.7-b3 |
896.7-b |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
896.7 |
\( 2^{7} \cdot 7 \) |
\( 2^{33} \cdot 7^{3} \) |
$1.29349$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$0.928520088$ |
2.105685636 |
\( \frac{10538337875}{200704} a - \frac{36575498625}{200704} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -12 a + 144\) , \( 463 a - 201\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-12a+144\right){x}+463a-201$ |
| 896.7-b4 |
896.7-b |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
896.7 |
\( 2^{7} \cdot 7 \) |
\( 2^{23} \cdot 7 \) |
$1.29349$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$2.785560266$ |
2.105685636 |
\( -\frac{831875}{112} a - \frac{166375}{112} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -7 a + 9\) , \( a - 15\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-7a+9\right){x}+a-15$ |
| 896.7-b5 |
896.7-b |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
896.7 |
\( 2^{7} \cdot 7 \) |
\( 2^{23} \cdot 7 \) |
$1.29349$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.785560266$ |
2.105685636 |
\( \frac{831875}{112} a - \frac{499125}{56} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -5 a + 6\) , \( 3 a + 16\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(-5a+6\right){x}+3a+16$ |
| 896.7-b6 |
896.7-b |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
896.7 |
\( 2^{7} \cdot 7 \) |
\( 2^{22} \cdot 7^{2} \) |
$1.29349$ |
$(a), (-a+1), (-2a+1)$ |
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 |
\( -\frac{15625}{28} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( a - 3\) , \( -5 a + 3\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(a-3\right){x}-5a+3$ |
| 896.7-b7 |
896.7-b |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
896.7 |
\( 2^{7} \cdot 7 \) |
\( 2^{30} \cdot 7^{6} \) |
$1.29349$ |
$(a), (-a+1), (-2a+1)$ |
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 |
\( \frac{9938375}{21952} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -24 a + 32\) , \( 97 a - 63\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-24a+32\right){x}+97a-63$ |
| 896.7-b8 |
896.7-b |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
896.7 |
\( 2^{7} \cdot 7 \) |
\( 2^{63} \cdot 7 \) |
$1.29349$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$0.309506696$ |
2.105685636 |
\( -\frac{70135314719125}{481036337152} a + \frac{179276652423375}{240518168576} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 255 a + 26\) , \( 2541 a - 2718\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(255a+26\right){x}+2541a-2718$ |
| 896.7-b9 |
896.7-b |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
896.7 |
\( 2^{7} \cdot 7 \) |
\( 2^{63} \cdot 7 \) |
$1.29349$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$1$ |
$0.309506696$ |
2.105685636 |
\( \frac{70135314719125}{481036337152} a + \frac{288417990127625}{481036337152} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -17 a - 361\) , \( 2579 a - 629\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-17a-361\right){x}+2579a-629$ |
| 896.7-b10 |
896.7-b |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
896.7 |
\( 2^{7} \cdot 7 \) |
\( 2^{24} \cdot 7^{12} \) |
$1.29349$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.464260044$ |
2.105685636 |
\( \frac{4956477625}{941192} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 176 a - 248\) , \( 1185 a - 767\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(176a-248\right){x}+1185a-767$ |
| 896.7-b11 |
896.7-b |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
896.7 |
\( 2^{7} \cdot 7 \) |
\( 2^{20} \cdot 7^{4} \) |
$1.29349$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.392780133$ |
2.105685636 |
\( \frac{128787625}{98} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 51 a - 73\) , \( -209 a + 135\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(51a-73\right){x}-209a+135$ |
| 896.7-b12 |
896.7-b |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
896.7 |
\( 2^{7} \cdot 7 \) |
\( 2^{36} \cdot 7^{4} \) |
$1.29349$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$0.154753348$ |
2.105685636 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 13651 a - 19113\) , \( 937477 a - 606603\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(13651a-19113\right){x}+937477a-606603$ |
*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.
