| 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 |
| 2009.3-a1 |
2009.3-a |
$4$ |
$10$ |
\(\Q(\zeta_{7})^+\) |
$3$ |
$[3, 0]$ |
2009.3 |
\( 7^{2} \cdot 41 \) |
\( 7^{6} \cdot 41^{5} \) |
$2.22194$ |
$(-a^2-a+2), (3a^2-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B.4.2 |
$1$ |
\( 2 \) |
$1$ |
$19.74415128$ |
1.410296520 |
\( \frac{653981503916958524755}{115856201} a^{2} - \frac{1469483101129546552831}{115856201} a + \frac{524452446825637320235}{115856201} \) |
\( \bigl[a^{2} - 2\) , \( a + 1\) , \( 0\) , \( -957 a^{2} + 2101 a - 741\) , \( 25291 a^{2} - 56714 a + 20237\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-957a^{2}+2101a-741\right){x}+25291a^{2}-56714a+20237$ |
| 2009.3-a2 |
2009.3-a |
$4$ |
$10$ |
\(\Q(\zeta_{7})^+\) |
$3$ |
$[3, 0]$ |
2009.3 |
\( 7^{2} \cdot 41 \) |
\( - 7^{6} \cdot 41^{10} \) |
$2.22194$ |
$(-a^2-a+2), (3a^2-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B.4.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$9.872075642$ |
1.410296520 |
\( \frac{174656123697499408263335}{13422659310152401} a^{2} + \frac{182915726357803972950650}{13422659310152401} a - \frac{115913951592431810832436}{13422659310152401} \) |
\( \bigl[a^{2} - 2\) , \( a + 1\) , \( 0\) , \( -1192 a^{2} + 1896 a - 631\) , \( 28308 a^{2} - 54292 a + 18578\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-1192a^{2}+1896a-631\right){x}+28308a^{2}-54292a+18578$ |
| 2009.3-a3 |
2009.3-a |
$4$ |
$10$ |
\(\Q(\zeta_{7})^+\) |
$3$ |
$[3, 0]$ |
2009.3 |
\( 7^{2} \cdot 41 \) |
\( 7^{6} \cdot 41 \) |
$2.22194$ |
$(-a^2-a+2), (3a^2-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2 \) |
$1$ |
$19.74415128$ |
1.410296520 |
\( \frac{1703161}{41} a^{2} - \frac{968480}{41} a - \frac{3784992}{41} \) |
\( \bigl[a^{2} - 2\) , \( a + 1\) , \( 0\) , \( -2 a^{2} + 6 a - 1\) , \( 0\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-2a^{2}+6a-1\right){x}$ |
| 2009.3-a4 |
2009.3-a |
$4$ |
$10$ |
\(\Q(\zeta_{7})^+\) |
$3$ |
$[3, 0]$ |
2009.3 |
\( 7^{2} \cdot 41 \) |
\( - 7^{6} \cdot 41^{2} \) |
$2.22194$ |
$(-a^2-a+2), (3a^2-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$9.872075642$ |
1.410296520 |
\( -\frac{6655766653200}{1681} a^{2} + \frac{3693705667625}{1681} a + \frac{14955417009784}{1681} \) |
\( \bigl[a^{2} - 2\) , \( a + 1\) , \( 0\) , \( 8 a^{2} - 24 a + 4\) , \( -7 a^{2} - 7 a - 7\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(8a^{2}-24a+4\right){x}-7a^{2}-7a-7$ |
| 2009.3-b1 |
2009.3-b |
$8$ |
$12$ |
\(\Q(\zeta_{7})^+\) |
$3$ |
$[3, 0]$ |
2009.3 |
\( 7^{2} \cdot 41 \) |
\( - 7^{18} \cdot 41^{3} \) |
$2.22194$ |
$(-a^2-a+2), (3a^2-a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.475299820$ |
$3.149090877$ |
1.924408709 |
\( \frac{608257561518375308711}{165479321} a^{2} - \frac{195248902607837764964}{23639903} a + \frac{487784684431565552627}{165479321} \) |
\( \bigl[a^{2} + a - 2\) , \( a - 1\) , \( a^{2} + a - 2\) , \( -1410 a^{2} + 2548 a - 811\) , \( 34294 a^{2} - 84492 a + 31470\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-1410a^{2}+2548a-811\right){x}+34294a^{2}-84492a+31470$ |
| 2009.3-b2 |
2009.3-b |
$8$ |
$12$ |
\(\Q(\zeta_{7})^+\) |
$3$ |
$[3, 0]$ |
2009.3 |
\( 7^{2} \cdot 41 \) |
\( - 7^{9} \cdot 41^{12} \) |
$2.22194$ |
$(-a^2-a+2), (3a^2-a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.475299820$ |
$1.574545438$ |
1.924408709 |
\( -\frac{148342019350411926123033}{157944432102563302567} a^{2} + \frac{15038935226638239263044}{157944432102563302567} a + \frac{712219321711936975477731}{157944432102563302567} \) |
\( \bigl[a^{2} + a - 2\) , \( a - 1\) , \( a^{2} + a - 2\) , \( 70 a^{2} + 208 a - 281\) , \( 978 a^{2} - 1050 a - 406\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(70a^{2}+208a-281\right){x}+978a^{2}-1050a-406$ |
| 2009.3-b3 |
2009.3-b |
$8$ |
$12$ |
\(\Q(\zeta_{7})^+\) |
$3$ |
$[3, 0]$ |
2009.3 |
\( 7^{2} \cdot 41 \) |
\( - 7^{7} \cdot 41^{4} \) |
$2.22194$ |
$(-a^2-a+2), (3a^2-a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1.425899462$ |
$1.574545438$ |
1.924408709 |
\( -\frac{390241014154595459}{19780327} a^{2} + \frac{216532581291157529}{19780327} a + \frac{876926260772898398}{19780327} \) |
\( \bigl[a^{2} + a - 2\) , \( a - 1\) , \( a^{2} + a - 2\) , \( 25 a^{2} + 28 a - 181\) , \( 141 a^{2} + 124 a - 877\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(25a^{2}+28a-181\right){x}+141a^{2}+124a-877$ |
| 2009.3-b4 |
2009.3-b |
$8$ |
$12$ |
\(\Q(\zeta_{7})^+\) |
$3$ |
$[3, 0]$ |
2009.3 |
\( 7^{2} \cdot 41 \) |
\( 7^{12} \cdot 41^{6} \) |
$2.22194$ |
$(-a^2-a+2), (3a^2-a-3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.237649910$ |
$12.59636350$ |
1.924408709 |
\( \frac{194949820018496933}{232755107809} a^{2} - \frac{440536895653478871}{232755107809} a + \frac{161247801416875024}{232755107809} \) |
\( \bigl[a^{2} + a - 2\) , \( a - 1\) , \( a^{2} + a - 2\) , \( -70 a^{2} + 138 a - 106\) , \( 530 a^{2} - 1323 a + 644\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-70a^{2}+138a-106\right){x}+530a^{2}-1323a+644$ |
| 2009.3-b5 |
2009.3-b |
$8$ |
$12$ |
\(\Q(\zeta_{7})^+\) |
$3$ |
$[3, 0]$ |
2009.3 |
\( 7^{2} \cdot 41 \) |
\( - 7^{9} \cdot 41^{3} \) |
$2.22194$ |
$(-a^2-a+2), (3a^2-a-3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.118824955$ |
$50.38545403$ |
1.924408709 |
\( -\frac{50936778397734}{482447} a^{2} + \frac{28371120578099}{482447} a + \frac{114582075491395}{482447} \) |
\( \bigl[a^{2} + a - 2\) , \( a - 1\) , \( a^{2} + a - 2\) , \( 5 a^{2} - 17 a - 51\) , \( -28 a^{2} + 36 a + 155\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(5a^{2}-17a-51\right){x}-28a^{2}+36a+155$ |
| 2009.3-b6 |
2009.3-b |
$8$ |
$12$ |
\(\Q(\zeta_{7})^+\) |
$3$ |
$[3, 0]$ |
2009.3 |
\( 7^{2} \cdot 41 \) |
\( 7^{8} \cdot 41^{2} \) |
$2.22194$ |
$(-a^2-a+2), (3a^2-a-3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{3} \) |
$0.712949731$ |
$12.59636350$ |
1.924408709 |
\( \frac{136608119934}{11767} a^{2} + \frac{15859229737}{1681} a - \frac{73949900041}{11767} \) |
\( \bigl[a^{2} + a - 2\) , \( a - 1\) , \( a^{2} + a - 2\) , \( -10 a^{2} - 7 a - 6\) , \( -41 a^{2} - 37 a + 12\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-10a^{2}-7a-6\right){x}-41a^{2}-37a+12$ |
| 2009.3-b7 |
2009.3-b |
$8$ |
$12$ |
\(\Q(\zeta_{7})^+\) |
$3$ |
$[3, 0]$ |
2009.3 |
\( 7^{2} \cdot 41 \) |
\( - 7^{7} \cdot 41 \) |
$2.22194$ |
$(-a^2-a+2), (3a^2-a-3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$0.356474865$ |
$50.38545403$ |
1.924408709 |
\( \frac{368219}{287} a^{2} + \frac{439186}{287} a + \frac{231671}{287} \) |
\( \bigl[a^{2} + a - 2\) , \( a - 1\) , \( a^{2} + a - 2\) , \( -2 a - 1\) , \( -2 a^{2}\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-2a-1\right){x}-2a^{2}$ |
| 2009.3-b8 |
2009.3-b |
$8$ |
$12$ |
\(\Q(\zeta_{7})^+\) |
$3$ |
$[3, 0]$ |
2009.3 |
\( 7^{2} \cdot 41 \) |
\( - 7^{10} \cdot 41 \) |
$2.22194$ |
$(-a^2-a+2), (3a^2-a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1.425899462$ |
$3.149090877$ |
1.924408709 |
\( \frac{1138065299097823549}{2009} a^{2} + \frac{912657509123949273}{2009} a - \frac{631578592566371794}{2009} \) |
\( \bigl[a^{2} + a - 2\) , \( a - 1\) , \( a^{2} + a - 2\) , \( -205 a^{2} - 122 a + 89\) , \( -2219 a^{2} - 1966 a + 1289\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-205a^{2}-122a+89\right){x}-2219a^{2}-1966a+1289$ |
| 2009.3-c1 |
2009.3-c |
$2$ |
$2$ |
\(\Q(\zeta_{7})^+\) |
$3$ |
$[3, 0]$ |
2009.3 |
\( 7^{2} \cdot 41 \) |
\( - 7^{9} \cdot 41^{3} \) |
$2.22194$ |
$(-a^2-a+2), (3a^2-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Nn |
$1$ |
\( 2 \) |
$1$ |
$21.68981779$ |
1.549272699 |
\( -\frac{1678397841}{68921} a^{2} + \frac{985287969}{68921} a + \frac{3838283631}{68921} \) |
\( \bigl[a^{2} - 2\) , \( a^{2} - a - 3\) , \( a^{2} + a - 2\) , \( a^{2} - 3 a - 7\) , \( -11 a^{2} + 10 a + 14\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(a^{2}-3a-7\right){x}-11a^{2}+10a+14$ |
| 2009.3-c2 |
2009.3-c |
$2$ |
$2$ |
\(\Q(\zeta_{7})^+\) |
$3$ |
$[3, 0]$ |
2009.3 |
\( 7^{2} \cdot 41 \) |
\( - 7^{9} \cdot 41^{6} \) |
$2.22194$ |
$(-a^2-a+2), (3a^2-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Nn |
$1$ |
\( 2^{2} \) |
$1$ |
$10.84490889$ |
1.549272699 |
\( \frac{139057029455589}{4750104241} a^{2} - \frac{137763761965398}{4750104241} a + \frac{33768669665754}{4750104241} \) |
\( \bigl[a^{2} - 2\) , \( a^{2} - a - 3\) , \( a^{2} + a - 2\) , \( -34 a^{2} + 32 a - 7\) , \( -39 a^{2} + 206 a - 56\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(-34a^{2}+32a-7\right){x}-39a^{2}+206a-56$ |
| 2009.3-d1 |
2009.3-d |
$6$ |
$8$ |
\(\Q(\zeta_{7})^+\) |
$3$ |
$[3, 0]$ |
2009.3 |
\( 7^{2} \cdot 41 \) |
\( 7^{7} \cdot 41 \) |
$2.22194$ |
$(-a^2-a+2), (3a^2-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$2.329012591$ |
1.330864337 |
\( \frac{7285472030388075562651}{287} a^{2} - \frac{16370307055736088309783}{287} a + \frac{5842494944318891366083}{287} \) |
\( \bigl[a^{2} + a - 1\) , \( 0\) , \( 0\) , \( -231 a^{2} + 551 a - 187\) , \( -3131 a^{2} + 7381 a - 2647\bigr] \) |
${y}^2+\left(a^{2}+a-1\right){x}{y}={x}^{3}+\left(-231a^{2}+551a-187\right){x}-3131a^{2}+7381a-2647$ |
| 2009.3-d2 |
2009.3-d |
$6$ |
$8$ |
\(\Q(\zeta_{7})^+\) |
$3$ |
$[3, 0]$ |
2009.3 |
\( 7^{2} \cdot 41 \) |
\( 7^{8} \cdot 41^{2} \) |
$2.22194$ |
$(-a^2-a+2), (3a^2-a-3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$18.63210072$ |
1.330864337 |
\( \frac{26102258538892}{11767} a^{2} - \frac{58651188873091}{11767} a + \frac{20932401548470}{11767} \) |
\( \bigl[a^{2} + a - 1\) , \( 0\) , \( 0\) , \( -21 a^{2} + 26 a - 12\) , \( -44 a^{2} + 122 a - 43\bigr] \) |
${y}^2+\left(a^{2}+a-1\right){x}{y}={x}^{3}+\left(-21a^{2}+26a-12\right){x}-44a^{2}+122a-43$ |
| 2009.3-d3 |
2009.3-d |
$6$ |
$8$ |
\(\Q(\zeta_{7})^+\) |
$3$ |
$[3, 0]$ |
2009.3 |
\( 7^{2} \cdot 41 \) |
\( 7^{14} \cdot 41^{8} \) |
$2.22194$ |
$(-a^2-a+2), (3a^2-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$4.658025182$ |
1.330864337 |
\( -\frac{2112059827406634793}{2738829353588503} a^{2} - \frac{7759896453669124638}{2738829353588503} a - \frac{1187066622611513396}{2738829353588503} \) |
\( \bigl[a^{2} + a - 1\) , \( 0\) , \( 0\) , \( -141 a^{2} - 69 a - 2\) , \( 1199 a^{2} + 1006 a - 433\bigr] \) |
${y}^2+\left(a^{2}+a-1\right){x}{y}={x}^{3}+\left(-141a^{2}-69a-2\right){x}+1199a^{2}+1006a-433$ |
| 2009.3-d4 |
2009.3-d |
$6$ |
$8$ |
\(\Q(\zeta_{7})^+\) |
$3$ |
$[3, 0]$ |
2009.3 |
\( 7^{2} \cdot 41 \) |
\( - 7^{7} \cdot 41 \) |
$2.22194$ |
$(-a^2-a+2), (3a^2-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$18.63210072$ |
1.330864337 |
\( -\frac{8527313}{287} a^{2} + \frac{15368820}{287} a + \frac{1935428}{287} \) |
\( \bigl[a^{2} + a - 1\) , \( 0\) , \( 0\) , \( -a^{2} + a - 2\) , \( -5 a^{2} - 2 a + 1\bigr] \) |
${y}^2+\left(a^{2}+a-1\right){x}{y}={x}^{3}+\left(-a^{2}+a-2\right){x}-5a^{2}-2a+1$ |
| 2009.3-d5 |
2009.3-d |
$6$ |
$8$ |
\(\Q(\zeta_{7})^+\) |
$3$ |
$[3, 0]$ |
2009.3 |
\( 7^{2} \cdot 41 \) |
\( 7^{10} \cdot 41^{4} \) |
$2.22194$ |
$(-a^2-a+2), (3a^2-a-3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$18.63210072$ |
1.330864337 |
\( \frac{2192037233085291}{138462289} a^{2} + \frac{2267219548655833}{138462289} a - \frac{566434328572957}{138462289} \) |
\( \bigl[a^{2} + a - 1\) , \( 0\) , \( 0\) , \( -131 a^{2} - 99 a + 3\) , \( 1047 a^{2} + 1119 a - 495\bigr] \) |
${y}^2+\left(a^{2}+a-1\right){x}{y}={x}^{3}+\left(-131a^{2}-99a+3\right){x}+1047a^{2}+1119a-495$ |
| 2009.3-d6 |
2009.3-d |
$6$ |
$8$ |
\(\Q(\zeta_{7})^+\) |
$3$ |
$[3, 0]$ |
2009.3 |
\( 7^{2} \cdot 41 \) |
\( - 7^{8} \cdot 41^{2} \) |
$2.22194$ |
$(-a^2-a+2), (3a^2-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$9.316050364$ |
1.330864337 |
\( \frac{16578578064906633289}{11767} a^{2} + \frac{13573746844227896798}{11767} a - \frac{8852809319695445404}{11767} \) |
\( \bigl[a^{2} + a - 1\) , \( 0\) , \( 0\) , \( -1881 a^{2} - 2129 a + 248\) , \( 79699 a^{2} + 72260 a - 34445\bigr] \) |
${y}^2+\left(a^{2}+a-1\right){x}{y}={x}^{3}+\left(-1881a^{2}-2129a+248\right){x}+79699a^{2}+72260a-34445$ |
| 2009.3-e1 |
2009.3-e |
$1$ |
$1$ |
\(\Q(\zeta_{7})^+\) |
$3$ |
$[3, 0]$ |
2009.3 |
\( 7^{2} \cdot 41 \) |
\( - 7^{4} \cdot 41 \) |
$2.22194$ |
$(-a^2-a+2), (3a^2-a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 1 \) |
$1$ |
$9.689094324$ |
1.384156332 |
\( -\frac{3232169285488}{41} a^{2} + \frac{7262751964617}{41} a - \frac{2592239079820}{41} \) |
\( \bigl[a\) , \( -a\) , \( 0\) , \( 6 a^{2} + 6 a - 16\) , \( -32 a^{2} + 3 a + 23\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(6a^{2}+6a-16\right){x}-32a^{2}+3a+23$ |
| 2009.3-f1 |
2009.3-f |
$1$ |
$1$ |
\(\Q(\zeta_{7})^+\) |
$3$ |
$[3, 0]$ |
2009.3 |
\( 7^{2} \cdot 41 \) |
\( - 7^{10} \cdot 41 \) |
$2.22194$ |
$(-a^2-a+2), (3a^2-a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 1 \) |
$1$ |
$9.397122448$ |
1.342446064 |
\( -\frac{3232169285488}{41} a^{2} + \frac{7262751964617}{41} a - \frac{2592239079820}{41} \) |
\( \bigl[a^{2} - 1\) , \( -a^{2} + 2\) , \( a\) , \( -20 a^{2} + 109 a - 50\) , \( 487 a^{2} - 323 a + 36\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}+\left(-20a^{2}+109a-50\right){x}+487a^{2}-323a+36$ |
| 2009.3-g1 |
2009.3-g |
$2$ |
$2$ |
\(\Q(\zeta_{7})^+\) |
$3$ |
$[3, 0]$ |
2009.3 |
\( 7^{2} \cdot 41 \) |
\( - 7^{3} \cdot 41^{3} \) |
$2.22194$ |
$(-a^2-a+2), (3a^2-a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Nn |
$1$ |
\( 2 \cdot 3 \) |
$0.044982973$ |
$69.46321216$ |
2.008711181 |
\( -\frac{1678397841}{68921} a^{2} + \frac{985287969}{68921} a + \frac{3838283631}{68921} \) |
\( \bigl[1\) , \( -1\) , \( a^{2} - 2\) , \( 6 a^{2} - 4 a - 14\) , \( 9 a^{2} - 5 a - 20\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-2\right){y}={x}^{3}-{x}^{2}+\left(6a^{2}-4a-14\right){x}+9a^{2}-5a-20$ |
| 2009.3-g2 |
2009.3-g |
$2$ |
$2$ |
\(\Q(\zeta_{7})^+\) |
$3$ |
$[3, 0]$ |
2009.3 |
\( 7^{2} \cdot 41 \) |
\( - 7^{3} \cdot 41^{6} \) |
$2.22194$ |
$(-a^2-a+2), (3a^2-a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Nn |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.089965947$ |
$17.36580304$ |
2.008711181 |
\( \frac{139057029455589}{4750104241} a^{2} - \frac{137763761965398}{4750104241} a + \frac{33768669665754}{4750104241} \) |
\( \bigl[1\) , \( -1\) , \( a^{2} - 2\) , \( -4 a^{2} + a + 1\) , \( 29 a^{2} - 22 a - 64\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-2\right){y}={x}^{3}-{x}^{2}+\left(-4a^{2}+a+1\right){x}+29a^{2}-22a-64$ |
| 2009.3-h1 |
2009.3-h |
$4$ |
$4$ |
\(\Q(\zeta_{7})^+\) |
$3$ |
$[3, 0]$ |
2009.3 |
\( 7^{2} \cdot 41 \) |
\( 7^{9} \cdot 41 \) |
$2.22194$ |
$(-a^2-a+2), (3a^2-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$10.93449901$ |
1.562071287 |
\( -\frac{3757099654268041163342}{287} a^{2} + \frac{2085033006198273477042}{287} a + \frac{1206018041753572571647}{41} \) |
\( \bigl[a^{2} + a - 1\) , \( -a^{2} - a + 3\) , \( 0\) , \( 2647 a^{2} - 1421 a - 6119\) , \( -80513 a^{2} + 45278 a + 180062\bigr] \) |
${y}^2+\left(a^{2}+a-1\right){x}{y}={x}^{3}+\left(-a^{2}-a+3\right){x}^{2}+\left(2647a^{2}-1421a-6119\right){x}-80513a^{2}+45278a+180062$ |
| 2009.3-h2 |
2009.3-h |
$4$ |
$4$ |
\(\Q(\zeta_{7})^+\) |
$3$ |
$[3, 0]$ |
2009.3 |
\( 7^{2} \cdot 41 \) |
\( 7^{18} \cdot 41^{4} \) |
$2.22194$ |
$(-a^2-a+2), (3a^2-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$5.467249507$ |
1.562071287 |
\( \frac{257433612414194}{6784652161} a^{2} - \frac{29980896276738}{969236023} a - \frac{454911131539607}{6784652161} \) |
\( \bigl[a^{2} + a - 1\) , \( -a^{2} - a + 3\) , \( 0\) , \( 157 a^{2} - 41 a - 399\) , \( -1131 a^{2} + 486 a + 2676\bigr] \) |
${y}^2+\left(a^{2}+a-1\right){x}{y}={x}^{3}+\left(-a^{2}-a+3\right){x}^{2}+\left(157a^{2}-41a-399\right){x}-1131a^{2}+486a+2676$ |
| 2009.3-h3 |
2009.3-h |
$4$ |
$4$ |
\(\Q(\zeta_{7})^+\) |
$3$ |
$[3, 0]$ |
2009.3 |
\( 7^{2} \cdot 41 \) |
\( 7^{12} \cdot 41^{2} \) |
$2.22194$ |
$(-a^2-a+2), (3a^2-a-3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$21.86899802$ |
1.562071287 |
\( -\frac{196685668098692}{82369} a^{2} + \frac{109152381994424}{82369} a + \frac{63135574000099}{11767} \) |
\( \bigl[a^{2} + a - 1\) , \( -a^{2} - a + 3\) , \( 0\) , \( 162 a^{2} - 91 a - 379\) , \( -1168 a^{2} + 646 a + 2591\bigr] \) |
${y}^2+\left(a^{2}+a-1\right){x}{y}={x}^{3}+\left(-a^{2}-a+3\right){x}^{2}+\left(162a^{2}-91a-379\right){x}-1168a^{2}+646a+2591$ |
| 2009.3-h4 |
2009.3-h |
$4$ |
$4$ |
\(\Q(\zeta_{7})^+\) |
$3$ |
$[3, 0]$ |
2009.3 |
\( 7^{2} \cdot 41 \) |
\( - 7^{9} \cdot 41 \) |
$2.22194$ |
$(-a^2-a+2), (3a^2-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$21.86899802$ |
1.562071287 |
\( \frac{1599727032}{287} a^{2} + \frac{1295404736}{287} a - \frac{124555775}{41} \) |
\( \bigl[a^{2} + a - 1\) , \( -a^{2} - a + 3\) , \( 0\) , \( 7 a^{2} - 11 a - 19\) , \( -21 a^{2} - 2 a + 32\bigr] \) |
${y}^2+\left(a^{2}+a-1\right){x}{y}={x}^{3}+\left(-a^{2}-a+3\right){x}^{2}+\left(7a^{2}-11a-19\right){x}-21a^{2}-2a+32$ |
*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.
