| 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 |
| 100.2-a1 |
100.2-a |
$12$ |
$24$ |
3.3.148.1 |
$3$ |
$[3, 0]$ |
100.2 |
\( 2^{2} \cdot 5^{2} \) |
\( - 2^{4} \cdot 5^{7} \) |
$2.34209$ |
$(a^2-a-2), (a^2-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$14.18378554$ |
1.165899989 |
\( -\frac{385146932}{5} a^{2} + \frac{268247176}{5} a + \frac{1242320604}{5} \) |
\( \bigl[a^{2} - a - 2\) , \( a + 1\) , \( a^{2} - 1\) , \( -1133977 a^{2} - 1326850 a + 522550\) , \( -1211652310 a^{2} - 1417737994 a + 558342867\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-1133977a^{2}-1326850a+522550\right){x}-1211652310a^{2}-1417737994a+558342867$ |
| 100.2-a2 |
100.2-a |
$12$ |
$24$ |
3.3.148.1 |
$3$ |
$[3, 0]$ |
100.2 |
\( 2^{2} \cdot 5^{2} \) |
\( - 2^{4} \cdot 5^{9} \) |
$2.34209$ |
$(a^2-a-2), (a^2-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$4.727928513$ |
1.165899989 |
\( \frac{179143376765057962508}{125} a^{2} + \frac{209613244321350839256}{125} a - \frac{82551261375569819076}{125} \) |
\( \bigl[a^{2} - a - 2\) , \( a + 1\) , \( a^{2} - 1\) , \( -91841802 a^{2} - 107462850 a + 42321725\) , \( -882708628396 a^{2} - 1032845437714 a + 406761958031\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-91841802a^{2}-107462850a+42321725\right){x}-882708628396a^{2}-1032845437714a+406761958031$ |
| 100.2-a3 |
100.2-a |
$12$ |
$24$ |
3.3.148.1 |
$3$ |
$[3, 0]$ |
100.2 |
\( 2^{2} \cdot 5^{2} \) |
\( - 2^{8} \cdot 5^{8} \) |
$2.34209$ |
$(a^2-a-2), (a^2-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$14.18378554$ |
1.165899989 |
\( \frac{13838352792668}{25} a^{2} - \frac{34335804621874}{25} a + \frac{9343051795654}{25} \) |
\( \bigl[a^{2} - a - 2\) , \( a + 1\) , \( a + 1\) , \( 14415 a^{2} + 16870 a - 6640\) , \( 1452659431 a^{2} + 1699737171 a - 669401630\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(14415a^{2}+16870a-6640\right){x}+1452659431a^{2}+1699737171a-669401630$ |
| 100.2-a4 |
100.2-a |
$12$ |
$24$ |
3.3.148.1 |
$3$ |
$[3, 0]$ |
100.2 |
\( 2^{2} \cdot 5^{2} \) |
\( - 2^{8} \cdot 5^{12} \) |
$2.34209$ |
$(a^2-a-2), (a^2-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$4.727928513$ |
1.165899989 |
\( -\frac{8271321267405818624506172}{15625} a^{2} + \frac{5698048560343235071057746}{15625} a + \frac{26586671253641020172342134}{15625} \) |
\( \bigl[a^{2} - a - 2\) , \( a + 1\) , \( a + 1\) , \( -129745 a^{2} - 151810 a + 59790\) , \( -39221573161 a^{2} - 45892632739 a + 18073737338\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-129745a^{2}-151810a+59790\right){x}-39221573161a^{2}-45892632739a+18073737338$ |
| 100.2-a5 |
100.2-a |
$12$ |
$24$ |
3.3.148.1 |
$3$ |
$[3, 0]$ |
100.2 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{10} \) |
$2.34209$ |
$(a^2-a-2), (a^2-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$56.73514216$ |
1.165899989 |
\( \frac{185785252}{625} a^{2} - \frac{445080936}{625} a + \frac{123160356}{625} \) |
\( \bigl[a^{2} - a - 2\) , \( a + 1\) , \( a + 1\) , \( -629720 a^{2} - 736825 a + 290185\) , \( 491951439 a^{2} + 575625731 a - 226696697\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-629720a^{2}-736825a+290185\right){x}+491951439a^{2}+575625731a-226696697$ |
| 100.2-a6 |
100.2-a |
$12$ |
$24$ |
3.3.148.1 |
$3$ |
$[3, 0]$ |
100.2 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{18} \) |
$2.34209$ |
$(a^2-a-2), (a^2-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$18.91171405$ |
1.165899989 |
\( -\frac{3077332109418143868}{244140625} a^{2} + \frac{2119953522630977224}{244140625} a + \frac{9891535601060896996}{244140625} \) |
\( \bigl[a^{2} - a - 2\) , \( a + 1\) , \( a + 1\) , \( -5764785 a^{2} - 6745295 a + 2656480\) , \( -13672472712 a^{2} - 15997975559 a + 6300427562\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-5764785a^{2}-6745295a+2656480\right){x}-13672472712a^{2}-15997975559a+6300427562$ |
| 100.2-a7 |
100.2-a |
$12$ |
$24$ |
3.3.148.1 |
$3$ |
$[3, 0]$ |
100.2 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{14} \) |
$2.34209$ |
$(a^2-a-2), (a^2-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$14.18378554$ |
1.165899989 |
\( \frac{148445904580292}{390625} a^{2} + \frac{173694846086594}{390625} a - \frac{68405381268774}{390625} \) |
\( \bigl[a^{2} - a - 2\) , \( a + 1\) , \( a + 1\) , \( -10028115 a^{2} - 11733760 a + 4621070\) , \( 31833826821 a^{2} + 37248330581 a - 14669381620\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-10028115a^{2}-11733760a+4621070\right){x}+31833826821a^{2}+37248330581a-14669381620$ |
| 100.2-a8 |
100.2-a |
$12$ |
$24$ |
3.3.148.1 |
$3$ |
$[3, 0]$ |
100.2 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{30} \) |
$2.34209$ |
$(a^2-a-2), (a^2-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$4.727928513$ |
1.165899989 |
\( \frac{3678043576600698623452}{59604644775390625} a^{2} - \frac{2506193844958703814786}{59604644775390625} a - \frac{11746914365786968746294}{59604644775390625} \) |
\( \bigl[a^{2} - a - 2\) , \( a + 1\) , \( a + 1\) , \( -11794565 a^{2} - 13800660 a + 5435070\) , \( 19845961659 a^{2} + 23221491551 a - 9145239962\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-11794565a^{2}-13800660a+5435070\right){x}+19845961659a^{2}+23221491551a-9145239962$ |
| 100.2-a9 |
100.2-a |
$12$ |
$24$ |
3.3.148.1 |
$3$ |
$[3, 0]$ |
100.2 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{9} \) |
$2.34209$ |
$(a^2-a-2), (a^2-a-1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$18.91171405$ |
1.165899989 |
\( \frac{3238786394956992}{125} a^{2} - \frac{8036058359040256}{125} a + \frac{2186604679552576}{125} \) |
\( \bigl[a^{2} - 1\) , \( -a - 1\) , \( a^{2} - a - 2\) , \( -648 a^{2} + 1600 a - 436\) , \( 15979 a^{2} - 39659 a + 10791\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-648a^{2}+1600a-436\right){x}+15979a^{2}-39659a+10791$ |
| 100.2-a10 |
100.2-a |
$12$ |
$24$ |
3.3.148.1 |
$3$ |
$[3, 0]$ |
100.2 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{7} \) |
$2.34209$ |
$(a^2-a-2), (a^2-a-1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$56.73514216$ |
1.165899989 |
\( \frac{43712}{5} a^{2} - \frac{105216}{5} a + \frac{28736}{5} \) |
\( \bigl[a^{2} - 1\) , \( -a - 1\) , \( a^{2} - a - 2\) , \( -8 a^{2} + 20 a - 6\) , \( 20 a^{2} - 49 a + 12\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-8a^{2}+20a-6\right){x}+20a^{2}-49a+12$ |
| 100.2-a11 |
100.2-a |
$12$ |
$24$ |
3.3.148.1 |
$3$ |
$[3, 0]$ |
100.2 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{8} \) |
$2.34209$ |
$(a^2-a-2), (a^2-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$56.73514216$ |
1.165899989 |
\( -\frac{108768}{25} a^{2} + \frac{75424}{25} a + \frac{407296}{25} \) |
\( \bigl[a^{2} - 1\) , \( -a^{2} + 2 a + 3\) , \( 0\) , \( -6979 a^{2} - 8164 a + 3220\) , \( -314976 a^{2} - 368548 a + 145146\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}={x}^{3}+\left(-a^{2}+2a+3\right){x}^{2}+\left(-6979a^{2}-8164a+3220\right){x}-314976a^{2}-368548a+145146$ |
| 100.2-a12 |
100.2-a |
$12$ |
$24$ |
3.3.148.1 |
$3$ |
$[3, 0]$ |
100.2 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{12} \) |
$2.34209$ |
$(a^2-a-2), (a^2-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$18.91171405$ |
1.165899989 |
\( \frac{7209817568672}{15625} a^{2} + \frac{8324376473504}{15625} a - \frac{3284389248384}{15625} \) |
\( \bigl[a^{2} - 1\) , \( -a^{2} + 2 a + 3\) , \( 0\) , \( -485159 a^{2} - 567674 a + 223570\) , \( -339852422 a^{2} - 397656728 a + 156607780\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}={x}^{3}+\left(-a^{2}+2a+3\right){x}^{2}+\left(-485159a^{2}-567674a+223570\right){x}-339852422a^{2}-397656728a+156607780$ |
*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.
