| 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 |
| 10.1-a1 |
10.1-a |
$6$ |
$8$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{4} \cdot 5^{2} \) |
$3.55105$ |
$(a^2-6), (-a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$126.0013261$ |
2.326982585 |
\( \frac{42724081}{400} a^{2} - \frac{180314633}{400} a + \frac{203829169}{400} \) |
\( \bigl[a^{2} - 5\) , \( -a^{2} - a + 4\) , \( a\) , \( -254283425430303815 a^{2} - 386052765748533969 a + 807826405432831715\) , \( -128265428101555296555965052 a^{2} - 194732406112317607687625258 a + 407483104922159986550542545\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}-a+4\right){x}^{2}+\left(-254283425430303815a^{2}-386052765748533969a+807826405432831715\right){x}-128265428101555296555965052a^{2}-194732406112317607687625258a+407483104922159986550542545$ |
| 10.1-a2 |
10.1-a |
$6$ |
$8$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{2} \cdot 5 \) |
$3.55105$ |
$(a^2-6), (-a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$31.50033154$ |
2.326982585 |
\( \frac{6198636053943}{20} a^{2} - \frac{22873813810939}{20} a + \frac{18345209369907}{20} \) |
\( \bigl[a^{2} - 5\) , \( -a^{2} - a + 4\) , \( a\) , \( -4049465429197136100 a^{2} - 6147893147574076769 a + 12864641476561585655\) , \( -8291016996382688583156230409 a^{2} - 12587411220000787426202062421 a + 26339516412587041281174042517\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}-a+4\right){x}^{2}+\left(-4049465429197136100a^{2}-6147893147574076769a+12864641476561585655\right){x}-8291016996382688583156230409a^{2}-12587411220000787426202062421a+26339516412587041281174042517$ |
| 10.1-a3 |
10.1-a |
$6$ |
$8$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{2} \cdot 5^{4} \) |
$3.55105$ |
$(a^2-6), (-a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$252.0026523$ |
2.326982585 |
\( \frac{255581}{2500} a^{2} - \frac{8033}{2500} a + \frac{4266969}{2500} \) |
\( \bigl[1\) , \( -a\) , \( a^{2} - 4\) , \( -793533281 a^{2} - 1204741195 a + 2520955258\) , \( 11680631678321 a^{2} + 17733519821337 a - 37107895199680\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-4\right){y}={x}^{3}-a{x}^{2}+\left(-793533281a^{2}-1204741195a+2520955258\right){x}+11680631678321a^{2}+17733519821337a-37107895199680$ |
| 10.1-a4 |
10.1-a |
$6$ |
$8$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2 \cdot 5^{8} \) |
$3.55105$ |
$(a^2-6), (-a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$126.0013261$ |
2.326982585 |
\( \frac{135221999073}{781250} a^{2} + \frac{335585887961}{781250} a - \frac{42363217423}{781250} \) |
\( \bigl[1\) , \( -a\) , \( a^{2} - 4\) , \( -10893142006 a^{2} - 16537954025 a + 34606139728\) , \( 1156292213663076 a^{2} + 1755481334824458 a - 3673394681594914\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-4\right){y}={x}^{3}-a{x}^{2}+\left(-10893142006a^{2}-16537954025a+34606139728\right){x}+1156292213663076a^{2}+1755481334824458a-3673394681594914$ |
| 10.1-a5 |
10.1-a |
$6$ |
$8$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2 \cdot 5^{2} \) |
$3.55105$ |
$(a^2-6), (-a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$126.0013261$ |
2.326982585 |
\( -\frac{3657}{50} a^{2} - \frac{49}{50} a + \frac{86007}{50} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a^{2} - 5\) , \( 4 a^{2} + 6 a - 8\) , \( 12 a^{2} + 18 a - 41\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(4a^{2}+6a-8\right){x}+12a^{2}+18a-41$ |
| 10.1-a6 |
10.1-a |
$6$ |
$8$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{8} \cdot 5 \) |
$3.55105$ |
$(a^2-6), (-a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$31.50033154$ |
2.326982585 |
\( -\frac{3912802297187}{1280} a^{2} - \frac{697237971589}{1280} a + \frac{26568133564637}{1280} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 225468796079696669707481 a^{2} + 342306432946871581914275 a - 716285958340025181167230\) , \( -102770037091536501869102455441620105963 a^{2} - 156025336642090576588977058556709893561 a + 326487459846688471086063418466138671196\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(225468796079696669707481a^{2}+342306432946871581914275a-716285958340025181167230\right){x}-102770037091536501869102455441620105963a^{2}-156025336642090576588977058556709893561a+326487459846688471086063418466138671196$ |
*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.
