| 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 |
| 14.1-a1 |
14.1-a |
$6$ |
$8$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( - 2^{2} \cdot 7^{4} \) |
$3.75588$ |
$(a^2-6), (a^2+2a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{2} \) |
$1$ |
$1.827484389$ |
1.079994816 |
\( \frac{1877523050205850819867}{9604} a^{2} + \frac{2850453053925631208941}{9604} a - \frac{5964654178350087194017}{9604} \) |
\( \bigl[a + 1\) , \( a^{2} - a - 6\) , \( a\) , \( 12659494600 a^{2} + 2255846982 a - 85958636601\) , \( 1249197047855543 a^{2} + 222599518707425 a - 8482113899832843\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-a-6\right){x}^{2}+\left(12659494600a^{2}+2255846982a-85958636601\right){x}+1249197047855543a^{2}+222599518707425a-8482113899832843$ |
| 14.1-a2 |
14.1-a |
$6$ |
$8$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{4} \cdot 7^{8} \) |
$3.75588$ |
$(a^2-6), (a^2+2a-3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$1$ |
$14.61987511$ |
1.079994816 |
\( \frac{15427621259743353}{92236816} a^{2} + \frac{23422306501830847}{92236816} a - \frac{49009686564823095}{92236816} \) |
\( \bigl[a + 1\) , \( a^{2} - a - 6\) , \( a\) , \( 800045825 a^{2} + 142563442 a - 5432353421\) , \( 19059955059430 a^{2} + 3396371157117 a - 129418101025383\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-a-6\right){x}^{2}+\left(800045825a^{2}+142563442a-5432353421\right){x}+19059955059430a^{2}+3396371157117a-129418101025383$ |
| 14.1-a3 |
14.1-a |
$6$ |
$8$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{8} \cdot 7^{4} \) |
$3.75588$ |
$(a^2-6), (a^2+2a-3)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$116.9590009$ |
1.079994816 |
\( \frac{2778614905}{614656} a^{2} + \frac{4124250559}{614656} a - \frac{6531491399}{614656} \) |
\( \bigl[a + 1\) , \( a^{2} - a - 6\) , \( a\) , \( 135425830 a^{2} + 24132082 a - 919548541\) , \( -991007863993 a^{2} - 176591734617 a + 6728995711641\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-a-6\right){x}^{2}+\left(135425830a^{2}+24132082a-919548541\right){x}-991007863993a^{2}-176591734617a+6728995711641$ |
| 14.1-a4 |
14.1-a |
$6$ |
$8$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{2} \cdot 7^{16} \) |
$3.75588$ |
$(a^2-6), (a^2+2a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{2} \) |
$1$ |
$1.827484389$ |
1.079994816 |
\( \frac{1859303337563245586309}{132931722278404} a^{2} - \frac{6876035583588327084941}{132931722278404} a + \frac{5520331263860774385921}{132931722278404} \) |
\( \bigl[a + 1\) , \( a^{2} - a - 6\) , \( a\) , \( -425483030 a^{2} - 75818338 a + 2889051679\) , \( 72233447083969 a^{2} + 12871572653085 a - 490468918899299\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-a-6\right){x}^{2}+\left(-425483030a^{2}-75818338a+2889051679\right){x}+72233447083969a^{2}+12871572653085a-490468918899299$ |
| 14.1-a5 |
14.1-a |
$6$ |
$8$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( - 2^{4} \cdot 7^{2} \) |
$3.75588$ |
$(a^2-6), (a^2+2a-3)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$233.9180018$ |
1.079994816 |
\( -\frac{1129805449}{784} a^{2} - \frac{201001775}{784} a + \frac{7672803655}{784} \) |
\( \bigl[a + 1\) , \( a^{2} - 5\) , \( a^{2} + a - 5\) , \( 2727719912262131 a^{2} + 486063540319786 a - 18521362200115984\) , \( -124929064793722765572661 a^{2} - 22261619768770883846309 a + 848274944932820465801609\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}+a-5\right){y}={x}^{3}+\left(a^{2}-5\right){x}^{2}+\left(2727719912262131a^{2}+486063540319786a-18521362200115984\right){x}-124929064793722765572661a^{2}-22261619768770883846309a+848274944932820465801609$ |
| 14.1-a6 |
14.1-a |
$6$ |
$8$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{16} \cdot 7^{2} \) |
$3.75588$ |
$(a^2-6), (a^2+2a-3)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$58.47950045$ |
1.079994816 |
\( \frac{1776643018601}{3211264} a^{2} - \frac{6569010809009}{3211264} a + \frac{5275811088297}{3211264} \) |
\( \bigl[a + 1\) , \( -a^{2} - a + 4\) , \( a\) , \( -17 a^{2} - 3 a + 112\) , \( -78 a^{2} - 14 a + 528\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}-a+4\right){x}^{2}+\left(-17a^{2}-3a+112\right){x}-78a^{2}-14a+528$ |
*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.
