| 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 |
| 224.1-a4 |
224.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
224.1 |
\( 2^{5} \cdot 7 \) |
\( 2^{12} \cdot 7 \) |
$0.91464$ |
$(a), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$3.472144299$ |
1.312347190 |
\( \frac{9225207}{7} a + \frac{485654}{7} \) |
\( \bigl[a\) , \( a - 1\) , \( a\) , \( -12 a + 6\) , \( 14 a - 13\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-12a+6\right){x}+14a-13$ |
| 448.1-a4 |
448.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
448.1 |
\( 2^{6} \cdot 7 \) |
\( 2^{6} \cdot 7 \) |
$1.08769$ |
$(a), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.554205750$ |
$4.910353558$ |
1.028572174 |
\( \frac{9225207}{7} a + \frac{485654}{7} \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( 4 a - 6\) , \( 5 a - 1\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(4a-6\right){x}+5a-1$ |
| 1568.1-a4 |
1568.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
1568.1 |
\( 2^{5} \cdot 7^{2} \) |
\( 2^{12} \cdot 7^{7} \) |
$1.48773$ |
$(a), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.312347190$ |
0.992041228 |
\( \frac{9225207}{7} a + \frac{485654}{7} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( 75 a - 37\) , \( 206 a + 116\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(75a-37\right){x}+206a+116$ |
| 3136.1-a4 |
3136.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3136.1 |
\( 2^{6} \cdot 7^{2} \) |
\( 2^{6} \cdot 7^{7} \) |
$1.76922$ |
$(a), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.855939195$ |
1.402958159 |
\( \frac{9225207}{7} a + \frac{485654}{7} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( -28 a + 47\) , \( 32 a + 147\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-28a+47\right){x}+32a+147$ |
| 3584.5-a4 |
3584.5-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3584.5 |
\( 2^{9} \cdot 7 \) |
\( 2^{24} \cdot 7 \) |
$1.82928$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.084208149$ |
$1.736072149$ |
2.845715037 |
\( \frac{9225207}{7} a + \frac{485654}{7} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -6 a + 59\) , \( -103 a + 13\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-6a+59\right){x}-103a+13$ |
| 7168.5-e4 |
7168.5-e |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.5 |
\( 2^{10} \cdot 7 \) |
\( 2^{18} \cdot 7 \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.975073107$ |
$2.455176779$ |
3.619352797 |
\( \frac{9225207}{7} a + \frac{485654}{7} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -11 a - 18\) , \( -48 a - 18\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-11a-18\right){x}-48a-18$ |
| 14336.7-b4 |
14336.7-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
14336.7 |
\( 2^{11} \cdot 7 \) |
\( 2^{30} \cdot 7 \) |
$2.58699$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.227588389$ |
1.855939195 |
\( \frac{9225207}{7} a + \frac{485654}{7} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -47 a - 71\) , \( 219 a + 167\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-47a-71\right){x}+219a+167$ |
| 14336.7-e4 |
14336.7-e |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
14336.7 |
\( 2^{11} \cdot 7 \) |
\( 2^{30} \cdot 7 \) |
$2.58699$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$2.023296860$ |
$1.227588389$ |
3.755115945 |
\( \frac{9225207}{7} a + \frac{485654}{7} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -47 a - 71\) , \( -219 a - 167\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-47a-71\right){x}-219a-167$ |
| 18144.1-a4 |
18144.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
18144.1 |
\( 2^{5} \cdot 3^{4} \cdot 7 \) |
\( 2^{12} \cdot 3^{12} \cdot 7 \) |
$2.74392$ |
$(a), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.370689056$ |
$1.157381433$ |
2.594521287 |
\( \frac{9225207}{7} a + \frac{485654}{7} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -96 a + 48\) , \( -241 a + 470\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-96a+48\right){x}-241a+470$ |
| 25088.5-f4 |
25088.5-f |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
25088.5 |
\( 2^{9} \cdot 7^{2} \) |
\( 2^{24} \cdot 7^{7} \) |
$2.97546$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.656173595$ |
1.984082456 |
\( \frac{9225207}{7} a + \frac{485654}{7} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 40 a - 416\) , \( 580 a - 3208\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(40a-416\right){x}+580a-3208$ |
| 27104.1-a4 |
27104.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
27104.1 |
\( 2^{5} \cdot 7 \cdot 11^{2} \) |
\( 2^{12} \cdot 7 \cdot 11^{6} \) |
$3.03351$ |
$(a), (-2a+1), (-2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.046890896$ |
1.582750263 |
\( \frac{9225207}{7} a + \frac{485654}{7} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 34 a - 168\) , \( -285 a + 750\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(34a-168\right){x}-285a+750$ |
| 27104.3-d4 |
27104.3-d |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
27104.3 |
\( 2^{5} \cdot 7 \cdot 11^{2} \) |
\( 2^{12} \cdot 7 \cdot 11^{6} \) |
$3.03351$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.046890896$ |
1.582750263 |
\( \frac{9225207}{7} a + \frac{485654}{7} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 31 a + 136\) , \( 488 a - 521\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(31a+136\right){x}+488a-521$ |
| 28672.7-j4 |
28672.7-j |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{24} \cdot 7 \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$1.736072149$ |
2.624694380 |
\( \frac{9225207}{7} a + \frac{485654}{7} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 42 a - 7\) , \( -37 a - 156\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(42a-7\right){x}-37a-156$ |
| 28672.7-u4 |
28672.7-u |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{24} \cdot 7 \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$1.736072149$ |
2.624694380 |
\( \frac{9225207}{7} a + \frac{485654}{7} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 42 a - 7\) , \( 37 a + 156\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(42a-7\right){x}+37a+156$ |
| 36288.1-e4 |
36288.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
36288.1 |
\( 2^{6} \cdot 3^{4} \cdot 7 \) |
\( 2^{6} \cdot 3^{12} \cdot 7 \) |
$3.26308$ |
$(a), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$2.239805762$ |
$1.636784519$ |
5.542591071 |
\( \frac{9225207}{7} a + \frac{485654}{7} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 37 a - 59\) , \( -156 a + 177\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(37a-59\right){x}-156a+177$ |
*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.
