| 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-a3 |
224.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
224.1 |
\( 2^{5} \cdot 7 \) |
\( 2^{9} \cdot 7^{4} \) |
$0.91464$ |
$(a), (-2a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$3.472144299$ |
1.312347190 |
\( -\frac{1482409}{49} a + \frac{341346}{7} \) |
\( \bigl[a\) , \( a - 1\) , \( a\) , \( -7 a + 1\) , \( -6 a + 11\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-7a+1\right){x}-6a+11$ |
| 448.1-a3 |
448.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
448.1 |
\( 2^{6} \cdot 7 \) |
\( 2^{15} \cdot 7^{4} \) |
$1.08769$ |
$(a), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.138551437$ |
$2.455176779$ |
1.028572174 |
\( -\frac{1482409}{49} a + \frac{341346}{7} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 6 a + 11\) , \( -13 a + 21\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(6a+11\right){x}-13a+21$ |
| 1568.1-a3 |
1568.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
1568.1 |
\( 2^{5} \cdot 7^{2} \) |
\( 2^{9} \cdot 7^{10} \) |
$1.48773$ |
$(a), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.312347190$ |
0.992041228 |
\( -\frac{1482409}{49} a + \frac{341346}{7} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( 40 a - 2\) , \( -25 a - 171\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(40a-2\right){x}-25a-171$ |
| 3136.1-a3 |
3136.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3136.1 |
\( 2^{6} \cdot 7^{2} \) |
\( 2^{15} \cdot 7^{10} \) |
$1.76922$ |
$(a), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.927969597$ |
1.402958159 |
\( -\frac{1482409}{49} a + \frac{341346}{7} \) |
\( \bigl[a\) , \( -a\) , \( 0\) , \( -42 a - 77\) , \( -203 a - 217\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(-42a-77\right){x}-203a-217$ |
| 3584.5-a3 |
3584.5-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3584.5 |
\( 2^{9} \cdot 7 \) |
\( 2^{21} \cdot 7^{4} \) |
$1.82928$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.084208149$ |
$1.736072149$ |
2.845715037 |
\( -\frac{1482409}{49} a + \frac{341346}{7} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -11 a + 34\) , \( 52 a + 20\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-11a+34\right){x}+52a+20$ |
| 7168.5-e3 |
7168.5-e |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.5 |
\( 2^{10} \cdot 7 \) |
\( 2^{27} \cdot 7^{4} \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.975073107$ |
$1.227588389$ |
3.619352797 |
\( -\frac{1482409}{49} a + \frac{341346}{7} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 45 a - 47\) , \( 131 a - 17\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(45a-47\right){x}+131a-17$ |
| 14336.7-b3 |
14336.7-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
14336.7 |
\( 2^{11} \cdot 7 \) |
\( 2^{27} \cdot 7^{4} \) |
$2.58699$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.227588389$ |
1.855939195 |
\( -\frac{1482409}{49} a + \frac{341346}{7} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -12 a - 56\) , \( -84 a - 164\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-12a-56\right){x}-84a-164$ |
| 14336.7-e3 |
14336.7-e |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
14336.7 |
\( 2^{11} \cdot 7 \) |
\( 2^{27} \cdot 7^{4} \) |
$2.58699$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.505824215$ |
$1.227588389$ |
3.755115945 |
\( -\frac{1482409}{49} a + \frac{341346}{7} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -12 a - 56\) , \( 84 a + 164\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-12a-56\right){x}+84a+164$ |
| 18144.1-a3 |
18144.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
18144.1 |
\( 2^{5} \cdot 3^{4} \cdot 7 \) |
\( 2^{9} \cdot 3^{12} \cdot 7^{4} \) |
$2.74392$ |
$(a), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.370689056$ |
$1.157381433$ |
2.594521287 |
\( -\frac{1482409}{49} a + \frac{341346}{7} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -51 a + 3\) , \( 209 a - 178\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-51a+3\right){x}+209a-178$ |
| 25088.5-f3 |
25088.5-f |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
25088.5 |
\( 2^{9} \cdot 7^{2} \) |
\( 2^{21} \cdot 7^{10} \) |
$2.97546$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.656173595$ |
1.984082456 |
\( -\frac{1482409}{49} a + \frac{341346}{7} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 75 a - 241\) , \( -568 a + 1356\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(75a-241\right){x}-568a+1356$ |
| 27104.1-a3 |
27104.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
27104.1 |
\( 2^{5} \cdot 7 \cdot 11^{2} \) |
\( 2^{9} \cdot 7^{4} \cdot 11^{6} \) |
$3.03351$ |
$(a), (-2a+1), (-2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.046890896$ |
1.582750263 |
\( -\frac{1482409}{49} a + \frac{341346}{7} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 39 a - 93\) , \( 175 a - 336\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(39a-93\right){x}+175a-336$ |
| 27104.3-d3 |
27104.3-d |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
27104.3 |
\( 2^{5} \cdot 7 \cdot 11^{2} \) |
\( 2^{9} \cdot 7^{4} \cdot 11^{6} \) |
$3.03351$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.046890896$ |
1.582750263 |
\( -\frac{1482409}{49} a + \frac{341346}{7} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -4 a + 91\) , \( -262 a + 105\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-4a+91\right){x}-262a+105$ |
| 28672.7-j3 |
28672.7-j |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{33} \cdot 7^{4} \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.868036074$ |
2.624694380 |
\( -\frac{1482409}{49} a + \frac{341346}{7} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -43 a + 137\) , \( 279 a + 211\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-43a+137\right){x}+279a+211$ |
| 28672.7-u3 |
28672.7-u |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{33} \cdot 7^{4} \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.868036074$ |
2.624694380 |
\( -\frac{1482409}{49} a + \frac{341346}{7} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -43 a + 137\) , \( -279 a - 211\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-43a+137\right){x}-279a-211$ |
| 36288.1-e3 |
36288.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
36288.1 |
\( 2^{6} \cdot 3^{4} \cdot 7 \) |
\( 2^{15} \cdot 3^{12} \cdot 7^{4} \) |
$3.26308$ |
$(a), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$2.239805762$ |
$0.818392259$ |
5.542591071 |
\( -\frac{1482409}{49} a + \frac{341346}{7} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 55 a + 100\) , \( 296 a - 665\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(55a+100\right){x}+296a-665$ |
*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.
