| 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 |
| 448.4-b4 |
448.4-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
448.4 |
\( 2^{6} \cdot 7 \) |
\( 2^{22} \cdot 7^{4} \) |
$1.08769$ |
$(a), (-a+1), (-2a+1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.598934821$ |
1.208681114 |
\( \frac{3543122}{49} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -40\) , \( -84\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-40{x}-84$ |
| 1792.5-a4 |
1792.5-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
1792.5 |
\( 2^{8} \cdot 7 \) |
\( 2^{22} \cdot 7^{4} \) |
$1.53823$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.119959949$ |
$1.598934821$ |
2.319893204 |
\( \frac{3543122}{49} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -40\) , \( 84\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-40{x}+84$ |
| 3584.4-b4 |
3584.4-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3584.4 |
\( 2^{9} \cdot 7 \) |
\( 2^{28} \cdot 7^{4} \) |
$1.82928$ |
$(a), (-a+1), (-2a+1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.130617655$ |
1.709333224 |
\( \frac{3543122}{49} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -40 a + 80\) , \( -84 a - 168\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-40a+80\right){x}-84a-168$ |
| 3584.7-b4 |
3584.7-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3584.7 |
\( 2^{9} \cdot 7 \) |
\( 2^{28} \cdot 7^{4} \) |
$1.82928$ |
$(a), (-a+1), (-2a+1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.130617655$ |
1.709333224 |
\( \frac{3543122}{49} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 40 a + 40\) , \( 84 a - 252\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(40a+40\right){x}+84a-252$ |
| 6272.4-d4 |
6272.4-d |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6272.4 |
\( 2^{7} \cdot 7^{2} \) |
\( 2^{22} \cdot 7^{10} \) |
$2.10397$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.782382402$ |
$0.604340557$ |
3.257043758 |
\( \frac{3543122}{49} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 282\) , \( 1458 a - 588\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a+282\right){x}+1458a-588$ |
| 6272.5-d4 |
6272.5-d |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6272.5 |
\( 2^{7} \cdot 7^{2} \) |
\( 2^{22} \cdot 7^{10} \) |
$2.10397$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.782382402$ |
$0.604340557$ |
3.257043758 |
\( \frac{3543122}{49} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 282\) , \( -1458 a + 588\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+282\right){x}-1458a+588$ |
| 7168.5-g4 |
7168.5-g |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.5 |
\( 2^{10} \cdot 7 \) |
\( 2^{28} \cdot 7^{4} \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1.075549531$ |
$1.130617655$ |
3.676945099 |
\( \frac{3543122}{49} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -40 a + 80\) , \( 84 a + 168\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-40a+80\right){x}+84a+168$ |
| 7168.7-g4 |
7168.7-g |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.7 |
\( 2^{10} \cdot 7 \) |
\( 2^{28} \cdot 7^{4} \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1.075549531$ |
$1.130617655$ |
3.676945099 |
\( \frac{3543122}{49} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 40 a + 40\) , \( -84 a + 252\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(40a+40\right){x}-84a+252$ |
| 25088.4-j4 |
25088.4-j |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
25088.4 |
\( 2^{9} \cdot 7^{2} \) |
\( 2^{28} \cdot 7^{10} \) |
$2.97546$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$3.812635761$ |
$0.427333306$ |
4.926438062 |
\( \frac{3543122}{49} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 282 a - 565\) , \( 3221 a - 4091\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(282a-565\right){x}+3221a-4091$ |
| 25088.7-j4 |
25088.7-j |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
25088.7 |
\( 2^{9} \cdot 7^{2} \) |
\( 2^{28} \cdot 7^{10} \) |
$2.97546$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$3.812635761$ |
$0.427333306$ |
4.926438062 |
\( \frac{3543122}{49} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -282 a - 283\) , \( -3221 a - 870\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-282a-283\right){x}-3221a-870$ |
| 28672.7-d4 |
28672.7-d |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{34} \cdot 7^{4} \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.688987630$ |
$0.799467410$ |
4.082894903 |
\( \frac{3543122}{49} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -161\) , \( 833\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-161{x}+833$ |
| 28672.7-p4 |
28672.7-p |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{34} \cdot 7^{4} \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.799467410$ |
2.417362229 |
\( \frac{3543122}{49} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -161\) , \( -833\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-161{x}-833$ |
| 36288.4-f4 |
36288.4-f |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
36288.4 |
\( 2^{6} \cdot 3^{4} \cdot 7 \) |
\( 2^{22} \cdot 3^{12} \cdot 7^{4} \) |
$3.26308$ |
$(a), (-a+1), (-2a+1), (3)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.532978273$ |
1.611574819 |
\( \frac{3543122}{49} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -363\) , \( 2630\bigr] \) |
${y}^2={x}^{3}-363{x}+2630$ |
*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.
