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-a6 |
448.4-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
448.4 |
\( 2^{6} \cdot 7 \) |
\( 2^{22} \cdot 7^{2} \) |
$1.08769$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.891959002$ |
$1.004073929$ |
1.436013054 |
\( \frac{1443468546}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -299\) , \( 1990\bigr] \) |
${y}^2={x}^{3}-299{x}+1990$ |
1792.5-c6 |
1792.5-c |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
1792.5 |
\( 2^{8} \cdot 7 \) |
\( 2^{22} \cdot 7^{2} \) |
$1.53823$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$1.004073929$ |
1.518017094 |
\( \frac{1443468546}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -299\) , \( -1990\bigr] \) |
${y}^2={x}^{3}-299{x}-1990$ |
3584.4-e6 |
3584.4-e |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3584.4 |
\( 2^{9} \cdot 7 \) |
\( 2^{28} \cdot 7^{2} \) |
$1.82928$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$0.709987484$ |
2.146800363 |
\( \frac{1443468546}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -299 a + 598\) , \( 1990 a + 3980\bigr] \) |
${y}^2={x}^{3}+\left(-299a+598\right){x}+1990a+3980$ |
3584.7-e6 |
3584.7-e |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3584.7 |
\( 2^{9} \cdot 7 \) |
\( 2^{28} \cdot 7^{2} \) |
$1.82928$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$0.709987484$ |
2.146800363 |
\( \frac{1443468546}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 299 a + 299\) , \( -1990 a + 5970\bigr] \) |
${y}^2={x}^{3}+\left(299a+299\right){x}-1990a+5970$ |
6272.4-a6 |
6272.4-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6272.4 |
\( 2^{7} \cdot 7^{2} \) |
\( 2^{22} \cdot 7^{8} \) |
$2.10397$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$0.379504273$ |
1.147513062 |
\( \frac{1443468546}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 2093\) , \( -27860 a + 13930\bigr] \) |
${y}^2={x}^{3}+2093{x}-27860a+13930$ |
6272.5-a6 |
6272.5-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6272.5 |
\( 2^{7} \cdot 7^{2} \) |
\( 2^{22} \cdot 7^{8} \) |
$2.10397$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$0.379504273$ |
1.147513062 |
\( \frac{1443468546}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 2093\) , \( 27860 a - 13930\bigr] \) |
${y}^2={x}^{3}+2093{x}+27860a-13930$ |
7168.5-d6 |
7168.5-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.5 |
\( 2^{10} \cdot 7 \) |
\( 2^{28} \cdot 7^{2} \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.709987484$ |
2.146800363 |
\( \frac{1443468546}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -299 a + 598\) , \( -1990 a - 3980\bigr] \) |
${y}^2={x}^{3}+\left(-299a+598\right){x}-1990a-3980$ |
7168.7-d6 |
7168.7-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.7 |
\( 2^{10} \cdot 7 \) |
\( 2^{28} \cdot 7^{2} \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.709987484$ |
2.146800363 |
\( \frac{1443468546}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 299 a + 299\) , \( 1990 a - 5970\bigr] \) |
${y}^2={x}^{3}+\left(299a+299\right){x}+1990a-5970$ |
25088.4-o6 |
25088.4-o |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
25088.4 |
\( 2^{9} \cdot 7^{2} \) |
\( 2^{28} \cdot 7^{8} \) |
$2.97546$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$16$ |
\( 2^{2} \) |
$1$ |
$0.268350045$ |
3.245657071 |
\( \frac{1443468546}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 2093 a - 4186\) , \( -69650 a + 83580\bigr] \) |
${y}^2={x}^{3}+\left(2093a-4186\right){x}-69650a+83580$ |
25088.7-o6 |
25088.7-o |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
25088.7 |
\( 2^{9} \cdot 7^{2} \) |
\( 2^{28} \cdot 7^{8} \) |
$2.97546$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$16$ |
\( 2^{2} \) |
$1$ |
$0.268350045$ |
3.245657071 |
\( \frac{1443468546}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -2093 a - 2093\) , \( 69650 a + 13930\bigr] \) |
${y}^2={x}^{3}+\left(-2093a-2093\right){x}+69650a+13930$ |
28672.7-a6 |
28672.7-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{34} \cdot 7^{2} \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$2.786954333$ |
$0.502036964$ |
4.230644320 |
\( \frac{1443468546}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -1196\) , \( 15920\bigr] \) |
${y}^2={x}^{3}-1196{x}+15920$ |
28672.7-m6 |
28672.7-m |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{34} \cdot 7^{2} \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$2.066648067$ |
$0.502036964$ |
6.274414190 |
\( \frac{1443468546}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -1196\) , \( -15920\bigr] \) |
${y}^2={x}^{3}-1196{x}-15920$ |
36288.4-d6 |
36288.4-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
36288.4 |
\( 2^{6} \cdot 3^{4} \cdot 7 \) |
\( 2^{22} \cdot 3^{12} \cdot 7^{2} \) |
$3.26308$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$5.176488807$ |
$0.334691309$ |
5.238665667 |
\( \frac{1443468546}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -2691\) , \( -53730\bigr] \) |
${y}^2={x}^{3}-2691{x}-53730$ |
*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.