| 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 |
| 224.6-a2 |
224.6-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
224.6 |
\( 2^{5} \cdot 7 \) |
\( 2^{6} \cdot 7^{2} \) |
$0.91464$ |
$(-a+1), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$6.944288598$ |
1.312347190 |
\( -\frac{3555}{7} a + \frac{15857}{7} \) |
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( -2\) , \( -a - 1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}-2{x}-a-1$ |
| 448.7-a2 |
448.7-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
448.7 |
\( 2^{6} \cdot 7 \) |
\( 2^{12} \cdot 7^{2} \) |
$1.08769$ |
$(-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.277102875$ |
$4.910353558$ |
1.028572174 |
\( -\frac{3555}{7} a + \frac{15857}{7} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -a + 2\) , \( -1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-a+2\right){x}-1$ |
| 1568.6-a2 |
1568.6-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
1568.6 |
\( 2^{5} \cdot 7^{2} \) |
\( 2^{6} \cdot 7^{8} \) |
$1.48773$ |
$(-a+1), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$2.624694380$ |
0.992041228 |
\( -\frac{3555}{7} a + \frac{15857}{7} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -5 a + 2\) , \( -6 a + 10\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-5a+2\right){x}-6a+10$ |
| 3136.7-a2 |
3136.7-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3136.7 |
\( 2^{6} \cdot 7^{2} \) |
\( 2^{12} \cdot 7^{8} \) |
$1.76922$ |
$(-a+1), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$1.855939195$ |
1.402958159 |
\( -\frac{3555}{7} a + \frac{15857}{7} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 7 a - 14\) , \( -14 a + 7\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(7a-14\right){x}-14a+7$ |
| 3584.6-a2 |
3584.6-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3584.6 |
\( 2^{9} \cdot 7 \) |
\( 2^{18} \cdot 7^{2} \) |
$1.82928$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.542104074$ |
$3.472144299$ |
2.845715037 |
\( -\frac{3555}{7} a + \frac{15857}{7} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( a + 3\) , \( 0\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(a+3\right){x}$ |
| 7168.7-e2 |
7168.7-e |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.7 |
\( 2^{10} \cdot 7 \) |
\( 2^{24} \cdot 7^{2} \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.487536553$ |
$2.455176779$ |
3.619352797 |
\( -\frac{3555}{7} a + \frac{15857}{7} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -5 a - 2\) , \( 5 a + 2\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-5a-2\right){x}+5a+2$ |
| 14336.6-b2 |
14336.6-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
14336.6 |
\( 2^{11} \cdot 7 \) |
\( 2^{24} \cdot 7^{2} \) |
$2.58699$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$2.455176779$ |
1.855939195 |
\( -\frac{3555}{7} a + \frac{15857}{7} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 4 a - 9\) , \( -3 a + 9\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(4a-9\right){x}-3a+9$ |
| 14336.6-e2 |
14336.6-e |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
14336.6 |
\( 2^{11} \cdot 7 \) |
\( 2^{24} \cdot 7^{2} \) |
$2.58699$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1.011648430$ |
$2.455176779$ |
3.755115945 |
\( -\frac{3555}{7} a + \frac{15857}{7} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 4 a - 9\) , \( 3 a - 9\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(4a-9\right){x}+3a-9$ |
| 18144.6-a2 |
18144.6-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
18144.6 |
\( 2^{5} \cdot 3^{4} \cdot 7 \) |
\( 2^{6} \cdot 3^{12} \cdot 7^{2} \) |
$2.74392$ |
$(-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.741378112$ |
$2.314762866$ |
2.594521287 |
\( -\frac{3555}{7} a + \frac{15857}{7} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 6 a - 4\) , \( 4 a\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(6a-4\right){x}+4a$ |
| 25088.6-e2 |
25088.6-e |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
25088.6 |
\( 2^{9} \cdot 7^{2} \) |
\( 2^{18} \cdot 7^{8} \) |
$2.97546$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.312347190$ |
1.984082456 |
\( -\frac{3555}{7} a + \frac{15857}{7} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -5 a - 26\) , \( -6 a - 24\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-5a-26\right){x}-6a-24$ |
| 27104.16-d2 |
27104.16-d |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
27104.16 |
\( 2^{5} \cdot 7 \cdot 11^{2} \) |
\( 2^{6} \cdot 7^{2} \cdot 11^{6} \) |
$3.03351$ |
$(-a+1), (-2a+1), (-2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$2.093781792$ |
1.582750263 |
\( -\frac{3555}{7} a + \frac{15857}{7} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -3 a + 12\) , \( -3 a - 3\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-3a+12\right){x}-3a-3$ |
| 27104.18-a2 |
27104.18-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
27104.18 |
\( 2^{5} \cdot 7 \cdot 11^{2} \) |
\( 2^{6} \cdot 7^{2} \cdot 11^{6} \) |
$3.03351$ |
$(-a+1), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$2.093781792$ |
1.582750263 |
\( -\frac{3555}{7} a + \frac{15857}{7} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -5 a - 10\) , \( -6 a + 16\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-5a-10\right){x}-6a+16$ |
| 28672.7-l2 |
28672.7-l |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{30} \cdot 7^{2} \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.736072149$ |
2.624694380 |
\( -\frac{3555}{7} a + \frac{15857}{7} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 3 a + 14\) , \( 17 a - 6\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(3a+14\right){x}+17a-6$ |
| 28672.7-s2 |
28672.7-s |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{30} \cdot 7^{2} \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.736072149$ |
2.624694380 |
\( -\frac{3555}{7} a + \frac{15857}{7} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 3 a + 14\) , \( -17 a + 6\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(3a+14\right){x}-17a+6$ |
| 36288.7-e2 |
36288.7-e |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
36288.7 |
\( 2^{6} \cdot 3^{4} \cdot 7 \) |
\( 2^{12} \cdot 3^{12} \cdot 7^{2} \) |
$3.26308$ |
$(-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1.119902881$ |
$1.636784519$ |
5.542591071 |
\( -\frac{3555}{7} a + \frac{15857}{7} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -9 a + 18\) , \( 27\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-9a+18\right){x}+27$ |
*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.
