| 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 |
| 200.1-a1 |
200.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
200.1 |
\( 2^{3} \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{2} \) |
$2.51472$ |
$(-a+4), (-a+3), (-a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$11.34030113$ |
3.030822964 |
\( -\frac{2249728}{5} \) |
\( \bigl[0\) , \( -a - 1\) , \( a\) , \( 18 a - 60\) , \( -61 a + 221\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(18a-60\right){x}-61a+221$ |
| 200.1-b1 |
200.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
200.1 |
\( 2^{3} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{8} \) |
$2.51472$ |
$(-a+4), (-a+3), (-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$8.151961419$ |
2.178703333 |
\( \frac{237276}{625} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 3\) , \( 9\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+3{x}+9$ |
| 200.1-b2 |
200.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
200.1 |
\( 2^{3} \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{4} \) |
$2.51472$ |
$(-a+4), (-a+3), (-a-3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$32.60784567$ |
2.178703333 |
\( \frac{148176}{25} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -2\) , \( -2\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-2{x}-2$ |
| 200.1-b3 |
200.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
200.1 |
\( 2^{3} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{2} \) |
$2.51472$ |
$(-a+4), (-a+3), (-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$16.30392283$ |
2.178703333 |
\( \frac{55296}{5} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -240 a - 898\) , \( -3596 a - 13455\bigr] \) |
${y}^2={x}^{3}+\left(-240a-898\right){x}-3596a-13455$ |
| 200.1-b4 |
200.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
200.1 |
\( 2^{3} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{2} \) |
$2.51472$ |
$(-a+4), (-a+3), (-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$32.60784567$ |
2.178703333 |
\( \frac{132304644}{5} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -27\) , \( 13\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-27{x}+13$ |
| 200.1-c1 |
200.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
200.1 |
\( 2^{3} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{4} \) |
$2.51472$ |
$(-a+4), (-a+3), (-a-3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$10.20222794$ |
1.363330055 |
\( \frac{19652}{25} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -4 a + 28\) , \( -12 a + 54\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-4a+28\right){x}-12a+54$ |
| 200.1-c2 |
200.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
200.1 |
\( 2^{3} \cdot 5^{2} \) |
\( 2^{10} \cdot 5^{8} \) |
$2.51472$ |
$(-a+4), (-a+3), (-a-3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$10.20222794$ |
1.363330055 |
\( \frac{2185454}{625} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 36 a - 122\) , \( -164 a + 622\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(36a-122\right){x}-164a+622$ |
| 200.1-c3 |
200.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
200.1 |
\( 2^{3} \cdot 5^{2} \) |
\( 2^{11} \cdot 5^{10} \) |
$2.51472$ |
$(-a+4), (-a+3), (-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$10.20222794$ |
1.363330055 |
\( -\frac{372673999201}{390625} a + \frac{1403355576808}{390625} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 506 a - 1882\) , \( -12140 a + 45430\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(506a-1882\right){x}-12140a+45430$ |
| 200.1-c4 |
200.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
200.1 |
\( 2^{3} \cdot 5^{2} \) |
\( 2^{11} \cdot 5^{10} \) |
$2.51472$ |
$(-a+4), (-a+3), (-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$2.550556986$ |
1.363330055 |
\( \frac{372673999201}{390625} a + \frac{1403355576808}{390625} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 206 a - 762\) , \( 2884 a - 10794\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(206a-762\right){x}+2884a-10794$ |
| 200.1-d1 |
200.1-d |
$1$ |
$1$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
200.1 |
\( 2^{3} \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{14} \) |
$2.51472$ |
$(-a+4), (-a+3), (-a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
|
$1$ |
\( 2 \cdot 7 \) |
$0.323963159$ |
$3.389799170$ |
4.108976077 |
\( \frac{12459008}{78125} \) |
\( \bigl[0\) , \( a + 1\) , \( a\) , \( -30 a + 120\) , \( -533 a + 1995\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-30a+120\right){x}-533a+1995$ |
| 200.1-e1 |
200.1-e |
$1$ |
$1$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
200.1 |
\( 2^{3} \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{14} \) |
$2.51472$ |
$(-a+4), (-a+3), (-a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
|
$1$ |
\( 2 \cdot 7 \) |
$0.323963159$ |
$3.389799170$ |
4.108976077 |
\( \frac{12459008}{78125} \) |
\( \bigl[0\) , \( -a + 1\) , \( a\) , \( 30 a + 120\) , \( 533 a + 1995\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(30a+120\right){x}+533a+1995$ |
| 200.1-f1 |
200.1-f |
$4$ |
$4$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
200.1 |
\( 2^{3} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{4} \) |
$2.51472$ |
$(-a+4), (-a+3), (-a-3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$10.20222794$ |
1.363330055 |
\( \frac{19652}{25} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 4 a + 28\) , \( 12 a + 54\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(4a+28\right){x}+12a+54$ |
| 200.1-f2 |
200.1-f |
$4$ |
$4$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
200.1 |
\( 2^{3} \cdot 5^{2} \) |
\( 2^{10} \cdot 5^{8} \) |
$2.51472$ |
$(-a+4), (-a+3), (-a-3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$10.20222794$ |
1.363330055 |
\( \frac{2185454}{625} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -36 a - 122\) , \( 164 a + 622\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-36a-122\right){x}+164a+622$ |
| 200.1-f3 |
200.1-f |
$4$ |
$4$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
200.1 |
\( 2^{3} \cdot 5^{2} \) |
\( 2^{11} \cdot 5^{10} \) |
$2.51472$ |
$(-a+4), (-a+3), (-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$2.550556986$ |
1.363330055 |
\( -\frac{372673999201}{390625} a + \frac{1403355576808}{390625} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -206 a - 762\) , \( -2884 a - 10794\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-206a-762\right){x}-2884a-10794$ |
| 200.1-f4 |
200.1-f |
$4$ |
$4$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
200.1 |
\( 2^{3} \cdot 5^{2} \) |
\( 2^{11} \cdot 5^{10} \) |
$2.51472$ |
$(-a+4), (-a+3), (-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$10.20222794$ |
1.363330055 |
\( \frac{372673999201}{390625} a + \frac{1403355576808}{390625} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -506 a - 1882\) , \( 12140 a + 45430\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-506a-1882\right){x}+12140a+45430$ |
| 200.1-g1 |
200.1-g |
$4$ |
$4$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
200.1 |
\( 2^{3} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{8} \) |
$2.51472$ |
$(-a+4), (-a+3), (-a-3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$4.406960782$ |
1.177809811 |
\( \frac{237276}{625} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -390 a + 1459\) , \( 14698 a - 54995\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-390a+1459\right){x}+14698a-54995$ |
| 200.1-g2 |
200.1-g |
$4$ |
$4$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
200.1 |
\( 2^{3} \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{4} \) |
$2.51472$ |
$(-a+4), (-a+3), (-a-3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$17.62784313$ |
1.177809811 |
\( \frac{148176}{25} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 210 a - 786\) , \( 3012 a - 11270\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(210a-786\right){x}+3012a-11270$ |
| 200.1-g3 |
200.1-g |
$4$ |
$4$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
200.1 |
\( 2^{3} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{2} \) |
$2.51472$ |
$(-a+4), (-a+3), (-a-3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$35.25568626$ |
1.177809811 |
\( \frac{55296}{5} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -2\) , \( 1\bigr] \) |
${y}^2={x}^{3}-2{x}+1$ |
| 200.1-g4 |
200.1-g |
$4$ |
$4$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
200.1 |
\( 2^{3} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{2} \) |
$2.51472$ |
$(-a+4), (-a+3), (-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$4.406960782$ |
1.177809811 |
\( \frac{132304644}{5} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -3210 a - 12011\) , \( -196302 a - 734495\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-3210a-12011\right){x}-196302a-734495$ |
| 200.1-h1 |
200.1-h |
$1$ |
$1$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
200.1 |
\( 2^{3} \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{2} \) |
$2.51472$ |
$(-a+4), (-a+3), (-a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$11.34030113$ |
3.030822964 |
\( -\frac{2249728}{5} \) |
\( \bigl[0\) , \( a - 1\) , \( a\) , \( -18 a - 60\) , \( 61 a + 221\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-18a-60\right){x}+61a+221$ |
*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.
