| 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 |
| 150.2-a1 |
150.2-a |
$2$ |
$5$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
150.2 |
\( 2 \cdot 3 \cdot 5^{2} \) |
\( 2^{2} \cdot 3 \cdot 5^{10} \) |
$1.53203$ |
$(-a+2), (a+3), (-a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.1.2 |
$25$ |
\( 2 \) |
$1$ |
$0.305671568$ |
3.119747377 |
\( \frac{134010805558487}{6} a - \frac{109419364548011}{2} \) |
\( \bigl[1\) , \( 0\) , \( a\) , \( 1551 a - 3814\) , \( 52326 a - 128206\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(1551a-3814\right){x}+52326a-128206$ |
| 150.2-a2 |
150.2-a |
$2$ |
$5$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
150.2 |
\( 2 \cdot 3 \cdot 5^{2} \) |
\( 2^{10} \cdot 3^{5} \cdot 5^{2} \) |
$1.53203$ |
$(-a+2), (a+3), (-a-1)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.1.1 |
$1$ |
\( 2 \cdot 5^{2} \) |
$1$ |
$7.641789202$ |
3.119747377 |
\( -\frac{14677}{864} a - \frac{56899}{288} \) |
\( \bigl[1\) , \( 0\) , \( a\) , \( a - 4\) , \( 6 a - 16\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-4\right){x}+6a-16$ |
| 150.2-b1 |
150.2-b |
$2$ |
$5$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
150.2 |
\( 2 \cdot 3 \cdot 5^{2} \) |
\( 2^{2} \cdot 3 \cdot 5^{10} \) |
$1.53203$ |
$(-a+2), (a+3), (-a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.4.2 |
$1$ |
\( 2 \) |
$0.331203668$ |
$7.449302149$ |
2.014489923 |
\( \frac{134010805558487}{6} a - \frac{109419364548011}{2} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -258 a - 706\) , \( 6124 a + 15188\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-258a-706\right){x}+6124a+15188$ |
| 150.2-b2 |
150.2-b |
$2$ |
$5$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
150.2 |
\( 2 \cdot 3 \cdot 5^{2} \) |
\( 2^{10} \cdot 3^{5} \cdot 5^{2} \) |
$1.53203$ |
$(-a+2), (a+3), (-a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.4.1 |
$1$ |
\( 2 \cdot 5 \) |
$0.066240733$ |
$7.449302149$ |
2.014489923 |
\( -\frac{14677}{864} a - \frac{56899}{288} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -8 a - 16\) , \( -46 a - 112\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-8a-16\right){x}-46a-112$ |
| 150.2-c1 |
150.2-c |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
150.2 |
\( 2 \cdot 3 \cdot 5^{2} \) |
\( - 2 \cdot 3^{14} \cdot 5^{8} \) |
$1.53203$ |
$(-a+2), (a+3), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 7 \) |
$1$ |
$1.291460924$ |
3.690657003 |
\( -\frac{15094574737}{109350} a + \frac{18458456171}{54675} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( 97 a - 245\) , \( 757 a - 1887\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(97a-245\right){x}+757a-1887$ |
| 150.2-c2 |
150.2-c |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
150.2 |
\( 2 \cdot 3 \cdot 5^{2} \) |
\( - 2^{2} \cdot 3^{7} \cdot 5^{7} \) |
$1.53203$ |
$(-a+2), (a+3), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 7 \) |
$1$ |
$2.582921849$ |
3.690657003 |
\( \frac{101010617}{405} a + \frac{164872187}{270} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( 2 a - 15\) , \( 12 a - 57\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(2a-15\right){x}+12a-57$ |
| 150.2-d1 |
150.2-d |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
150.2 |
\( 2 \cdot 3 \cdot 5^{2} \) |
\( - 2 \cdot 3^{14} \cdot 5^{8} \) |
$1.53203$ |
$(-a+2), (a+3), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 7 \) |
$0.048871045$ |
$6.153854797$ |
1.718902670 |
\( -\frac{15094574737}{109350} a + \frac{18458456171}{54675} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -196 a - 486\) , \( 4679 a + 11464\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-196a-486\right){x}+4679a+11464$ |
| 150.2-d2 |
150.2-d |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
150.2 |
\( 2 \cdot 3 \cdot 5^{2} \) |
\( - 2^{2} \cdot 3^{7} \cdot 5^{7} \) |
$1.53203$ |
$(-a+2), (a+3), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 7 \) |
$0.024435522$ |
$12.30770959$ |
1.718902670 |
\( \frac{101010617}{405} a + \frac{164872187}{270} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -251 a - 616\) , \( 3129 a + 7664\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-251a-616\right){x}+3129a+7664$ |
| 150.2-e1 |
150.2-e |
$1$ |
$1$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
150.2 |
\( 2 \cdot 3 \cdot 5^{2} \) |
\( 2^{2} \cdot 3 \cdot 5^{8} \) |
$1.53203$ |
$(-a+2), (a+3), (-a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \cdot 3 \) |
$0.063952765$ |
$10.62463594$ |
1.664366669 |
\( -\frac{117133}{6} a - \frac{95441}{2} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -26 a - 59\) , \( 118 a + 291\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-26a-59\right){x}+118a+291$ |
| 150.2-f1 |
150.2-f |
$1$ |
$1$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
150.2 |
\( 2 \cdot 3 \cdot 5^{2} \) |
\( 2^{2} \cdot 3 \cdot 5^{8} \) |
$1.53203$ |
$(-a+2), (a+3), (-a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$4.333702660$ |
1.769226702 |
\( -\frac{117133}{6} a - \frac{95441}{2} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -a + 9\) , \( -12 a + 33\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-a+9\right){x}-12a+33$ |
| 150.2-g1 |
150.2-g |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
150.2 |
\( 2 \cdot 3 \cdot 5^{2} \) |
\( - 2^{14} \cdot 3^{3} \cdot 5^{9} \) |
$1.53203$ |
$(-a+2), (a+3), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 7 \) |
$1$ |
$1.899509180$ |
2.714149815 |
\( \frac{5257055}{288} a - \frac{16436863}{384} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -127 a - 315\) , \( 209 a + 507\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-127a-315\right){x}+209a+507$ |
| 150.2-g2 |
150.2-g |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
150.2 |
\( 2 \cdot 3 \cdot 5^{2} \) |
\( 2^{7} \cdot 3^{6} \cdot 5^{9} \) |
$1.53203$ |
$(-a+2), (a+3), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 7 \) |
$1$ |
$1.899509180$ |
2.714149815 |
\( -\frac{686817279595}{432} a + \frac{420680385779}{108} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -1607 a - 3995\) , \( 53329 a + 130427\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-1607a-3995\right){x}+53329a+130427$ |
| 150.2-h1 |
150.2-h |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
150.2 |
\( 2 \cdot 3 \cdot 5^{2} \) |
\( - 2^{14} \cdot 3^{3} \cdot 5^{9} \) |
$1.53203$ |
$(-a+2), (a+3), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.470052001$ |
$6.334860766$ |
1.215646641 |
\( \frac{5257055}{288} a - \frac{16436863}{384} \) |
\( \bigl[1\) , \( 1\) , \( a\) , \( 71 a - 181\) , \( -505 a + 1231\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(71a-181\right){x}-505a+1231$ |
| 150.2-h2 |
150.2-h |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
150.2 |
\( 2 \cdot 3 \cdot 5^{2} \) |
\( 2^{7} \cdot 3^{6} \cdot 5^{9} \) |
$1.53203$ |
$(-a+2), (a+3), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.940104002$ |
$3.167430383$ |
1.215646641 |
\( -\frac{686817279595}{432} a + \frac{420680385779}{108} \) |
\( \bigl[1\) , \( 1\) , \( a\) , \( 1151 a - 2901\) , \( -33585 a + 81951\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(1151a-2901\right){x}-33585a+81951$ |
*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.
