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 |
450.3-a1 |
450.3-a |
$1$ |
$1$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
450.3 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( - 2^{13} \cdot 3^{7} \cdot 5^{2} \) |
$2.60299$ |
$(2,a), (3,a+1), (5,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$22.94110692$ |
7.254614994 |
\( -\frac{5929}{6} a - \frac{3925}{3} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( a - 8\) , \( 2 a - 3\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(a-8\right){x}+2a-3$ |
450.3-b1 |
450.3-b |
$2$ |
$5$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
450.3 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( - 2^{17} \cdot 3^{11} \cdot 5^{10} \) |
$2.60299$ |
$(2,a), (3,a+1), (5,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.4.1 |
$1$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$1.284580539$ |
4.062200343 |
\( -\frac{259064095}{1944} a - \frac{318409405}{972} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 1781 a - 5733\) , \( -69214 a + 218498\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(1781a-5733\right){x}-69214a+218498$ |
450.3-b2 |
450.3-b |
$2$ |
$5$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
450.3 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( - 2^{13} \cdot 3^{7} \cdot 5^{2} \) |
$2.60299$ |
$(2,a), (3,a+1), (5,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.4.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$6.422902698$ |
4.062200343 |
\( -\frac{29499775}{6} a + \frac{46646975}{3} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 161 a - 513\) , \( 2378 a - 7522\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(161a-513\right){x}+2378a-7522$ |
450.3-c1 |
450.3-c |
$2$ |
$7$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
450.3 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2 \cdot 3^{7} \cdot 5^{6} \) |
$2.60299$ |
$(2,a), (3,a+1), (5,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$7$ |
7B.6.3 |
$49$ |
\( 2 \) |
$1$ |
$0.459097436$ |
7.113788473 |
\( -\frac{574055084970269951}{6} a - \frac{907661070264560078}{3} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -60681 a - 193668\) , \( 14402517 a + 45516541\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-60681a-193668\right){x}+14402517a+45516541$ |
450.3-c2 |
450.3-c |
$2$ |
$7$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
450.3 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{7} \cdot 3^{13} \cdot 5^{6} \) |
$2.60299$ |
$(2,a), (3,a+1), (5,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$7$ |
7B.6.1 |
$1$ |
\( 2 \cdot 7 \) |
$1$ |
$3.213682052$ |
7.113788473 |
\( -\frac{7261339}{34992} a + \frac{5642407}{8748} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -6 a - 18\) , \( 267 a + 841\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-6a-18\right){x}+267a+841$ |
450.3-d1 |
450.3-d |
$4$ |
$6$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
450.3 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( - 2^{18} \cdot 3^{3} \cdot 5^{9} \) |
$2.60299$ |
$(2,a), (3,a+1), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$7.498297114$ |
2.371169745 |
\( -\frac{546421}{50} a - \frac{161087}{40} \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( 5 a - 100\) , \( 100 a - 125\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(5a-100\right){x}+100a-125$ |
450.3-d2 |
450.3-d |
$4$ |
$6$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
450.3 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( - 2^{2} \cdot 3^{9} \cdot 5^{7} \) |
$2.60299$ |
$(2,a), (3,a+1), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$7.498297114$ |
2.371169745 |
\( -\frac{77254}{5} a + \frac{100565}{2} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( 111 a - 357\) , \( -1013 a + 3201\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(111a-357\right){x}-1013a+3201$ |
450.3-d3 |
450.3-d |
$4$ |
$6$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
450.3 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2 \cdot 3^{9} \cdot 5^{8} \) |
$2.60299$ |
$(2,a), (3,a+1), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$7.498297114$ |
2.371169745 |
\( -\frac{15308292191}{10} a + \frac{24204545642}{5} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( 1786 a - 5657\) , \( -71168 a + 225051\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(1786a-5657\right){x}-71168a+225051$ |
450.3-d4 |
450.3-d |
$4$ |
$6$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
450.3 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{15} \cdot 3^{3} \cdot 5^{12} \) |
$2.60299$ |
$(2,a), (3,a+1), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$7.498297114$ |
2.371169745 |
\( \frac{122257133981}{500} a + \frac{96653122463}{125} \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( -195 a - 900\) , \( 2980 a + 10675\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(-195a-900\right){x}+2980a+10675$ |
450.3-e1 |
450.3-e |
$2$ |
$2$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
450.3 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( - 2^{16} \cdot 3^{7} \cdot 5^{11} \) |
$2.60299$ |
$(2,a), (3,a+1), (5,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.494232175$ |
$3.362932028$ |
4.204739475 |
\( -\frac{738259}{750} a + \frac{938257}{300} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( 30 a - 65\) , \( -175 a + 110\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(30a-65\right){x}-175a+110$ |
450.3-e2 |
450.3-e |
$2$ |
$2$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
450.3 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( - 2^{14} \cdot 3^{8} \cdot 5^{16} \) |
$2.60299$ |
$(2,a), (3,a+1), (5,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.988464351$ |
$1.681466014$ |
4.204739475 |
\( \frac{210156181}{56250} a + \frac{684296471}{56250} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( -170 a - 265\) , \( -2135 a - 3290\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-170a-265\right){x}-2135a-3290$ |
450.3-f1 |
450.3-f |
$2$ |
$3$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
450.3 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( - 2^{3} \cdot 3^{7} \cdot 5^{8} \) |
$2.60299$ |
$(2,a), (3,a+1), (5,a)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$8.736672867$ |
1.841852362 |
\( -\frac{533474309}{12} a + \frac{843496315}{6} \) |
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 10 a - 56\) , \( -13 a + 248\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(10a-56\right){x}-13a+248$ |
450.3-f2 |
450.3-f |
$2$ |
$3$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
450.3 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( - 2^{21} \cdot 3^{9} \cdot 5^{8} \) |
$2.60299$ |
$(2,a), (3,a+1), (5,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$2.912224289$ |
1.841852362 |
\( -\frac{225727}{864} a + \frac{400355}{432} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 351 a + 1117\) , \( -25774 a - 81502\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(351a+1117\right){x}-25774a-81502$ |
450.3-g1 |
450.3-g |
$2$ |
$3$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
450.3 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{11} \cdot 3^{15} \cdot 5^{2} \) |
$2.60299$ |
$(2,a), (3,a+1), (5,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$8.044960389$ |
$0.424816695$ |
4.323002413 |
\( -\frac{23469020634623}{1259712} a - \frac{18555184937575}{314928} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( 10 a - 182\) , \( 158 a - 1174\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(10a-182\right){x}+158a-1174$ |
450.3-g2 |
450.3-g |
$2$ |
$3$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
450.3 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{33} \cdot 3^{9} \cdot 5^{2} \) |
$2.60299$ |
$(2,a), (3,a+1), (5,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$24.13488116$ |
$0.141605565$ |
4.323002413 |
\( \frac{62509658925710141}{3538944} a - \frac{49418224549259105}{884736} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( 2870 a - 9157\) , \( 152827 a - 484589\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(2870a-9157\right){x}+152827a-484589$ |
450.3-h1 |
450.3-h |
$2$ |
$3$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
450.3 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( - 2 \cdot 3^{3} \cdot 5^{10} \) |
$2.60299$ |
$(2,a), (3,a+1), (5,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1$ |
$3.868067703$ |
1.223190408 |
\( -\frac{172364765}{2} a + 272489285 \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -198 a - 636\) , \( 2489 a + 7858\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-198a-636\right){x}+2489a+7858$ |
450.3-h2 |
450.3-h |
$2$ |
$3$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
450.3 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( - 2^{15} \cdot 3^{9} \cdot 5^{10} \) |
$2.60299$ |
$(2,a), (3,a+1), (5,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1$ |
$3.868067703$ |
1.223190408 |
\( -\frac{295}{4} a + \frac{3205}{2} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 31 a + 17\) , \( 86 a - 2\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(31a+17\right){x}+86a-2$ |
450.3-i1 |
450.3-i |
$2$ |
$3$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
450.3 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{19} \cdot 3^{9} \cdot 5^{6} \) |
$2.60299$ |
$(2,a), (3,a+1), (5,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \cdot 7 \) |
$0.477384821$ |
$3.258409817$ |
6.886560190 |
\( \frac{1099493}{16} a - \frac{462131}{2} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 1006 a - 3188\) , \( -28864 a + 91268\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(1006a-3188\right){x}-28864a+91268$ |
450.3-i2 |
450.3-i |
$2$ |
$3$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
450.3 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{21} \cdot 3^{3} \cdot 5^{6} \) |
$2.60299$ |
$(2,a), (3,a+1), (5,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3 \cdot 7 \) |
$0.159128273$ |
$3.258409817$ |
6.886560190 |
\( \frac{454513}{2048} a + \frac{260987}{256} \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 22\) , \( -15 a + 31\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+22{x}-15a+31$ |
450.3-j1 |
450.3-j |
$2$ |
$3$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
450.3 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( - 2 \cdot 3^{9} \cdot 5^{4} \) |
$2.60299$ |
$(2,a), (3,a+1), (5,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$9$ |
\( 2 \) |
$1$ |
$1.467034057$ |
4.175252124 |
\( -\frac{172364765}{2} a + 272489285 \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 128 a - 403\) , \( 1447 a - 4583\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(128a-403\right){x}+1447a-4583$ |
450.3-j2 |
450.3-j |
$2$ |
$3$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
450.3 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( - 2^{3} \cdot 3^{3} \cdot 5^{4} \) |
$2.60299$ |
$(2,a), (3,a+1), (5,a)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$13.20330651$ |
4.175252124 |
\( -\frac{295}{4} a + \frac{3205}{2} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 3 a - 3\) , \( 2 a - 3\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(3a-3\right){x}+2a-3$ |
450.3-k1 |
450.3-k |
$4$ |
$15$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
450.3 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( - 2^{15} \cdot 3^{7} \cdot 5^{4} \) |
$2.60299$ |
$(2,a), (3,a+1), (5,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 5$ |
3B, 5B.4.2 |
$1$ |
\( 2 \) |
$1$ |
$3.602619814$ |
1.139248415 |
\( -\frac{97959672159615035}{12} a - \frac{154887841432390445}{6} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( -340 a - 6105\) , \( 56355 a + 42690\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-340a-6105\right){x}+56355a+42690$ |
450.3-k2 |
450.3-k |
$4$ |
$15$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
450.3 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( - 2 \cdot 3^{9} \cdot 5^{4} \) |
$2.60299$ |
$(2,a), (3,a+1), (5,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 5$ |
3B, 5B.4.2 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$1.200873271$ |
1.139248415 |
\( -\frac{130644467741576305}{54} a + \frac{206567040871853915}{27} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( -532 a - 2251\) , \( 15096 a + 43018\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-532a-2251\right){x}+15096a+43018$ |
450.3-k3 |
450.3-k |
$4$ |
$15$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
450.3 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( - 2^{15} \cdot 3^{11} \cdot 5^{8} \) |
$2.60299$ |
$(2,a), (3,a+1), (5,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 5$ |
3B, 5B.4.1 |
$1$ |
\( 2 \) |
$1$ |
$3.602619814$ |
1.139248415 |
\( -\frac{78338627675}{62208} a + \frac{123816286975}{31104} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( 314 a - 1057\) , \( -5258 a + 16911\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(314a-1057\right){x}-5258a+16911$ |
450.3-k4 |
450.3-k |
$4$ |
$15$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
450.3 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( - 2^{17} \cdot 3^{21} \cdot 5^{8} \) |
$2.60299$ |
$(2,a), (3,a+1), (5,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 5$ |
3B, 5B.4.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$1.200873271$ |
1.139248415 |
\( -\frac{30057855025}{114791256} a + \frac{101192416175}{57395628} \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( 735 a + 2220\) , \( -15720 a - 49925\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(735a+2220\right){x}-15720a-49925$ |
450.3-l1 |
450.3-l |
$4$ |
$4$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
450.3 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( - 2^{20} \cdot 3^{11} \cdot 5^{7} \) |
$2.60299$ |
$(2,a), (3,a+1), (5,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.683879708$ |
$2.440475417$ |
2.599055159 |
\( -\frac{7361303}{4860} a + \frac{9044707}{3888} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 260 a - 843\) , \( -3460 a + 10897\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(260a-843\right){x}-3460a+10897$ |
450.3-l2 |
450.3-l |
$4$ |
$4$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
450.3 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( - 2^{14} \cdot 3^{26} \cdot 5^{10} \) |
$2.60299$ |
$(2,a), (3,a+1), (5,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1.683879708$ |
$0.610118854$ |
2.599055159 |
\( \frac{20775046733269}{34867844010} a + \frac{361175517267013}{174339220050} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -1540 a + 4557\) , \( 158740 a - 503703\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-1540a+4557\right){x}+158740a-503703$ |
450.3-l3 |
450.3-l |
$4$ |
$4$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
450.3 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{16} \cdot 3^{16} \cdot 5^{8} \) |
$2.60299$ |
$(2,a), (3,a+1), (5,a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$3.367759416$ |
$1.220237708$ |
2.599055159 |
\( \frac{184784183669}{118098} a + \frac{5854047089047}{1180980} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 1060 a - 3643\) , \( 32220 a - 103903\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(1060a-3643\right){x}+32220a-103903$ |
450.3-l4 |
450.3-l |
$4$ |
$4$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
450.3 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{14} \cdot 3^{11} \cdot 5^{7} \) |
$2.60299$ |
$(2,a), (3,a+1), (5,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$6.735518833$ |
$0.305059427$ |
2.599055159 |
\( \frac{37688339331809089}{2430} a + \frac{23836231835693689}{486} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 16460 a - 56643\) , \( 2170020 a - 6984103\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(16460a-56643\right){x}+2170020a-6984103$ |
450.3-m1 |
450.3-m |
$4$ |
$15$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
450.3 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( - 2^{3} \cdot 3^{7} \cdot 5^{4} \) |
$2.60299$ |
$(2,a), (3,a+1), (5,a)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 5$ |
3B.1.1, 5B.4.2 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1.485977887$ |
$3.602619814$ |
6.771591819 |
\( -\frac{97959672159615035}{12} a - \frac{154887841432390445}{6} \) |
\( \bigl[a + 1\) , \( 0\) , \( a\) , \( -85 a - 1528\) , \( 7002 a + 4572\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-85a-1528\right){x}+7002a+4572$ |
450.3-m2 |
450.3-m |
$4$ |
$15$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
450.3 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( - 2^{13} \cdot 3^{9} \cdot 5^{4} \) |
$2.60299$ |
$(2,a), (3,a+1), (5,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 5$ |
3B.1.2, 5B.4.2 |
$1$ |
\( 2^{2} \) |
$4.457933663$ |
$1.200873271$ |
6.771591819 |
\( -\frac{130644467741576305}{54} a + \frac{206567040871853915}{27} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -2129 a - 9013\) , \( 127656 a + 356418\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2129a-9013\right){x}+127656a+356418$ |
450.3-m3 |
450.3-m |
$4$ |
$15$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
450.3 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( - 2^{27} \cdot 3^{11} \cdot 5^{8} \) |
$2.60299$ |
$(2,a), (3,a+1), (5,a)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 5$ |
3B.1.1, 5B.4.1 |
$1$ |
\( 2^{2} \cdot 3^{2} \cdot 5 \) |
$0.297195577$ |
$3.602619814$ |
6.771591819 |
\( -\frac{78338627675}{62208} a + \frac{123816286975}{31104} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 1256 a - 4228\) , \( -42064 a + 135288\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(1256a-4228\right){x}-42064a+135288$ |
450.3-m4 |
450.3-m |
$4$ |
$15$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
450.3 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( - 2^{5} \cdot 3^{21} \cdot 5^{8} \) |
$2.60299$ |
$(2,a), (3,a+1), (5,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 5$ |
3B.1.2, 5B.4.1 |
$1$ |
\( 2^{2} \cdot 5 \) |
$0.891586732$ |
$1.200873271$ |
6.771591819 |
\( -\frac{30057855025}{114791256} a + \frac{101192416175}{57395628} \) |
\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( 182 a + 557\) , \( -2243 a - 7159\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(182a+557\right){x}-2243a-7159$ |
450.3-n1 |
450.3-n |
$2$ |
$3$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
450.3 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{3} \cdot 3^{9} \cdot 5^{4} \) |
$2.60299$ |
$(2,a), (3,a+1), (5,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$1.578502414$ |
1.497498876 |
\( \frac{1181545}{108} a - \frac{1128415}{27} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( -2 a - 11\) , \( -9 a - 32\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-2a-11\right){x}-9a-32$ |
450.3-n2 |
450.3-n |
$2$ |
$3$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
450.3 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{21} \cdot 3^{7} \cdot 5^{4} \) |
$2.60299$ |
$(2,a), (3,a+1), (5,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1$ |
$4.735507243$ |
1.497498876 |
\( \frac{8885}{96} a + \frac{33055}{24} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( -40 a + 135\) , \( 215 a - 670\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-40a+135\right){x}+215a-670$ |
450.3-o1 |
450.3-o |
$4$ |
$15$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
450.3 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{18} \cdot 3^{6} \cdot 5^{2} \) |
$2.60299$ |
$(2,a), (3,a+1), (5,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 5$ |
3B, 5B.4.2 |
$1$ |
\( 2 \) |
$0.977110452$ |
$3.677182728$ |
2.272421378 |
\( -\frac{349938025}{8} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( -400 a - 1305\) , \( 7199 a + 22690\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-400a-1305\right){x}+7199a+22690$ |
450.3-o2 |
450.3-o |
$4$ |
$15$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
450.3 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{22} \cdot 3^{6} \cdot 5^{10} \) |
$2.60299$ |
$(2,a), (3,a+1), (5,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 5$ |
3B, 5B.4.1 |
$1$ |
\( 2 \) |
$1.628517420$ |
$2.206309637$ |
2.272421378 |
\( -\frac{121945}{32} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( -240 a - 785\) , \( -4945 a - 15590\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-240a-785\right){x}-4945a-15590$ |
450.3-o3 |
450.3-o |
$4$ |
$15$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
450.3 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{14} \cdot 3^{6} \cdot 5^{2} \) |
$2.60299$ |
$(2,a), (3,a+1), (5,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 5$ |
3B, 5B.4.2 |
$1$ |
\( 2 \) |
$0.325703484$ |
$11.03154818$ |
2.272421378 |
\( -\frac{25}{2} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( -5\) , \( 23 a + 70\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}-5{x}+23a+70$ |
450.3-o4 |
450.3-o |
$4$ |
$15$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
450.3 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{42} \cdot 3^{6} \cdot 5^{10} \) |
$2.60299$ |
$(2,a), (3,a+1), (5,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 5$ |
3B, 5B.4.1 |
$1$ |
\( 2 \) |
$4.885552262$ |
$0.735436545$ |
2.272421378 |
\( \frac{46969655}{32768} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( 1760 a + 5715\) , \( 36455 a + 114910\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(1760a+5715\right){x}+36455a+114910$ |
450.3-p1 |
450.3-p |
$4$ |
$15$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
450.3 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{6} \cdot 3^{6} \cdot 5^{2} \) |
$2.60299$ |
$(2,a), (3,a+1), (5,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 5$ |
3B, 5B.4.2 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$3.677182728$ |
3.488481838 |
\( -\frac{349938025}{8} \) |
\( \bigl[a + 1\) , \( 0\) , \( a\) , \( -100 a - 328\) , \( 850 a + 2672\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-100a-328\right){x}+850a+2672$ |
450.3-p2 |
450.3-p |
$4$ |
$15$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
450.3 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{10} \cdot 3^{6} \cdot 5^{10} \) |
$2.60299$ |
$(2,a), (3,a+1), (5,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 5$ |
3B, 5B.4.1 |
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$2.206309637$ |
3.488481838 |
\( -\frac{121945}{32} \) |
\( \bigl[a + 1\) , \( 0\) , \( a\) , \( -60 a - 198\) , \( -648 a - 2048\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-60a-198\right){x}-648a-2048$ |
450.3-p3 |
450.3-p |
$4$ |
$15$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
450.3 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{2} \cdot 3^{6} \cdot 5^{2} \) |
$2.60299$ |
$(2,a), (3,a+1), (5,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 5$ |
3B, 5B.4.2 |
$1$ |
\( 2 \) |
$1$ |
$11.03154818$ |
3.488481838 |
\( -\frac{25}{2} \) |
\( \bigl[a + 1\) , \( 0\) , \( a\) , \( -3\) , \( 3 a + 7\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-3{x}+3a+7$ |
450.3-p4 |
450.3-p |
$4$ |
$15$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
450.3 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{30} \cdot 3^{6} \cdot 5^{10} \) |
$2.60299$ |
$(2,a), (3,a+1), (5,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 5$ |
3B, 5B.4.1 |
$1$ |
\( 2 \cdot 3 \cdot 5 \) |
$1$ |
$0.735436545$ |
3.488481838 |
\( \frac{46969655}{32768} \) |
\( \bigl[a + 1\) , \( 0\) , \( a\) , \( 440 a + 1427\) , \( 4777 a + 15077\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(440a+1427\right){x}+4777a+15077$ |
450.3-q1 |
450.3-q |
$4$ |
$4$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
450.3 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( - 2^{8} \cdot 3^{11} \cdot 5^{7} \) |
$2.60299$ |
$(2,a), (3,a+1), (5,a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$1$ |
$2.440475417$ |
3.086984356 |
\( -\frac{7361303}{4860} a + \frac{9044707}{3888} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 65 a - 210\) , \( -465 a + 1467\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(65a-210\right){x}-465a+1467$ |
450.3-q2 |
450.3-q |
$4$ |
$4$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
450.3 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( - 2^{2} \cdot 3^{26} \cdot 5^{10} \) |
$2.60299$ |
$(2,a), (3,a+1), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{5} \) |
$1$ |
$0.610118854$ |
3.086984356 |
\( \frac{20775046733269}{34867844010} a + \frac{361175517267013}{174339220050} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -385 a + 1140\) , \( 20035 a - 63533\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-385a+1140\right){x}+20035a-63533$ |
450.3-q3 |
450.3-q |
$4$ |
$4$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
450.3 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{16} \cdot 5^{8} \) |
$2.60299$ |
$(2,a), (3,a+1), (5,a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$4$ |
\( 2^{6} \) |
$1$ |
$1.220237708$ |
3.086984356 |
\( \frac{184784183669}{118098} a + \frac{5854047089047}{1180980} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 265 a - 910\) , \( 3895 a - 12533\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(265a-910\right){x}+3895a-12533$ |
450.3-q4 |
450.3-q |
$4$ |
$4$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
450.3 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{2} \cdot 3^{11} \cdot 5^{7} \) |
$2.60299$ |
$(2,a), (3,a+1), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$16$ |
\( 2^{4} \) |
$1$ |
$0.305059427$ |
3.086984356 |
\( \frac{37688339331809089}{2430} a + \frac{23836231835693689}{486} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 4115 a - 14160\) , \( 269195 a - 865933\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(4115a-14160\right){x}+269195a-865933$ |
450.3-r1 |
450.3-r |
$2$ |
$3$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
450.3 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( - 2^{15} \cdot 3^{7} \cdot 5^{8} \) |
$2.60299$ |
$(2,a), (3,a+1), (5,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3 \) |
$0.278486055$ |
$8.736672867$ |
4.616371793 |
\( -\frac{533474309}{12} a + \frac{843496315}{6} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( 40 a - 235\) , \( -145 a + 2210\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(40a-235\right){x}-145a+2210$ |
450.3-r2 |
450.3-r |
$2$ |
$3$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
450.3 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( - 2^{9} \cdot 3^{9} \cdot 5^{8} \) |
$2.60299$ |
$(2,a), (3,a+1), (5,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3^{3} \) |
$0.092828685$ |
$2.912224289$ |
4.616371793 |
\( -\frac{225727}{864} a + \frac{400355}{432} \) |
\( \bigl[1\) , \( a\) , \( a\) , \( 88 a + 282\) , \( -3126 a - 9888\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(88a+282\right){x}-3126a-9888$ |
450.3-s1 |
450.3-s |
$2$ |
$3$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
450.3 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{15} \cdot 3^{9} \cdot 5^{4} \) |
$2.60299$ |
$(2,a), (3,a+1), (5,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.763049502$ |
$1.578502414$ |
4.570663091 |
\( \frac{1181545}{108} a - \frac{1128415}{27} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -9 a - 53\) , \( -24 a - 222\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-9a-53\right){x}-24a-222$ |
*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.