| 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 |
| 225.1-a1 |
225.1-a |
$4$ |
$10$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 2^{12} \cdot 3^{20} \cdot 5^{6} \) |
$2.18884$ |
$(3,a+1), (3,a+2), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B.1.4 |
$1$ |
\( 2^{3} \) |
$1$ |
$5.346334508$ |
1.690659418 |
\( -\frac{873722816}{59049} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 2390 a - 7568\) , \( -120440 a + 380882\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(2390a-7568\right){x}-120440a+380882$ |
| 225.1-a2 |
225.1-a |
$4$ |
$10$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 2^{12} \cdot 3^{4} \cdot 5^{6} \) |
$2.18884$ |
$(3,a+1), (3,a+2), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B.1.3 |
$1$ |
\( 2^{3} \) |
$1$ |
$5.346334508$ |
1.690659418 |
\( \frac{64}{9} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -10 a + 32\) , \( 480 a - 1518\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-10a+32\right){x}+480a-1518$ |
| 225.1-a3 |
225.1-a |
$4$ |
$10$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{2} \cdot 5^{6} \) |
$2.18884$ |
$(3,a+1), (3,a+2), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B.1.3 |
$1$ |
\( 2^{2} \) |
$1$ |
$10.69266901$ |
1.690659418 |
\( \frac{85184}{3} \) |
\( \bigl[a\) , \( 1\) , \( a + 1\) , \( 27 a - 88\) , \( 167 a - 531\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(27a-88\right){x}+167a-531$ |
| 225.1-a4 |
225.1-a |
$4$ |
$10$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{10} \cdot 5^{6} \) |
$2.18884$ |
$(3,a+1), (3,a+2), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B.1.4 |
$1$ |
\( 2^{2} \) |
$1$ |
$10.69266901$ |
1.690659418 |
\( \frac{58591911104}{243} \) |
\( \bigl[a\) , \( 1\) , \( a + 1\) , \( 2427 a - 7688\) , \( -113058 a + 357519\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(2427a-7688\right){x}-113058a+357519$ |
| 225.1-b1 |
225.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( - 3^{3} \cdot 5^{3} \) |
$2.18884$ |
$(3,a+1), (3,a+2), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$8.423044762$ |
1.331800314 |
\( -\frac{389888}{9} a + \frac{1232192}{9} \) |
\( \bigl[a\) , \( a - 1\) , \( a + 1\) , \( a - 3\) , \( -2\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(a-3\right){x}-2$ |
| 225.1-b2 |
225.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( - 2^{12} \cdot 3^{3} \cdot 5^{3} \) |
$2.18884$ |
$(3,a+1), (3,a+2), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$8.423044762$ |
1.331800314 |
\( \frac{389888}{9} a + \frac{1232192}{9} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -2 a - 5\) , \( -5 a - 20\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-2a-5\right){x}-5a-20$ |
| 225.1-c1 |
225.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{12} \cdot 5^{10} \) |
$2.18884$ |
$(3,a+1), (3,a+2), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$2.116565657$ |
6.023851464 |
\( \frac{24897088}{18225} \) |
\( \bigl[a\) , \( 0\) , \( a + 1\) , \( -183 a + 575\) , \( 1077 a - 3409\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-183a+575\right){x}+1077a-3409$ |
| 225.1-c2 |
225.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 2^{12} \cdot 3^{6} \cdot 5^{14} \) |
$2.18884$ |
$(3,a+1), (3,a+2), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$4.233131314$ |
6.023851464 |
\( \frac{36594368}{16875} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 830 a - 2628\) , \( 10720 a - 33902\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(830a-2628\right){x}+10720a-33902$ |
| 225.1-d1 |
225.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( - 3^{21} \cdot 5^{9} \) |
$2.18884$ |
$(3,a+1), (3,a+2), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 7 \) |
$1$ |
$1.205394626$ |
1.334127375 |
\( -\frac{4551038720}{4782969} a + \frac{16020314432}{4782969} \) |
\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( 41 a - 53\) , \( 78 a - 877\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(41a-53\right){x}+78a-877$ |
| 225.1-d2 |
225.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( - 2^{12} \cdot 3^{21} \cdot 5^{9} \) |
$2.18884$ |
$(3,a+1), (3,a+2), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 7 \) |
$1$ |
$1.205394626$ |
1.334127375 |
\( \frac{4551038720}{4782969} a + \frac{16020314432}{4782969} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -170 a - 205\) , \( -255 a - 5100\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-170a-205\right){x}-255a-5100$ |
| 225.1-e1 |
225.1-e |
$4$ |
$6$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{8} \cdot 5^{6} \) |
$2.18884$ |
$(3,a+1), (3,a+2), (5,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.171988259$ |
$8.972311773$ |
2.927887655 |
\( -\frac{654080}{729} a - \frac{990400}{729} \) |
\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( -184 a - 573\) , \( 2936 a + 9288\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-184a-573\right){x}+2936a+9288$ |
| 225.1-e2 |
225.1-e |
$4$ |
$6$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 2^{12} \cdot 3^{8} \cdot 5^{6} \) |
$2.18884$ |
$(3,a+1), (3,a+2), (5,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$0.515964779$ |
$8.972311773$ |
2.927887655 |
\( \frac{654080}{729} a - \frac{990400}{729} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 30 a + 95\) , \( -95 a - 300\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(30a+95\right){x}-95a-300$ |
| 225.1-e3 |
225.1-e |
$4$ |
$6$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{4} \cdot 5^{6} \) |
$2.18884$ |
$(3,a+1), (3,a+2), (5,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1.031929558$ |
$17.94462354$ |
2.927887655 |
\( -\frac{102519040}{27} a + \frac{324248000}{27} \) |
\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( -9 a - 23\) , \( -4 a - 12\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-9a-23\right){x}-4a-12$ |
| 225.1-e4 |
225.1-e |
$4$ |
$6$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 2^{12} \cdot 3^{4} \cdot 5^{6} \) |
$2.18884$ |
$(3,a+1), (3,a+2), (5,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$0.343976519$ |
$17.94462354$ |
2.927887655 |
\( \frac{102519040}{27} a + \frac{324248000}{27} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -3070 a - 9705\) , \( 167885 a + 530900\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-3070a-9705\right){x}+167885a+530900$ |
| 225.1-f1 |
225.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 2^{12} \cdot 3^{12} \cdot 5^{10} \) |
$2.18884$ |
$(3,a+1), (3,a+2), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.116565657$ |
0.669316829 |
\( \frac{24897088}{18225} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -730 a + 2312\) , \( 10080 a - 31878\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-730a+2312\right){x}+10080a-31878$ |
| 225.1-f2 |
225.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{6} \cdot 5^{14} \) |
$2.18884$ |
$(3,a+1), (3,a+2), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$4.233131314$ |
0.669316829 |
\( \frac{36594368}{16875} \) |
\( \bigl[a\) , \( 1\) , \( a + 1\) , \( 207 a - 658\) , \( 1547 a - 4896\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(207a-658\right){x}+1547a-4896$ |
| 225.1-g1 |
225.1-g |
$2$ |
$5$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{2} \cdot 5^{8} \) |
$2.18884$ |
$(3,a+1), (3,a+2), (5,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$5$ |
5B.1.3 |
$1$ |
\( 1 \) |
$7.900543714$ |
$1.967118283$ |
4.914591842 |
\( -\frac{102400}{3} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -8\) , \( -7\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}-8{x}-7$ |
| 225.1-g2 |
225.1-g |
$2$ |
$5$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 2^{12} \cdot 3^{10} \cdot 5^{4} \) |
$2.18884$ |
$(3,a+1), (3,a+2), (5,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$5$ |
5B.1.4 |
$1$ |
\( 1 \) |
$1.580108742$ |
$9.835591419$ |
4.914591842 |
\( \frac{20480}{243} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 7\) , \( 27\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+7{x}+27$ |
| 225.1-h1 |
225.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( - 2^{12} \cdot 3^{21} \cdot 5^{9} \) |
$2.18884$ |
$(3,a+1), (3,a+2), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 7 \) |
$1$ |
$1.205394626$ |
1.334127375 |
\( -\frac{4551038720}{4782969} a + \frac{16020314432}{4782969} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 170 a - 205\) , \( 255 a - 5100\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(170a-205\right){x}+255a-5100$ |
| 225.1-h2 |
225.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( - 3^{21} \cdot 5^{9} \) |
$2.18884$ |
$(3,a+1), (3,a+2), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 7 \) |
$1$ |
$1.205394626$ |
1.334127375 |
\( \frac{4551038720}{4782969} a + \frac{16020314432}{4782969} \) |
\( \bigl[a\) , \( a - 1\) , \( a + 1\) , \( -42 a - 53\) , \( -79 a - 877\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-42a-53\right){x}-79a-877$ |
| 225.1-i1 |
225.1-i |
$2$ |
$3$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 2^{12} \cdot 3^{12} \cdot 5^{2} \) |
$2.18884$ |
$(3,a+1), (3,a+2), (5,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B |
$1$ |
\( 3 \) |
$0.211784497$ |
$14.53499520$ |
2.920319134 |
\( -\frac{7046864896}{19683} a - \frac{22283386880}{19683} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -12 a + 30\) , \( -198 a + 630\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-12a+30\right){x}-198a+630$ |
| 225.1-i2 |
225.1-i |
$2$ |
$3$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{12} \cdot 5^{2} \) |
$2.18884$ |
$(3,a+1), (3,a+2), (5,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B |
$1$ |
\( 3^{2} \) |
$0.070594832$ |
$14.53499520$ |
2.920319134 |
\( \frac{7046864896}{19683} a - \frac{22283386880}{19683} \) |
\( \bigl[0\) , \( a\) , \( 1\) , \( 643 a - 2030\) , \( -16466 a + 52071\bigr] \) |
${y}^2+{y}={x}^{3}+a{x}^{2}+\left(643a-2030\right){x}-16466a+52071$ |
| 225.1-j1 |
225.1-j |
$2$ |
$5$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 2^{12} \cdot 3^{2} \cdot 5^{8} \) |
$2.18884$ |
$(3,a+1), (3,a+2), (5,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$5$ |
5B.1.2 |
$1$ |
\( 3 \) |
$1.385300339$ |
$1.967118283$ |
2.585209067 |
\( -\frac{102400}{3} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -33\) , \( -87\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-33{x}-87$ |
| 225.1-j2 |
225.1-j |
$2$ |
$5$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{10} \cdot 5^{4} \) |
$2.18884$ |
$(3,a+1), (3,a+2), (5,a)$ |
$1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$5$ |
5B.1.1 |
$1$ |
\( 3 \cdot 5^{2} \) |
$0.277060067$ |
$9.835591419$ |
2.585209067 |
\( \frac{20480}{243} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( 2\) , \( 4\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}+2{x}+4$ |
| 225.1-k1 |
225.1-k |
$2$ |
$3$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{12} \cdot 5^{2} \) |
$2.18884$ |
$(3,a+1), (3,a+2), (5,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B |
$1$ |
\( 3^{2} \) |
$0.070594832$ |
$14.53499520$ |
2.920319134 |
\( -\frac{7046864896}{19683} a - \frac{22283386880}{19683} \) |
\( \bigl[0\) , \( -a\) , \( 1\) , \( -643 a - 2030\) , \( 16466 a + 52071\bigr] \) |
${y}^2+{y}={x}^{3}-a{x}^{2}+\left(-643a-2030\right){x}+16466a+52071$ |
| 225.1-k2 |
225.1-k |
$2$ |
$3$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 2^{12} \cdot 3^{12} \cdot 5^{2} \) |
$2.18884$ |
$(3,a+1), (3,a+2), (5,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B |
$1$ |
\( 3 \) |
$0.211784497$ |
$14.53499520$ |
2.920319134 |
\( \frac{7046864896}{19683} a - \frac{22283386880}{19683} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 12 a + 30\) , \( 198 a + 630\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(12a+30\right){x}+198a+630$ |
| 225.1-l1 |
225.1-l |
$4$ |
$6$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 2^{12} \cdot 3^{8} \cdot 5^{6} \) |
$2.18884$ |
$(3,a+1), (3,a+2), (5,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$0.515964779$ |
$8.972311773$ |
2.927887655 |
\( -\frac{654080}{729} a - \frac{990400}{729} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -30 a + 95\) , \( 95 a - 300\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-30a+95\right){x}+95a-300$ |
| 225.1-l2 |
225.1-l |
$4$ |
$6$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{8} \cdot 5^{6} \) |
$2.18884$ |
$(3,a+1), (3,a+2), (5,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.171988259$ |
$8.972311773$ |
2.927887655 |
\( \frac{654080}{729} a - \frac{990400}{729} \) |
\( \bigl[a\) , \( a - 1\) , \( 1\) , \( 183 a - 573\) , \( -2936 a + 9288\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(183a-573\right){x}-2936a+9288$ |
| 225.1-l3 |
225.1-l |
$4$ |
$6$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 2^{12} \cdot 3^{4} \cdot 5^{6} \) |
$2.18884$ |
$(3,a+1), (3,a+2), (5,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$0.343976519$ |
$17.94462354$ |
2.927887655 |
\( -\frac{102519040}{27} a + \frac{324248000}{27} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 3070 a - 9705\) , \( -167885 a + 530900\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(3070a-9705\right){x}-167885a+530900$ |
| 225.1-l4 |
225.1-l |
$4$ |
$6$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{4} \cdot 5^{6} \) |
$2.18884$ |
$(3,a+1), (3,a+2), (5,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1.031929558$ |
$17.94462354$ |
2.927887655 |
\( \frac{102519040}{27} a + \frac{324248000}{27} \) |
\( \bigl[a\) , \( a - 1\) , \( 1\) , \( 8 a - 23\) , \( 4 a - 12\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(8a-23\right){x}+4a-12$ |
| 225.1-m1 |
225.1-m |
$4$ |
$10$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{20} \cdot 5^{6} \) |
$2.18884$ |
$(3,a+1), (3,a+2), (5,a)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 2^{3} \cdot 5^{2} \) |
$1$ |
$5.346334508$ |
1.690659418 |
\( -\frac{873722816}{59049} \) |
\( \bigl[a\) , \( 0\) , \( a + 1\) , \( 597 a - 1895\) , \( -14458 a + 45716\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(597a-1895\right){x}-14458a+45716$ |
| 225.1-m2 |
225.1-m |
$4$ |
$10$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{4} \cdot 5^{6} \) |
$2.18884$ |
$(3,a+1), (3,a+2), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B.1.2 |
$1$ |
\( 2^{3} \) |
$1$ |
$5.346334508$ |
1.690659418 |
\( \frac{64}{9} \) |
\( \bigl[a\) , \( 0\) , \( a + 1\) , \( -3 a + 5\) , \( 57 a - 184\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-3a+5\right){x}+57a-184$ |
| 225.1-m3 |
225.1-m |
$4$ |
$10$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 2^{12} \cdot 3^{2} \cdot 5^{6} \) |
$2.18884$ |
$(3,a+1), (3,a+2), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B.1.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$10.69266901$ |
1.690659418 |
\( \frac{85184}{3} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 110 a - 348\) , \( 1120 a - 3542\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(110a-348\right){x}+1120a-3542$ |
| 225.1-m4 |
225.1-m |
$4$ |
$10$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 2^{12} \cdot 3^{10} \cdot 5^{6} \) |
$2.18884$ |
$(3,a+1), (3,a+2), (5,a)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 2^{2} \cdot 5^{2} \) |
$1$ |
$10.69266901$ |
1.690659418 |
\( \frac{58591911104}{243} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 9710 a - 30748\) , \( -923880 a + 2921658\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(9710a-30748\right){x}-923880a+2921658$ |
| 225.1-n1 |
225.1-n |
$2$ |
$2$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( - 2^{12} \cdot 3^{3} \cdot 5^{3} \) |
$2.18884$ |
$(3,a+1), (3,a+2), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$8.423044762$ |
1.331800314 |
\( -\frac{389888}{9} a + \frac{1232192}{9} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 2 a - 5\) , \( 5 a - 20\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(2a-5\right){x}+5a-20$ |
| 225.1-n2 |
225.1-n |
$2$ |
$2$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( - 3^{3} \cdot 5^{3} \) |
$2.18884$ |
$(3,a+1), (3,a+2), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$8.423044762$ |
1.331800314 |
\( \frac{389888}{9} a + \frac{1232192}{9} \) |
\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( -2 a - 3\) , \( -a - 2\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-2a-3\right){x}-a-2$ |
*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.
