| 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 |
| 100.1-a1 |
100.1-a |
$2$ |
$5$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{30} \cdot 5^{6} \) |
$2.27822$ |
$(2,a), (2,a+1), (5,a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 5$ |
3Ns, 5B.1.4 |
$1$ |
\( 1 \) |
$1$ |
$6.104047643$ |
0.757113929 |
\( -\frac{1680914269}{32768} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( 3964 a - 17953\) , \( -280263 a + 1269909\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(3964a-17953\right){x}-280263a+1269909$ |
| 100.1-a2 |
100.1-a |
$2$ |
$5$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{6} \cdot 5^{6} \) |
$2.27822$ |
$(2,a), (2,a+1), (5,a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 5$ |
3Ns, 5B.1.3 |
$1$ |
\( 1 \) |
$1$ |
$6.104047643$ |
0.757113929 |
\( \frac{1331}{8} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( -36 a + 172\) , \( 772 a - 3496\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-36a+172\right){x}+772a-3496$ |
| 100.1-b1 |
100.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( - 2^{27} \cdot 5^{9} \) |
$2.27822$ |
$(2,a), (2,a+1), (5,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$2.456420716$ |
5.484266848 |
\( -\frac{14765955127}{102400} a + \frac{4191057561}{6400} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( 52 a - 91\) , \( 231 a - 842\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(52a-91\right){x}+231a-842$ |
| 100.1-b2 |
100.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{12} \cdot 5^{12} \) |
$2.27822$ |
$(2,a), (2,a+1), (5,a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3Ns |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$1$ |
$4.912841432$ |
5.484266848 |
\( \frac{16194277}{8000} \) |
\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( -843 a - 2973\) , \( -8757 a - 30923\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-843a-2973\right){x}-8757a-30923$ |
| 100.1-b3 |
100.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{6} \cdot 5^{18} \) |
$2.27822$ |
$(2,a), (2,a+1), (5,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$4.912841432$ |
5.484266848 |
\( \frac{10260751717}{125000} \) |
\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( -7243 a - 25573\) , \( 679363 a + 2398917\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-7243a-25573\right){x}+679363a+2398917$ |
| 100.1-b4 |
100.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( - 2^{27} \cdot 5^{9} \) |
$2.27822$ |
$(2,a), (2,a+1), (5,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$2.456420716$ |
5.484266848 |
\( \frac{14765955127}{102400} a + \frac{52290965849}{102400} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -11020 a - 38912\) , \( -1295700 a - 4575284\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-11020a-38912\right){x}-1295700a-4575284$ |
| 100.1-c1 |
100.1-c |
$4$ |
$15$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{18} \cdot 5^{8} \) |
$2.27822$ |
$(2,a), (2,a+1), (5,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 5$ |
3B, 5B.1.2 |
$1$ |
\( 3^{3} \) |
$1.978032737$ |
$0.508604290$ |
6.738303625 |
\( -\frac{349938025}{8} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 227818 a - 1032272\) , \( 119423852 a - 541124864\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(227818a-1032272\right){x}+119423852a-541124864$ |
| 100.1-c2 |
100.1-c |
$4$ |
$15$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{10} \cdot 5^{4} \) |
$2.27822$ |
$(2,a), (2,a+1), (5,a+2)$ |
$1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 5$ |
3B, 5B.1.1 |
$1$ |
\( 5^{2} \) |
$1.186819642$ |
$22.88719308$ |
6.738303625 |
\( -\frac{121945}{32} \) |
\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( 24939 a - 113001\) , \( -5149703 a + 23333959\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(24939a-113001\right){x}-5149703a+23333959$ |
| 100.1-c3 |
100.1-c |
$4$ |
$15$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{14} \cdot 5^{8} \) |
$2.27822$ |
$(2,a), (2,a+1), (5,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 5$ |
3B, 5B.1.2 |
$1$ |
\( 1 \) |
$5.934098211$ |
$4.577438616$ |
6.738303625 |
\( -\frac{25}{2} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 943 a - 4272\) , \( 377227 a - 1709264\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(943a-4272\right){x}+377227a-1709264$ |
| 100.1-c4 |
100.1-c |
$4$ |
$15$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{30} \cdot 5^{4} \) |
$2.27822$ |
$(2,a), (2,a+1), (5,a+2)$ |
$1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 5$ |
3B, 5B.1.1 |
$1$ |
\( 3^{3} \cdot 5^{2} \) |
$0.395606547$ |
$2.543021453$ |
6.738303625 |
\( \frac{46969655}{32768} \) |
\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -181461 a + 822224\) , \( 38009182 a - 172224511\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-181461a+822224\right){x}+38009182a-172224511$ |
| 100.1-d1 |
100.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( - 2^{30} \cdot 5^{6} \) |
$2.27822$ |
$(2,a), (2,a+1), (5,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.144288566$ |
$8.765306349$ |
3.764901191 |
\( -\frac{6318305}{4096} a + \frac{29023665}{4096} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 132295 a - 599440\) , \( -48735135 a + 220825180\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(132295a-599440\right){x}-48735135a+220825180$ |
| 100.1-d2 |
100.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( - 2^{18} \cdot 5^{6} \) |
$2.27822$ |
$(2,a), (2,a+1), (5,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.288577133$ |
$8.765306349$ |
3.764901191 |
\( \frac{6318305}{4096} a + \frac{1419085}{256} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( -8376 a + 37957\) , \( -3435741 a + 15567787\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-8376a+37957\right){x}-3435741a+15567787$ |
| 100.1-e1 |
100.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( - 2^{3} \cdot 5^{9} \) |
$2.27822$ |
$(2,a), (2,a+1), (5,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$14.48046409$ |
1.796080521 |
\( -\frac{10045}{4} a + \frac{22811}{2} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( 2 a + 7\) , \( 6 a + 23\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(2a+7\right){x}+6a+23$ |
| 100.1-e2 |
100.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( - 2^{15} \cdot 5^{9} \) |
$2.27822$ |
$(2,a), (2,a+1), (5,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$14.48046409$ |
1.796080521 |
\( \frac{10045}{4} a + \frac{35577}{4} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -16 a - 56\) , \( 35 a + 128\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-16a-56\right){x}+35a+128$ |
| 100.1-f1 |
100.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( - 2^{15} \cdot 5^{9} \) |
$2.27822$ |
$(2,a), (2,a+1), (5,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$14.48046409$ |
1.796080521 |
\( -\frac{10045}{4} a + \frac{22811}{2} \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( 3265 a - 14763\) , \( -195110 a + 884102\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(3265a-14763\right){x}-195110a+884102$ |
| 100.1-f2 |
100.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( - 2^{3} \cdot 5^{9} \) |
$2.27822$ |
$(2,a), (2,a+1), (5,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$14.48046409$ |
1.796080521 |
\( \frac{10045}{4} a + \frac{35577}{4} \) |
\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 7\) , \( -5 a + 21\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+7{x}-5a+21$ |
| 100.1-g1 |
100.1-g |
$2$ |
$2$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( - 2^{18} \cdot 5^{6} \) |
$2.27822$ |
$(2,a), (2,a+1), (5,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.288577133$ |
$8.765306349$ |
3.764901191 |
\( -\frac{6318305}{4096} a + \frac{29023665}{4096} \) |
\( \bigl[1\) , \( -a\) , \( 1\) , \( 8376 a + 29581\) , \( 3435741 a + 12132046\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(8376a+29581\right){x}+3435741a+12132046$ |
| 100.1-g2 |
100.1-g |
$2$ |
$2$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( - 2^{30} \cdot 5^{6} \) |
$2.27822$ |
$(2,a), (2,a+1), (5,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.144288566$ |
$8.765306349$ |
3.764901191 |
\( \frac{6318305}{4096} a + \frac{1419085}{256} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -658 a - 2328\) , \( 16221 a + 57276\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-658a-2328\right){x}+16221a+57276$ |
| 100.1-h1 |
100.1-h |
$4$ |
$15$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{6} \cdot 5^{8} \) |
$2.27822$ |
$(2,a), (2,a+1), (5,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 5$ |
3B.1.2, 5B.1.3 |
$1$ |
\( 1 \) |
$15.71822282$ |
$0.508604290$ |
1.983155543 |
\( -\frac{349938025}{8} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -126\) , \( -552\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-126{x}-552$ |
| 100.1-h2 |
100.1-h |
$4$ |
$15$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{22} \cdot 5^{4} \) |
$2.27822$ |
$(2,a), (2,a+1), (5,a+2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 5$ |
3B.1.1, 5B.1.4 |
$1$ |
\( 3 \) |
$1.047881521$ |
$22.88719308$ |
1.983155543 |
\( -\frac{121945}{32} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( -23 a - 88\) , \( 96 a + 336\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-23a-88\right){x}+96a+336$ |
| 100.1-h3 |
100.1-h |
$4$ |
$15$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{2} \cdot 5^{8} \) |
$2.27822$ |
$(2,a), (2,a+1), (5,a+2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 5$ |
3B.1.1, 5B.1.3 |
$1$ |
\( 3 \) |
$5.239407609$ |
$4.577438616$ |
1.983155543 |
\( -\frac{25}{2} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( -2\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}-2$ |
| 100.1-h4 |
100.1-h |
$4$ |
$15$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{42} \cdot 5^{4} \) |
$2.27822$ |
$(2,a), (2,a+1), (5,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 5$ |
3B.1.2, 5B.1.4 |
$1$ |
\( 1 \) |
$3.143644565$ |
$2.543021453$ |
1.983155543 |
\( \frac{46969655}{32768} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( 202 a + 712\) , \( -674 a - 2384\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(202a+712\right){x}-674a-2384$ |
| 100.1-i1 |
100.1-i |
$4$ |
$4$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( - 2^{15} \cdot 5^{9} \) |
$2.27822$ |
$(2,a), (2,a+1), (5,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2^{3} \) |
$1$ |
$2.456420716$ |
0.609362983 |
\( -\frac{14765955127}{102400} a + \frac{4191057561}{6400} \) |
\( \bigl[1\) , \( a - 1\) , \( a\) , \( 151 a - 680\) , \( 1820 a - 8248\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(151a-680\right){x}+1820a-8248$ |
| 100.1-i2 |
100.1-i |
$4$ |
$4$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{24} \cdot 5^{12} \) |
$2.27822$ |
$(2,a), (2,a+1), (5,a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3Ns |
$1$ |
\( 2^{4} \) |
$1$ |
$4.912841432$ |
0.609362983 |
\( \frac{16194277}{8000} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 185 a - 840\) , \( 1185 a - 5380\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(185a-840\right){x}+1185a-5380$ |
| 100.1-i3 |
100.1-i |
$4$ |
$4$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{18} \cdot 5^{18} \) |
$2.27822$ |
$(2,a), (2,a+1), (5,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2^{2} \) |
$1$ |
$4.912841432$ |
0.609362983 |
\( \frac{10260751717}{125000} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 1585 a - 7240\) , \( -67575 a + 306300\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(1585a-7240\right){x}-67575a+306300$ |
| 100.1-i4 |
100.1-i |
$4$ |
$4$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( - 2^{15} \cdot 5^{9} \) |
$2.27822$ |
$(2,a), (2,a+1), (5,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2^{3} \) |
$1$ |
$2.456420716$ |
0.609362983 |
\( \frac{14765955127}{102400} a + \frac{52290965849}{102400} \) |
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -152 a - 529\) , \( -1821 a - 6428\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-152a-529\right){x}-1821a-6428$ |
| 100.1-j1 |
100.1-j |
$2$ |
$5$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{42} \cdot 5^{6} \) |
$2.27822$ |
$(2,a), (2,a+1), (5,a+2)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 5$ |
3Ns, 5B.1.1 |
$1$ |
\( 3^{2} \cdot 5^{2} \) |
$1$ |
$6.104047643$ |
6.814025364 |
\( -\frac{1680914269}{32768} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 867 a - 3968\) , \( -27959 a + 126716\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(867a-3968\right){x}-27959a+126716$ |
| 100.1-j2 |
100.1-j |
$2$ |
$5$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{18} \cdot 5^{6} \) |
$2.27822$ |
$(2,a), (2,a+1), (5,a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 5$ |
3Ns, 5B.1.2 |
$1$ |
\( 3^{2} \) |
$1$ |
$6.104047643$ |
6.814025364 |
\( \frac{1331}{8} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -8 a + 32\) , \( 71 a - 324\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-8a+32\right){x}+71a-324$ |
*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.
