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 |
605.2-a1 |
605.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
605.2 |
\( 5 \cdot 11^{2} \) |
\( - 5^{3} \cdot 11^{9} \) |
$0.99097$ |
$(-2a+1), (-3a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2 \) |
$1$ |
$6.076619226$ |
1.358773366 |
\( -\frac{20192}{25} a + \frac{32421}{25} \) |
\( \bigl[\phi\) , \( \phi\) , \( 0\) , \( 8 \phi - 15\) , \( 11 \phi + 17\bigr] \) |
${y}^2+\phi{x}{y}={x}^{3}+\phi{x}^{2}+\left(8\phi-15\right){x}+11\phi+17$ |
605.2-a2 |
605.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
605.2 |
\( 5 \cdot 11^{2} \) |
\( 5^{6} \cdot 11^{9} \) |
$0.99097$ |
$(-2a+1), (-3a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2^{2} \) |
$1$ |
$3.038309613$ |
1.358773366 |
\( -\frac{393466}{25} a + \frac{17856881}{125} \) |
\( \bigl[\phi\) , \( \phi\) , \( 0\) , \( 3 \phi - 195\) , \( 847 \phi - 500\bigr] \) |
${y}^2+\phi{x}{y}={x}^{3}+\phi{x}^{2}+\left(3\phi-195\right){x}+847\phi-500$ |
605.2-b1 |
605.2-b |
$8$ |
$12$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
605.2 |
\( 5 \cdot 11^{2} \) |
\( - 5 \cdot 11^{7} \) |
$0.99097$ |
$(-2a+1), (-3a+2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$11.27636307$ |
1.260735718 |
\( -\frac{45227}{55} a + \frac{72206}{55} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -2\) , \( 7 \phi + 3\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-2{x}+7\phi+3$ |
605.2-b2 |
605.2-b |
$8$ |
$12$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
605.2 |
\( 5 \cdot 11^{2} \) |
\( - 5^{3} \cdot 11^{9} \) |
$0.99097$ |
$(-2a+1), (-3a+2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$3.758787690$ |
1.260735718 |
\( -\frac{754904381777}{33275} a + \frac{1221461532231}{33275} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( 65 \phi - 82\) , \( -390 \phi + 231\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(65\phi-82\right){x}-390\phi+231$ |
605.2-b3 |
605.2-b |
$8$ |
$12$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
605.2 |
\( 5 \cdot 11^{2} \) |
\( 5^{4} \cdot 11^{7} \) |
$0.99097$ |
$(-2a+1), (-3a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.409545383$ |
1.260735718 |
\( -\frac{48555143354501}{275} a + \frac{78563872776324}{275} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( 140 \phi - 407\) , \( 1855 \phi - 3286\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(140\phi-407\right){x}+1855\phi-3286$ |
605.2-b4 |
605.2-b |
$8$ |
$12$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
605.2 |
\( 5 \cdot 11^{2} \) |
\( - 5^{3} \cdot 11^{18} \) |
$0.99097$ |
$(-2a+1), (-3a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$0.939696922$ |
1.260735718 |
\( \frac{114278307303626907}{78460709418025} a + \frac{89325070732461329}{78460709418025} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -935 \phi - 387\) , \( 8620 \phi + 7934\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(-935\phi-387\right){x}+8620\phi+7934$ |
605.2-b5 |
605.2-b |
$8$ |
$12$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
605.2 |
\( 5 \cdot 11^{2} \) |
\( 5^{6} \cdot 11^{12} \) |
$0.99097$ |
$(-2a+1), (-3a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$1.879393845$ |
1.260735718 |
\( \frac{1485675267531}{221445125} a + \frac{2666389392178}{221445125} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -260 \phi - 287\) , \( -3445 \phi - 1696\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(-260\phi-287\right){x}-3445\phi-1696$ |
605.2-b6 |
605.2-b |
$8$ |
$12$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
605.2 |
\( 5 \cdot 11^{2} \) |
\( 5^{2} \cdot 11^{8} \) |
$0.99097$ |
$(-2a+1), (-3a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$5.638181535$ |
1.260735718 |
\( -\frac{132583563}{605} a + \frac{59730809}{121} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -35 \phi - 52\) , \( 210 \phi + 51\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(-35\phi-52\right){x}+210\phi+51$ |
605.2-b7 |
605.2-b |
$8$ |
$12$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
605.2 |
\( 5 \cdot 11^{2} \) |
\( 5^{12} \cdot 11^{9} \) |
$0.99097$ |
$(-2a+1), (-3a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.469848461$ |
1.260735718 |
\( \frac{4560282420936767}{20796875} a + \frac{563715628160969}{4159375} \) |
\( \bigl[\phi + 1\) , \( \phi - 1\) , \( \phi\) , \( 832 \phi - 2982\) , \( 18800 \phi - 57148\bigr] \) |
${y}^2+\left(\phi+1\right){x}{y}+\phi{y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(832\phi-2982\right){x}+18800\phi-57148$ |
605.2-b8 |
605.2-b |
$8$ |
$12$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
605.2 |
\( 5 \cdot 11^{2} \) |
\( - 5 \cdot 11^{10} \) |
$0.99097$ |
$(-2a+1), (-3a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.819090767$ |
1.260735718 |
\( \frac{626283905886387}{73205} a + \frac{387064721079604}{73205} \) |
\( \bigl[\phi + 1\) , \( \phi - 1\) , \( \phi\) , \( -48 \phi - 177\) , \( 1428 \phi - 947\bigr] \) |
${y}^2+\left(\phi+1\right){x}{y}+\phi{y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(-48\phi-177\right){x}+1428\phi-947$ |
605.2-c1 |
605.2-c |
$2$ |
$2$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
605.2 |
\( 5 \cdot 11^{2} \) |
\( - 5^{3} \cdot 11^{3} \) |
$0.99097$ |
$(-2a+1), (-3a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2 \cdot 3 \) |
$0.044025197$ |
$19.13415901$ |
1.130178257 |
\( -\frac{20192}{25} a + \frac{32421}{25} \) |
\( \bigl[\phi + 1\) , \( -\phi - 1\) , \( \phi + 1\) , \( -\phi - 2\) , \( 0\bigr] \) |
${y}^2+\left(\phi+1\right){x}{y}+\left(\phi+1\right){y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(-\phi-2\right){x}$ |
605.2-c2 |
605.2-c |
$2$ |
$2$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
605.2 |
\( 5 \cdot 11^{2} \) |
\( 5^{6} \cdot 11^{3} \) |
$0.99097$ |
$(-2a+1), (-3a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.022012598$ |
$19.13415901$ |
1.130178257 |
\( -\frac{393466}{25} a + \frac{17856881}{125} \) |
\( \bigl[\phi + 1\) , \( -\phi - 1\) , \( \phi + 1\) , \( -6 \phi - 17\) , \( 13 \phi + 28\bigr] \) |
${y}^2+\left(\phi+1\right){x}{y}+\left(\phi+1\right){y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(-6\phi-17\right){x}+13\phi+28$ |
*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.