| 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 |
| 605.1-a1 |
605.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
605.1 |
\( 5 \cdot 11^{2} \) |
\( 5^{8} \cdot 11^{9} \) |
$0.99097$ |
$(-2a+1), (-3a+2), (-3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.730701665$ |
1.307118876 |
\( \frac{145013028772769}{133974300625} a - \frac{234637911487596}{133974300625} \) |
\( \bigl[\phi + 1\) , \( \phi\) , \( 1\) , \( 4 \phi - 13\) , \( -1591 \phi - 1011\bigr] \) |
${y}^2+\left(\phi+1\right){x}{y}+{y}={x}^{3}+\phi{x}^{2}+\left(4\phi-13\right){x}-1591\phi-1011$ |
| 605.1-a2 |
605.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
605.1 |
\( 5 \cdot 11^{2} \) |
\( - 5 \cdot 11^{3} \) |
$0.99097$ |
$(-2a+1), (-3a+2), (-3a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$23.38245330$ |
1.307118876 |
\( -\frac{4826927}{605} a + \frac{8607801}{605} \) |
\( \bigl[\phi\) , \( \phi - 1\) , \( 1\) , \( \phi - 1\) , \( -\phi + 2\bigr] \) |
${y}^2+\phi{x}{y}+{y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(\phi-1\right){x}-\phi+2$ |
| 605.1-a3 |
605.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
605.1 |
\( 5 \cdot 11^{2} \) |
\( 5^{2} \cdot 11^{6} \) |
$0.99097$ |
$(-2a+1), (-3a+2), (-3a+1)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$11.69122665$ |
1.307118876 |
\( -\frac{54723249}{73205} a + \frac{252614698}{73205} \) |
\( \bigl[\phi\) , \( \phi - 1\) , \( 1\) , \( \phi - 6\) , \( \phi - 2\bigr] \) |
${y}^2+\phi{x}{y}+{y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(\phi-6\right){x}+\phi-2$ |
| 605.1-a4 |
605.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
605.1 |
\( 5 \cdot 11^{2} \) |
\( 5^{4} \cdot 11^{6} \) |
$0.99097$ |
$(-2a+1), (-3a+2), (-3a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$2.922806663$ |
1.307118876 |
\( -\frac{1566703575423}{366025} a + \frac{511296585637}{73205} \) |
\( \bigl[\phi\) , \( \phi - 1\) , \( 1\) , \( 36 \phi - 91\) , \( 147 \phi - 322\bigr] \) |
${y}^2+\phi{x}{y}+{y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(36\phi-91\right){x}+147\phi-322$ |
| 605.1-a5 |
605.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
605.1 |
\( 5 \cdot 11^{2} \) |
\( - 5 \cdot 11^{9} \) |
$0.99097$ |
$(-2a+1), (-3a+2), (-3a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$5.845613327$ |
1.307118876 |
\( \frac{857730789364547}{1071794405} a + \frac{530836755494779}{1071794405} \) |
\( \bigl[\phi\) , \( \phi - 1\) , \( 1\) , \( -34 \phi - 1\) , \( 83 \phi + 2\bigr] \) |
${y}^2+\phi{x}{y}+{y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(-34\phi-1\right){x}+83\phi+2$ |
| 605.1-a6 |
605.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
605.1 |
\( 5 \cdot 11^{2} \) |
\( 5^{2} \cdot 11^{3} \) |
$0.99097$ |
$(-2a+1), (-3a+2), (-3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$0.730701665$ |
1.307118876 |
\( -\frac{25085621087436781}{605} a + \frac{40591422821635852}{605} \) |
\( \bigl[\phi\) , \( \phi - 1\) , \( 1\) , \( 586 \phi - 1466\) , \( 10927 \phi - 22432\bigr] \) |
${y}^2+\phi{x}{y}+{y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(586\phi-1466\right){x}+10927\phi-22432$ |
| 605.1-b1 |
605.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
605.1 |
\( 5 \cdot 11^{2} \) |
\( 5^{8} \cdot 11^{9} \) |
$0.99097$ |
$(-2a+1), (-3a+2), (-3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.730701665$ |
1.307118876 |
\( -\frac{145013028772769}{133974300625} a - \frac{89624882714827}{133974300625} \) |
\( \bigl[\phi\) , \( \phi - 1\) , \( 0\) , \( -3 \phi - 10\) , \( 1581 \phi - 2595\bigr] \) |
${y}^2+\phi{x}{y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(-3\phi-10\right){x}+1581\phi-2595$ |
| 605.1-b2 |
605.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
605.1 |
\( 5 \cdot 11^{2} \) |
\( - 5 \cdot 11^{9} \) |
$0.99097$ |
$(-2a+1), (-3a+2), (-3a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$5.845613327$ |
1.307118876 |
\( -\frac{857730789364547}{1071794405} a + \frac{1388567544859326}{1071794405} \) |
\( \bigl[\phi + 1\) , \( \phi\) , \( 0\) , \( 35 \phi - 34\) , \( -84 \phi + 119\bigr] \) |
${y}^2+\left(\phi+1\right){x}{y}={x}^{3}+\phi{x}^{2}+\left(35\phi-34\right){x}-84\phi+119$ |
| 605.1-b3 |
605.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
605.1 |
\( 5 \cdot 11^{2} \) |
\( 5^{2} \cdot 11^{6} \) |
$0.99097$ |
$(-2a+1), (-3a+2), (-3a+1)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$11.69122665$ |
1.307118876 |
\( \frac{54723249}{73205} a + \frac{197891449}{73205} \) |
\( \bigl[\phi + 1\) , \( \phi\) , \( 0\) , \( -4\) , \( -7 \phi - 2\bigr] \) |
${y}^2+\left(\phi+1\right){x}{y}={x}^{3}+\phi{x}^{2}-4{x}-7\phi-2$ |
| 605.1-b4 |
605.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
605.1 |
\( 5 \cdot 11^{2} \) |
\( - 5 \cdot 11^{3} \) |
$0.99097$ |
$(-2a+1), (-3a+2), (-3a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$23.38245330$ |
1.307118876 |
\( \frac{4826927}{605} a + \frac{3780874}{605} \) |
\( \bigl[\phi + 1\) , \( \phi\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2+\left(\phi+1\right){x}{y}={x}^{3}+\phi{x}^{2}+{x}$ |
| 605.1-b5 |
605.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
605.1 |
\( 5 \cdot 11^{2} \) |
\( 5^{4} \cdot 11^{6} \) |
$0.99097$ |
$(-2a+1), (-3a+2), (-3a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$2.922806663$ |
1.307118876 |
\( \frac{1566703575423}{366025} a + \frac{989779352762}{366025} \) |
\( \bigl[\phi + 1\) , \( \phi\) , \( 0\) , \( -35 \phi - 54\) , \( -238 \phi - 211\bigr] \) |
${y}^2+\left(\phi+1\right){x}{y}={x}^{3}+\phi{x}^{2}+\left(-35\phi-54\right){x}-238\phi-211$ |
| 605.1-b6 |
605.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
605.1 |
\( 5 \cdot 11^{2} \) |
\( 5^{2} \cdot 11^{3} \) |
$0.99097$ |
$(-2a+1), (-3a+2), (-3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$0.730701665$ |
1.307118876 |
\( \frac{25085621087436781}{605} a + \frac{15505801734199071}{605} \) |
\( \bigl[\phi + 1\) , \( \phi\) , \( 0\) , \( -585 \phi - 879\) , \( -12393 \phi - 12091\bigr] \) |
${y}^2+\left(\phi+1\right){x}{y}={x}^{3}+\phi{x}^{2}+\left(-585\phi-879\right){x}-12393\phi-12091$ |
| 605.1-c1 |
605.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
605.1 |
\( 5 \cdot 11^{2} \) |
\( - 5 \cdot 11^{10} \) |
$0.99097$ |
$(-2a+1), (-3a+2), (-3a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.192245246$ |
$1.058161673$ |
1.128398811 |
\( -\frac{649638087939825642}{1071794405} a + \frac{1051136507981046141}{1071794405} \) |
\( \bigl[\phi\) , \( -\phi - 1\) , \( 0\) , \( 48 \phi - 38\) , \( -1458 \phi - 1109\bigr] \) |
${y}^2+\phi{x}{y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(48\phi-38\right){x}-1458\phi-1109$ |
| 605.1-c2 |
605.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
605.1 |
\( 5 \cdot 11^{2} \) |
\( 5^{2} \cdot 11^{2} \) |
$0.99097$ |
$(-2a+1), (-3a+2), (-3a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.596122623$ |
$16.93058676$ |
1.128398811 |
\( \frac{59319}{55} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+{x}$ |
| 605.1-c3 |
605.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
605.1 |
\( 5 \cdot 11^{2} \) |
\( 5^{4} \cdot 11^{4} \) |
$0.99097$ |
$(-2a+1), (-3a+2), (-3a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.298061311$ |
$16.93058676$ |
1.128398811 |
\( \frac{8120601}{3025} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -4\) , \( 3\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-4{x}+3$ |
| 605.1-c4 |
605.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
605.1 |
\( 5 \cdot 11^{2} \) |
\( 5^{2} \cdot 11^{8} \) |
$0.99097$ |
$(-2a+1), (-3a+2), (-3a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.596122623$ |
$4.232646692$ |
1.128398811 |
\( \frac{2749884201}{73205} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -29\) , \( -52\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-29{x}-52$ |
| 605.1-c5 |
605.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
605.1 |
\( 5 \cdot 11^{2} \) |
\( 5^{8} \cdot 11^{2} \) |
$0.99097$ |
$(-2a+1), (-3a+2), (-3a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.149030655$ |
$16.93058676$ |
1.128398811 |
\( \frac{22930509321}{6875} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -59\) , \( 190\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-59{x}+190$ |
| 605.1-c6 |
605.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
605.1 |
\( 5 \cdot 11^{2} \) |
\( - 5 \cdot 11^{10} \) |
$0.99097$ |
$(-2a+1), (-3a+2), (-3a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.192245246$ |
$1.058161673$ |
1.128398811 |
\( \frac{649638087939825642}{1071794405} a + \frac{401498420041220499}{1071794405} \) |
\( \bigl[\phi + 1\) , \( 1\) , \( \phi + 1\) , \( -48 \phi + 9\) , \( 1410 \phi - 2558\bigr] \) |
${y}^2+\left(\phi+1\right){x}{y}+\left(\phi+1\right){y}={x}^{3}+{x}^{2}+\left(-48\phi+9\right){x}+1410\phi-2558$ |
*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.
