| 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 |
| 2601.1-a1 |
2601.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2601.1 |
\( 3^{2} \cdot 17^{2} \) |
\( 3^{2} \cdot 17^{6} \) |
$1.42695$ |
$(3), (17)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 3 \) |
$1$ |
$0.739701511$ |
0.992413717 |
\( -\frac{23100424192}{14739} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -59\) , \( -196\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}-59{x}-196$ |
| 2601.1-a2 |
2601.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2601.1 |
\( 3^{2} \cdot 17^{2} \) |
\( 3^{6} \cdot 17^{2} \) |
$1.42695$ |
$(3), (17)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$6.657313600$ |
0.992413717 |
\( \frac{32768}{459} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( 1\) , \( -1\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}+{x}-1$ |
| 2601.1-b1 |
2601.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2601.1 |
\( 3^{2} \cdot 17^{2} \) |
\( 3^{2} \cdot 17^{2} \) |
$1.42695$ |
$(3), (17)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.156183025$ |
$13.85209150$ |
1.935058847 |
\( \frac{4096}{51} a + \frac{4096}{51} \) |
\( \bigl[0\) , \( -\phi + 1\) , \( \phi\) , \( 1\) , \( 0\bigr] \) |
${y}^2+\phi{y}={x}^{3}+\left(-\phi+1\right){x}^{2}+{x}$ |
| 2601.1-c1 |
2601.1-c |
$1$ |
$1$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2601.1 |
\( 3^{2} \cdot 17^{2} \) |
\( 3^{10} \cdot 17^{2} \) |
$1.42695$ |
$(3), (17)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 5 \) |
$0.095013753$ |
$4.638211492$ |
1.970842967 |
\( \frac{37232158404608}{1377} a - \frac{10631101456384}{243} \) |
\( \bigl[0\) , \( 1\) , \( \phi + 1\) , \( -49 \phi - 83\) , \( -479 \phi - 165\bigr] \) |
${y}^2+\left(\phi+1\right){y}={x}^{3}+{x}^{2}+\left(-49\phi-83\right){x}-479\phi-165$ |
| 2601.1-d1 |
2601.1-d |
$1$ |
$1$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2601.1 |
\( 3^{2} \cdot 17^{2} \) |
\( 3^{2} \cdot 17^{2} \) |
$1.42695$ |
$(3), (17)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.156183025$ |
$13.85209150$ |
1.935058847 |
\( -\frac{4096}{51} a + \frac{8192}{51} \) |
\( \bigl[0\) , \( \phi\) , \( \phi + 1\) , \( 1\) , \( -\phi\bigr] \) |
${y}^2+\left(\phi+1\right){y}={x}^{3}+\phi{x}^{2}+{x}-\phi$ |
| 2601.1-e1 |
2601.1-e |
$1$ |
$1$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2601.1 |
\( 3^{2} \cdot 17^{2} \) |
\( 3^{10} \cdot 17^{2} \) |
$1.42695$ |
$(3), (17)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 5 \) |
$0.095013753$ |
$4.638211492$ |
1.970842967 |
\( -\frac{37232158404608}{1377} a - \frac{69032249544704}{4131} \) |
\( \bigl[0\) , \( 1\) , \( \phi\) , \( 49 \phi - 132\) , \( 478 \phi - 643\bigr] \) |
${y}^2+\phi{y}={x}^{3}+{x}^{2}+\left(49\phi-132\right){x}+478\phi-643$ |
| 2601.1-f1 |
2601.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2601.1 |
\( 3^{2} \cdot 17^{2} \) |
\( 3^{4} \cdot 17^{2} \) |
$1.42695$ |
$(3), (17)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.229582294$ |
$20.74488657$ |
2.129925700 |
\( \frac{126503}{153} a + \frac{3125234}{153} \) |
\( \bigl[\phi + 1\) , \( -1\) , \( \phi\) , \( -2 \phi - 3\) , \( \phi\bigr] \) |
${y}^2+\left(\phi+1\right){x}{y}+\phi{y}={x}^{3}-{x}^{2}+\left(-2\phi-3\right){x}+\phi$ |
| 2601.1-f2 |
2601.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2601.1 |
\( 3^{2} \cdot 17^{2} \) |
\( - 3^{2} \cdot 17^{4} \) |
$1.42695$ |
$(3), (17)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.459164588$ |
$10.37244328$ |
2.129925700 |
\( \frac{171166398845}{867} a + \frac{35262225577}{289} \) |
\( \bigl[\phi\) , \( \phi + 1\) , \( 0\) , \( -7 \phi + 5\) , \( 38 \phi - 59\bigr] \) |
${y}^2+\phi{x}{y}={x}^{3}+\left(\phi+1\right){x}^{2}+\left(-7\phi+5\right){x}+38\phi-59$ |
| 2601.1-g1 |
2601.1-g |
$2$ |
$2$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2601.1 |
\( 3^{2} \cdot 17^{2} \) |
\( 3^{16} \cdot 17^{4} \) |
$1.42695$ |
$(3), (17)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.857315986$ |
$2.796524062$ |
2.144393471 |
\( -\frac{796857355}{632043} a - \frac{1612314913}{1896129} \) |
\( \bigl[1\) , \( -\phi - 1\) , \( \phi + 1\) , \( -5 \phi - 18\) , \( 87 \phi - 55\bigr] \) |
${y}^2+{x}{y}+\left(\phi+1\right){y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(-5\phi-18\right){x}+87\phi-55$ |
| 2601.1-g2 |
2601.1-g |
$2$ |
$2$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2601.1 |
\( 3^{2} \cdot 17^{2} \) |
\( 3^{8} \cdot 17^{2} \) |
$1.42695$ |
$(3), (17)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.428657993$ |
$11.18609625$ |
2.144393471 |
\( \frac{7741898803}{1377} a + \frac{5131974418}{1377} \) |
\( \bigl[1\) , \( -\phi - 1\) , \( \phi + 1\) , \( -28\) , \( 60 \phi - 18\bigr] \) |
${y}^2+{x}{y}+\left(\phi+1\right){y}={x}^{3}+\left(-\phi-1\right){x}^{2}-28{x}+60\phi-18$ |
| 2601.1-h1 |
2601.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2601.1 |
\( 3^{2} \cdot 17^{2} \) |
\( - 3^{2} \cdot 17^{4} \) |
$1.42695$ |
$(3), (17)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.459164588$ |
$10.37244328$ |
2.129925700 |
\( -\frac{171166398845}{867} a + \frac{276953075576}{867} \) |
\( \bigl[\phi + 1\) , \( \phi - 1\) , \( \phi\) , \( 8 \phi - 4\) , \( -42 \phi - 9\bigr] \) |
${y}^2+\left(\phi+1\right){x}{y}+\phi{y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(8\phi-4\right){x}-42\phi-9$ |
| 2601.1-h2 |
2601.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2601.1 |
\( 3^{2} \cdot 17^{2} \) |
\( 3^{4} \cdot 17^{2} \) |
$1.42695$ |
$(3), (17)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.229582294$ |
$20.74488657$ |
2.129925700 |
\( -\frac{126503}{153} a + \frac{3251737}{153} \) |
\( \bigl[\phi\) , \( -\phi\) , \( \phi + 1\) , \( -4\) , \( -2 \phi + 1\bigr] \) |
${y}^2+\phi{x}{y}+\left(\phi+1\right){y}={x}^{3}-\phi{x}^{2}-4{x}-2\phi+1$ |
| 2601.1-i1 |
2601.1-i |
$2$ |
$2$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2601.1 |
\( 3^{2} \cdot 17^{2} \) |
\( 3^{16} \cdot 17^{4} \) |
$1.42695$ |
$(3), (17)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.857315986$ |
$2.796524062$ |
2.144393471 |
\( \frac{796857355}{632043} a - \frac{4002886978}{1896129} \) |
\( \bigl[1\) , \( \phi + 1\) , \( \phi + 1\) , \( 6 \phi - 23\) , \( -83 \phi + 10\bigr] \) |
${y}^2+{x}{y}+\left(\phi+1\right){y}={x}^{3}+\left(\phi+1\right){x}^{2}+\left(6\phi-23\right){x}-83\phi+10$ |
| 2601.1-i2 |
2601.1-i |
$2$ |
$2$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2601.1 |
\( 3^{2} \cdot 17^{2} \) |
\( 3^{8} \cdot 17^{2} \) |
$1.42695$ |
$(3), (17)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.428657993$ |
$11.18609625$ |
2.144393471 |
\( -\frac{7741898803}{1377} a + \frac{12873873221}{1377} \) |
\( \bigl[1\) , \( \phi + 1\) , \( \phi + 1\) , \( \phi - 28\) , \( -61 \phi + 15\bigr] \) |
${y}^2+{x}{y}+\left(\phi+1\right){y}={x}^{3}+\left(\phi+1\right){x}^{2}+\left(\phi-28\right){x}-61\phi+15$ |
| 2601.1-j1 |
2601.1-j |
$2$ |
$2$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2601.1 |
\( 3^{2} \cdot 17^{2} \) |
\( 3^{10} \cdot 17^{4} \) |
$1.42695$ |
$(3), (17)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$7.747229763$ |
1.732333238 |
\( -\frac{24389}{70227} \) |
\( \bigl[\phi + 1\) , \( -\phi - 1\) , \( 1\) , \( -\phi - 1\) , \( 23 \phi + 17\bigr] \) |
${y}^2+\left(\phi+1\right){x}{y}+{y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(-\phi-1\right){x}+23\phi+17$ |
| 2601.1-j2 |
2601.1-j |
$2$ |
$2$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2601.1 |
\( 3^{2} \cdot 17^{2} \) |
\( 3^{20} \cdot 17^{2} \) |
$1.42695$ |
$(3), (17)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$7.747229763$ |
1.732333238 |
\( \frac{69375867029}{1003833} \) |
\( \bigl[\phi + 1\) , \( -\phi - 1\) , \( 1\) , \( -86 \phi - 86\) , \( 567 \phi + 425\bigr] \) |
${y}^2+\left(\phi+1\right){x}{y}+{y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(-86\phi-86\right){x}+567\phi+425$ |
*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.
