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 |
6.1-a1 |
6.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{58}) \) |
$2$ |
$[2, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{9} \cdot 3^{13} \) |
$2.13020$ |
$(2,a), (3,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$11.14443713$ |
$1.068209178$ |
1.563149251 |
\( -\frac{143450747135}{96} a - \frac{136563262831}{12} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -319 a - 2325\) , \( -9530 a - 72446\bigr] \) |
${y}^2+\left(w+1\right){x}{y}+{y}={x}^3-w{x}^2+\left(-319w-2325\right){x}-9530w-72446$ |
6.1-a2 |
6.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{58}) \) |
$2$ |
$[2, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{3} \cdot 3^{15} \) |
$2.13020$ |
$(2,a), (3,a+2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$3.714812378$ |
$9.613882602$ |
1.563149251 |
\( -\frac{19891}{108} a - \frac{20362}{27} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -9 a + 50\) , \( -39 a - 58\bigr] \) |
${y}^2+\left(w+1\right){x}{y}+{y}={x}^3-w{x}^2+\left(-9w+50\right){x}-39w-58$ |
6.1-b1 |
6.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{58}) \) |
$2$ |
$[2, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{9} \cdot 3 \) |
$2.13020$ |
$(2,a), (3,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3^{2} \) |
$4.127195577$ |
$1.068209178$ |
5.210025720 |
\( -\frac{143450747135}{96} a - \frac{136563262831}{12} \) |
\( \bigl[a + 1\) , \( a\) , \( a\) , \( 179 a - 1168\) , \( 3418 a - 25384\bigr] \) |
${y}^2+\left(w+1\right){x}{y}+w{y}={x}^3+w{x}^2+\left(179w-1168\right){x}+3418w-25384$ |
6.1-b2 |
6.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{58}) \) |
$2$ |
$[2, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{3} \cdot 3^{3} \) |
$2.13020$ |
$(2,a), (3,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \) |
$1.375731859$ |
$9.613882602$ |
5.210025720 |
\( -\frac{19891}{108} a - \frac{20362}{27} \) |
\( \bigl[a + 1\) , \( a\) , \( a\) , \( 9 a + 127\) , \( 61 a + 185\bigr] \) |
${y}^2+\left(w+1\right){x}{y}+w{y}={x}^3+w{x}^2+\left(9w+127\right){x}+61w+185$ |
6.2-a1 |
6.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{58}) \) |
$2$ |
$[2, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( 2^{9} \cdot 3^{13} \) |
$2.13020$ |
$(2,a), (3,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$11.14443713$ |
$1.068209178$ |
1.563149251 |
\( \frac{143450747135}{96} a - \frac{136563262831}{12} \) |
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 318 a - 2325\) , \( 9530 a - 72446\bigr] \) |
${y}^2+\left(w+1\right){x}{y}+{y}={x}^3+\left(318w-2325\right){x}+9530w-72446$ |
6.2-a2 |
6.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{58}) \) |
$2$ |
$[2, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( 2^{3} \cdot 3^{15} \) |
$2.13020$ |
$(2,a), (3,a+1)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$3.714812378$ |
$9.613882602$ |
1.563149251 |
\( \frac{19891}{108} a - \frac{20362}{27} \) |
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 8 a + 50\) , \( 39 a - 58\bigr] \) |
${y}^2+\left(w+1\right){x}{y}+{y}={x}^3+\left(8w+50\right){x}+39w-58$ |
6.2-b1 |
6.2-b |
$2$ |
$3$ |
\(\Q(\sqrt{58}) \) |
$2$ |
$[2, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( 2^{9} \cdot 3 \) |
$2.13020$ |
$(2,a), (3,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3^{2} \) |
$4.127195577$ |
$1.068209178$ |
5.210025720 |
\( \frac{143450747135}{96} a - \frac{136563262831}{12} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -150 a - 1139\) , \( -4586 a - 34925\bigr] \) |
${y}^2+\left(w+1\right){x}{y}={x}^3+w{x}^2+\left(-150w-1139\right){x}-4586w-34925$ |
6.2-b2 |
6.2-b |
$2$ |
$3$ |
\(\Q(\sqrt{58}) \) |
$2$ |
$[2, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( 2^{3} \cdot 3^{3} \) |
$2.13020$ |
$(2,a), (3,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \) |
$1.375731859$ |
$9.613882602$ |
5.210025720 |
\( \frac{19891}{108} a - \frac{20362}{27} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 20 a + 156\) , \( 66 a + 504\bigr] \) |
${y}^2+\left(w+1\right){x}{y}={x}^3+w{x}^2+\left(20w+156\right){x}+66w+504$ |
9.2-a1 |
9.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{58}) \) |
$2$ |
$[2, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{18} \) |
$2.35745$ |
$(3,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3$ |
3B |
$1$ |
\( 1 \) |
$0.871525355$ |
$25.18165950$ |
2.881710687 |
\( -2304 a - 16064 \) |
\( \bigl[a\) , \( -1\) , \( 1\) , \( -2 a + 57\) , \( -5 a + 84\bigr] \) |
${y}^2+w{x}{y}+{y}={x}^3-{x}^2+\left(-2w+57\right){x}-5w+84$ |
9.2-a2 |
9.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{58}) \) |
$2$ |
$[2, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{6} \) |
$2.35745$ |
$(3,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3$ |
3B |
$1$ |
\( 1 \) |
$2.614576066$ |
$8.393886503$ |
2.881710687 |
\( 2304 a - 16064 \) |
\( \bigl[a\) , \( -a\) , \( a + 1\) , \( -10 a + 60\) , \( -25 a + 186\bigr] \) |
${y}^2+w{x}{y}+\left(w+1\right){y}={x}^3-w{x}^2+\left(-10w+60\right){x}-25w+186$ |
9.2-b1 |
9.2-b |
$2$ |
$3$ |
\(\Q(\sqrt{58}) \) |
$2$ |
$[2, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{6} \) |
$2.35745$ |
$(3,a+2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$10.59927041$ |
$25.18165950$ |
3.894070531 |
\( -2304 a - 16064 \) |
\( \bigl[a\) , \( a + 1\) , \( 1\) , \( -173 a - 1293\) , \( 2428 a + 18509\bigr] \) |
${y}^2+w{x}{y}+{y}={x}^3+\left(w+1\right){x}^2+\left(-173w-1293\right){x}+2428w+18509$ |
9.2-b2 |
9.2-b |
$2$ |
$3$ |
\(\Q(\sqrt{58}) \) |
$2$ |
$[2, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{18} \) |
$2.35745$ |
$(3,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$3.533090138$ |
$8.393886503$ |
3.894070531 |
\( 2304 a - 16064 \) |
\( \bigl[a\) , \( a + 1\) , \( 1\) , \( 842 a + 6437\) , \( 21107 a + 160764\bigr] \) |
${y}^2+w{x}{y}+{y}={x}^3+\left(w+1\right){x}^2+\left(842w+6437\right){x}+21107w+160764$ |
9.3-a1 |
9.3-a |
$2$ |
$3$ |
\(\Q(\sqrt{58}) \) |
$2$ |
$[2, 0]$ |
9.3 |
\( 3^{2} \) |
\( 3^{6} \) |
$2.35745$ |
$(3,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3$ |
3B |
$1$ |
\( 1 \) |
$2.614576066$ |
$8.393886503$ |
2.881710687 |
\( -2304 a - 16064 \) |
\( \bigl[a\) , \( a\) , \( a + 1\) , \( 9 a + 60\) , \( 24 a + 186\bigr] \) |
${y}^2+w{x}{y}+\left(w+1\right){y}={x}^3+w{x}^2+\left(9w+60\right){x}+24w+186$ |
9.3-a2 |
9.3-a |
$2$ |
$3$ |
\(\Q(\sqrt{58}) \) |
$2$ |
$[2, 0]$ |
9.3 |
\( 3^{2} \) |
\( 3^{18} \) |
$2.35745$ |
$(3,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3$ |
3B |
$1$ |
\( 1 \) |
$0.871525355$ |
$25.18165950$ |
2.881710687 |
\( 2304 a - 16064 \) |
\( \bigl[a\) , \( -1\) , \( 1\) , \( a + 57\) , \( 5 a + 84\bigr] \) |
${y}^2+w{x}{y}+{y}={x}^3-{x}^2+\left(w+57\right){x}+5w+84$ |
9.3-b1 |
9.3-b |
$2$ |
$3$ |
\(\Q(\sqrt{58}) \) |
$2$ |
$[2, 0]$ |
9.3 |
\( 3^{2} \) |
\( 3^{18} \) |
$2.35745$ |
$(3,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$3.533090138$ |
$8.393886503$ |
3.894070531 |
\( -2304 a - 16064 \) |
\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -843 a + 6437\) , \( -21107 a + 160764\bigr] \) |
${y}^2+w{x}{y}+{y}={x}^3+\left(-w+1\right){x}^2+\left(-843w+6437\right){x}-21107w+160764$ |
9.3-b2 |
9.3-b |
$2$ |
$3$ |
\(\Q(\sqrt{58}) \) |
$2$ |
$[2, 0]$ |
9.3 |
\( 3^{2} \) |
\( 3^{6} \) |
$2.35745$ |
$(3,a+1)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$10.59927041$ |
$25.18165950$ |
3.894070531 |
\( 2304 a - 16064 \) |
\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( 172 a - 1293\) , \( -2428 a + 18509\bigr] \) |
${y}^2+w{x}{y}+{y}={x}^3+\left(-w+1\right){x}^2+\left(172w-1293\right){x}-2428w+18509$ |
18.1-a1 |
18.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{58}) \) |
$2$ |
$[2, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2^{5} \cdot 3^{9} \) |
$2.80350$ |
$(2,a), (3,a+1), (3,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \cdot 5 \cdot 7 \) |
$0.075167323$ |
$11.80483819$ |
8.155924008 |
\( -\frac{14917528805}{17496} a - \frac{28401838139}{4374} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -2 a - 14\) , \( 4 a + 28\bigr] \) |
${y}^2+{x}{y}={x}^3+\left(-2w-14\right){x}+4w+28$ |
18.1-b1 |
18.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{58}) \) |
$2$ |
$[2, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2^{5} \cdot 3^{21} \) |
$2.80350$ |
$(2,a), (3,a+1), (3,a+2)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.488834762$ |
$11.80483819$ |
3.030875629 |
\( -\frac{14917528805}{17496} a - \frac{28401838139}{4374} \) |
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -28551 a - 217414\) , \( 7317221 a + 55726302\bigr] \) |
${y}^2+{x}{y}+\left(w+1\right){y}={x}^3-w{x}^2+\left(-28551w-217414\right){x}+7317221w+55726302$ |
18.1-c1 |
18.1-c |
$1$ |
$1$ |
\(\Q(\sqrt{58}) \) |
$2$ |
$[2, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2^{5} \cdot 3^{9} \) |
$2.80350$ |
$(2,a), (3,a+1), (3,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \cdot 5 \cdot 7 \) |
$0.075167323$ |
$11.80483819$ |
8.155924008 |
\( \frac{14917528805}{17496} a - \frac{28401838139}{4374} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( 2 a - 14\) , \( -4 a + 28\bigr] \) |
${y}^2+{x}{y}={x}^3+\left(2w-14\right){x}-4w+28$ |
18.1-d1 |
18.1-d |
$1$ |
$1$ |
\(\Q(\sqrt{58}) \) |
$2$ |
$[2, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2^{5} \cdot 3^{21} \) |
$2.80350$ |
$(2,a), (3,a+1), (3,a+2)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.488834762$ |
$11.80483819$ |
3.030875629 |
\( \frac{14917528805}{17496} a - \frac{28401838139}{4374} \) |
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( 1181 a + 9018\) , \( -308087 a - 2346314\bigr] \) |
${y}^2+{x}{y}+\left(w+1\right){y}={x}^3-w{x}^2+\left(1181w+9018\right){x}-308087w-2346314$ |
18.2-a1 |
18.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{58}) \) |
$2$ |
$[2, 0]$ |
18.2 |
\( 2 \cdot 3^{2} \) |
\( 2 \cdot 3^{21} \) |
$2.80350$ |
$(2,a), (3,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$0.356815455$ |
$28.69564216$ |
2.688905903 |
\( \frac{14977819}{54} a - \frac{57073330}{27} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( -7 a - 56\) , \( 31 a + 286\bigr] \) |
${y}^2+{x}{y}={x}^3+\left(w+1\right){x}^2+\left(-7w-56\right){x}+31w+286$ |
18.2-b1 |
18.2-b |
$2$ |
$5$ |
\(\Q(\sqrt{58}) \) |
$2$ |
$[2, 0]$ |
18.2 |
\( 2 \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{6} \) |
$2.80350$ |
$(2,a), (3,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B |
$1$ |
\( 2 \) |
$1.759933877$ |
$7.987152497$ |
3.691512356 |
\( -\frac{1030301}{16} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( -57 a - 443\) , \( -1332 a - 10142\bigr] \) |
${y}^2+w{x}{y}+w{y}={x}^3+\left(w+1\right){x}^2+\left(-57w-443\right){x}-1332w-10142$ |
18.2-b2 |
18.2-b |
$2$ |
$5$ |
\(\Q(\sqrt{58}) \) |
$2$ |
$[2, 0]$ |
18.2 |
\( 2 \cdot 3^{2} \) |
\( 2^{52} \cdot 3^{6} \) |
$2.80350$ |
$(2,a), (3,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B |
$1$ |
\( 2 \) |
$8.799669385$ |
$1.597430499$ |
3.691512356 |
\( \frac{237176659}{1048576} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( 423 a + 3217\) , \( 35688 a + 271798\bigr] \) |
${y}^2+w{x}{y}+w{y}={x}^3+\left(w+1\right){x}^2+\left(423w+3217\right){x}+35688w+271798$ |
18.2-c1 |
18.2-c |
$4$ |
$15$ |
\(\Q(\sqrt{58}) \) |
$2$ |
$[2, 0]$ |
18.2 |
\( 2 \cdot 3^{2} \) |
\( - 2 \cdot 3^{19} \) |
$2.80350$ |
$(2,a), (3,a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 5$ |
3B, 5B |
$1$ |
\( 2 \) |
$1$ |
$28.66559015$ |
3.763976388 |
\( \frac{659809975}{6} a - \frac{2512474129}{3} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( 108 a - 810\) , \( -1415 a + 10778\bigr] \) |
${y}^2+{x}{y}={x}^3-w{x}^2+\left(108w-810\right){x}-1415w+10778$ |
18.2-c2 |
18.2-c |
$4$ |
$15$ |
\(\Q(\sqrt{58}) \) |
$2$ |
$[2, 0]$ |
18.2 |
\( 2 \cdot 3^{2} \) |
\( - 2^{15} \cdot 3^{21} \) |
$2.80350$ |
$(2,a), (3,a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 5$ |
3B, 5B |
$1$ |
\( 2 \cdot 3 \cdot 5 \) |
$1$ |
$1.911039343$ |
3.763976388 |
\( \frac{52587136443509}{3673320192} a + \frac{199350876909259}{1836660096} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -1381 a - 10507\) , \( 68995 a + 525473\bigr] \) |
${y}^2+\left(w+1\right){x}{y}+\left(w+1\right){y}={x}^3-{x}^2+\left(-1381w-10507\right){x}+68995w+525473$ |
18.2-c3 |
18.2-c |
$4$ |
$15$ |
\(\Q(\sqrt{58}) \) |
$2$ |
$[2, 0]$ |
18.2 |
\( 2 \cdot 3^{2} \) |
\( - 2^{3} \cdot 3^{9} \) |
$2.80350$ |
$(2,a), (3,a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 5$ |
3B, 5B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$9.555196717$ |
3.763976388 |
\( \frac{67270949}{108} a + \frac{256128031}{54} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -91 a - 682\) , \( -1925 a - 14635\bigr] \) |
${y}^2+\left(w+1\right){x}{y}+\left(w+1\right){y}={x}^3-{x}^2+\left(-91w-682\right){x}-1925w-14635$ |
18.2-c4 |
18.2-c |
$4$ |
$15$ |
\(\Q(\sqrt{58}) \) |
$2$ |
$[2, 0]$ |
18.2 |
\( 2 \cdot 3^{2} \) |
\( - 2^{5} \cdot 3^{23} \) |
$2.80350$ |
$(2,a), (3,a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 5$ |
3B, 5B |
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$5.733118030$ |
3.763976388 |
\( \frac{1300957717863869095}{1944} a + \frac{4953899399787263939}{972} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( -417 a + 165\) , \( -4610 a + 106691\bigr] \) |
${y}^2+{x}{y}={x}^3-w{x}^2+\left(-417w+165\right){x}-4610w+106691$ |
18.2-d1 |
18.2-d |
$1$ |
$1$ |
\(\Q(\sqrt{58}) \) |
$2$ |
$[2, 0]$ |
18.2 |
\( 2 \cdot 3^{2} \) |
\( - 2 \cdot 3^{3} \) |
$2.80350$ |
$(2,a), (3,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$0.405148425$ |
$30.70729030$ |
3.267169368 |
\( \frac{1043}{2} a + 5525 \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( -67 a - 474\) , \( 409 a + 3151\bigr] \) |
${y}^2+\left(w+1\right){x}{y}+{y}={x}^3-{x}^2+\left(-67w-474\right){x}+409w+3151$ |
18.2-e1 |
18.2-e |
$4$ |
$15$ |
\(\Q(\sqrt{58}) \) |
$2$ |
$[2, 0]$ |
18.2 |
\( 2 \cdot 3^{2} \) |
\( - 2 \cdot 3^{7} \) |
$2.80350$ |
$(2,a), (3,a+2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 5$ |
3B.1.1, 5B |
$1$ |
\( 2^{2} \) |
$2.575793123$ |
$28.66559015$ |
4.308988665 |
\( \frac{659809975}{6} a - \frac{2512474129}{3} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( 19920 a - 151680\) , \( -4265323 a + 32483758\bigr] \) |
${y}^2+{x}{y}={x}^3+\left(w+1\right){x}^2+\left(19920w-151680\right){x}-4265323w+32483758$ |
18.2-e2 |
18.2-e |
$4$ |
$15$ |
\(\Q(\sqrt{58}) \) |
$2$ |
$[2, 0]$ |
18.2 |
\( 2 \cdot 3^{2} \) |
\( - 2^{15} \cdot 3^{33} \) |
$2.80350$ |
$(2,a), (3,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 5$ |
3B.1.2, 5B |
$1$ |
\( 2^{2} \) |
$4.292988538$ |
$1.911039343$ |
4.308988665 |
\( \frac{52587136443509}{3673320192} a + \frac{199350876909259}{1836660096} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( 374815 a - 2854480\) , \( 734172264 a - 5591289358\bigr] \) |
${y}^2+{x}{y}={x}^3+\left(w+1\right){x}^2+\left(374815w-2854480\right){x}+734172264w-5591289358$ |
18.2-e3 |
18.2-e |
$4$ |
$15$ |
\(\Q(\sqrt{58}) \) |
$2$ |
$[2, 0]$ |
18.2 |
\( 2 \cdot 3^{2} \) |
\( - 2^{3} \cdot 3^{21} \) |
$2.80350$ |
$(2,a), (3,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 5$ |
3B.1.2, 5B |
$1$ |
\( 2^{2} \) |
$0.858597707$ |
$9.555196717$ |
4.308988665 |
\( \frac{67270949}{108} a + \frac{256128031}{54} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( 15925 a - 121255\) , \( -5999556 a + 45691283\bigr] \) |
${y}^2+{x}{y}={x}^3+\left(w+1\right){x}^2+\left(15925w-121255\right){x}-5999556w+45691283$ |
18.2-e4 |
18.2-e |
$4$ |
$15$ |
\(\Q(\sqrt{58}) \) |
$2$ |
$[2, 0]$ |
18.2 |
\( 2 \cdot 3^{2} \) |
\( - 2^{5} \cdot 3^{11} \) |
$2.80350$ |
$(2,a), (3,a+2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 5$ |
3B.1.1, 5B |
$1$ |
\( 2^{2} \) |
$12.87896561$ |
$5.733118030$ |
4.308988665 |
\( \frac{1300957717863869095}{1944} a + \frac{4953899399787263939}{972} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( -40005 a + 304695\) , \( -21638158 a + 164791327\bigr] \) |
${y}^2+{x}{y}={x}^3+\left(w+1\right){x}^2+\left(-40005w+304695\right){x}-21638158w+164791327$ |
18.2-f1 |
18.2-f |
$2$ |
$5$ |
\(\Q(\sqrt{58}) \) |
$2$ |
$[2, 0]$ |
18.2 |
\( 2 \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{6} \) |
$2.80350$ |
$(2,a), (3,a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B |
$1$ |
\( 2^{3} \) |
$1$ |
$7.987152497$ |
4.195058012 |
\( -\frac{1030301}{16} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( -17 a - 109\) , \( -66 a - 485\bigr] \) |
${y}^2+{x}{y}={x}^3-w{x}^2+\left(-17w-109\right){x}-66w-485$ |
18.2-f2 |
18.2-f |
$2$ |
$5$ |
\(\Q(\sqrt{58}) \) |
$2$ |
$[2, 0]$ |
18.2 |
\( 2 \cdot 3^{2} \) |
\( 2^{40} \cdot 3^{6} \) |
$2.80350$ |
$(2,a), (3,a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B |
$1$ |
\( 2^{3} \cdot 5 \) |
$1$ |
$1.597430499$ |
4.195058012 |
\( \frac{237176659}{1048576} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( 103 a + 806\) , \( 3804 a + 28990\bigr] \) |
${y}^2+{x}{y}={x}^3-w{x}^2+\left(103w+806\right){x}+3804w+28990$ |
18.2-g1 |
18.2-g |
$1$ |
$1$ |
\(\Q(\sqrt{58}) \) |
$2$ |
$[2, 0]$ |
18.2 |
\( 2 \cdot 3^{2} \) |
\( 2 \cdot 3^{9} \) |
$2.80350$ |
$(2,a), (3,a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$28.69564216$ |
7.535844822 |
\( \frac{14977819}{54} a - \frac{57073330}{27} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( 195 a - 1467\) , \( -3587 a + 27303\bigr] \) |
${y}^2+{x}{y}={x}^3-w{x}^2+\left(195w-1467\right){x}-3587w+27303$ |
18.2-h1 |
18.2-h |
$1$ |
$1$ |
\(\Q(\sqrt{58}) \) |
$2$ |
$[2, 0]$ |
18.2 |
\( 2 \cdot 3^{2} \) |
\( - 2 \cdot 3^{15} \) |
$2.80350$ |
$(2,a), (3,a+2)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$0.277854524$ |
$30.70729030$ |
4.481309736 |
\( \frac{1043}{2} a + 5525 \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( -204 a + 1576\) , \( 1907 a - 14512\bigr] \) |
${y}^2+{x}{y}+w{y}={x}^3+\left(w+1\right){x}^2+\left(-204w+1576\right){x}+1907w-14512$ |
18.3-a1 |
18.3-a |
$1$ |
$1$ |
\(\Q(\sqrt{58}) \) |
$2$ |
$[2, 0]$ |
18.3 |
\( 2 \cdot 3^{2} \) |
\( 2 \cdot 3^{21} \) |
$2.80350$ |
$(2,a), (3,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$0.356815455$ |
$28.69564216$ |
2.688905903 |
\( -\frac{14977819}{54} a - \frac{57073330}{27} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( 7 a - 56\) , \( -31 a + 286\bigr] \) |
${y}^2+{x}{y}={x}^3+\left(-w+1\right){x}^2+\left(7w-56\right){x}-31w+286$ |
18.3-b1 |
18.3-b |
$2$ |
$5$ |
\(\Q(\sqrt{58}) \) |
$2$ |
$[2, 0]$ |
18.3 |
\( 2 \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{6} \) |
$2.80350$ |
$(2,a), (3,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B |
$1$ |
\( 2 \) |
$1.759933877$ |
$7.987152497$ |
3.691512356 |
\( -\frac{1030301}{16} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 57 a - 443\) , \( 1332 a - 10142\bigr] \) |
${y}^2+w{x}{y}+w{y}={x}^3+\left(-w+1\right){x}^2+\left(57w-443\right){x}+1332w-10142$ |
18.3-b2 |
18.3-b |
$2$ |
$5$ |
\(\Q(\sqrt{58}) \) |
$2$ |
$[2, 0]$ |
18.3 |
\( 2 \cdot 3^{2} \) |
\( 2^{52} \cdot 3^{6} \) |
$2.80350$ |
$(2,a), (3,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B |
$1$ |
\( 2 \) |
$8.799669385$ |
$1.597430499$ |
3.691512356 |
\( \frac{237176659}{1048576} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -423 a + 3217\) , \( -35688 a + 271798\bigr] \) |
${y}^2+w{x}{y}+w{y}={x}^3+\left(-w+1\right){x}^2+\left(-423w+3217\right){x}-35688w+271798$ |
18.3-c1 |
18.3-c |
$4$ |
$15$ |
\(\Q(\sqrt{58}) \) |
$2$ |
$[2, 0]$ |
18.3 |
\( 2 \cdot 3^{2} \) |
\( - 2 \cdot 3^{19} \) |
$2.80350$ |
$(2,a), (3,a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 5$ |
3B, 5B |
$1$ |
\( 2 \) |
$1$ |
$28.66559015$ |
3.763976388 |
\( -\frac{659809975}{6} a - \frac{2512474129}{3} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( -108 a - 810\) , \( 1415 a + 10778\bigr] \) |
${y}^2+{x}{y}={x}^3+w{x}^2+\left(-108w-810\right){x}+1415w+10778$ |
18.3-c2 |
18.3-c |
$4$ |
$15$ |
\(\Q(\sqrt{58}) \) |
$2$ |
$[2, 0]$ |
18.3 |
\( 2 \cdot 3^{2} \) |
\( - 2^{3} \cdot 3^{9} \) |
$2.80350$ |
$(2,a), (3,a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 5$ |
3B, 5B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$9.555196717$ |
3.763976388 |
\( -\frac{67270949}{108} a + \frac{256128031}{54} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 89 a - 682\) , \( 1924 a - 14635\bigr] \) |
${y}^2+\left(w+1\right){x}{y}+\left(w+1\right){y}={x}^3+\left(-w-1\right){x}^2+\left(89w-682\right){x}+1924w-14635$ |
18.3-c3 |
18.3-c |
$4$ |
$15$ |
\(\Q(\sqrt{58}) \) |
$2$ |
$[2, 0]$ |
18.3 |
\( 2 \cdot 3^{2} \) |
\( - 2^{15} \cdot 3^{21} \) |
$2.80350$ |
$(2,a), (3,a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 5$ |
3B, 5B |
$1$ |
\( 2 \cdot 3 \cdot 5 \) |
$1$ |
$1.911039343$ |
3.763976388 |
\( -\frac{52587136443509}{3673320192} a + \frac{199350876909259}{1836660096} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 1379 a - 10507\) , \( -68996 a + 525473\bigr] \) |
${y}^2+\left(w+1\right){x}{y}+\left(w+1\right){y}={x}^3+\left(-w-1\right){x}^2+\left(1379w-10507\right){x}-68996w+525473$ |
18.3-c4 |
18.3-c |
$4$ |
$15$ |
\(\Q(\sqrt{58}) \) |
$2$ |
$[2, 0]$ |
18.3 |
\( 2 \cdot 3^{2} \) |
\( - 2^{5} \cdot 3^{23} \) |
$2.80350$ |
$(2,a), (3,a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 5$ |
3B, 5B |
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$5.733118030$ |
3.763976388 |
\( -\frac{1300957717863869095}{1944} a + \frac{4953899399787263939}{972} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( 417 a + 165\) , \( 4610 a + 106691\bigr] \) |
${y}^2+{x}{y}={x}^3+w{x}^2+\left(417w+165\right){x}+4610w+106691$ |
18.3-d1 |
18.3-d |
$1$ |
$1$ |
\(\Q(\sqrt{58}) \) |
$2$ |
$[2, 0]$ |
18.3 |
\( 2 \cdot 3^{2} \) |
\( - 2 \cdot 3^{3} \) |
$2.80350$ |
$(2,a), (3,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$0.405148425$ |
$30.70729030$ |
3.267169368 |
\( -\frac{1043}{2} a + 5525 \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( 66 a - 474\) , \( -409 a + 3151\bigr] \) |
${y}^2+\left(w+1\right){x}{y}+{y}={x}^3+\left(-w-1\right){x}^2+\left(66w-474\right){x}-409w+3151$ |
18.3-e1 |
18.3-e |
$4$ |
$15$ |
\(\Q(\sqrt{58}) \) |
$2$ |
$[2, 0]$ |
18.3 |
\( 2 \cdot 3^{2} \) |
\( - 2 \cdot 3^{7} \) |
$2.80350$ |
$(2,a), (3,a+1)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 5$ |
3B.1.1, 5B |
$1$ |
\( 2^{2} \) |
$2.575793123$ |
$28.66559015$ |
4.308988665 |
\( -\frac{659809975}{6} a - \frac{2512474129}{3} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -19920 a - 151680\) , \( 4265323 a + 32483758\bigr] \) |
${y}^2+{x}{y}={x}^3+\left(-w+1\right){x}^2+\left(-19920w-151680\right){x}+4265323w+32483758$ |
18.3-e2 |
18.3-e |
$4$ |
$15$ |
\(\Q(\sqrt{58}) \) |
$2$ |
$[2, 0]$ |
18.3 |
\( 2 \cdot 3^{2} \) |
\( - 2^{3} \cdot 3^{21} \) |
$2.80350$ |
$(2,a), (3,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 5$ |
3B.1.2, 5B |
$1$ |
\( 2^{2} \) |
$0.858597707$ |
$9.555196717$ |
4.308988665 |
\( -\frac{67270949}{108} a + \frac{256128031}{54} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -15925 a - 121255\) , \( 5999556 a + 45691283\bigr] \) |
${y}^2+{x}{y}={x}^3+\left(-w+1\right){x}^2+\left(-15925w-121255\right){x}+5999556w+45691283$ |
18.3-e3 |
18.3-e |
$4$ |
$15$ |
\(\Q(\sqrt{58}) \) |
$2$ |
$[2, 0]$ |
18.3 |
\( 2 \cdot 3^{2} \) |
\( - 2^{15} \cdot 3^{33} \) |
$2.80350$ |
$(2,a), (3,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 5$ |
3B.1.2, 5B |
$1$ |
\( 2^{2} \) |
$4.292988538$ |
$1.911039343$ |
4.308988665 |
\( -\frac{52587136443509}{3673320192} a + \frac{199350876909259}{1836660096} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -374815 a - 2854480\) , \( -734172264 a - 5591289358\bigr] \) |
${y}^2+{x}{y}={x}^3+\left(-w+1\right){x}^2+\left(-374815w-2854480\right){x}-734172264w-5591289358$ |
18.3-e4 |
18.3-e |
$4$ |
$15$ |
\(\Q(\sqrt{58}) \) |
$2$ |
$[2, 0]$ |
18.3 |
\( 2 \cdot 3^{2} \) |
\( - 2^{5} \cdot 3^{11} \) |
$2.80350$ |
$(2,a), (3,a+1)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 5$ |
3B.1.1, 5B |
$1$ |
\( 2^{2} \) |
$12.87896561$ |
$5.733118030$ |
4.308988665 |
\( -\frac{1300957717863869095}{1944} a + \frac{4953899399787263939}{972} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( 40005 a + 304695\) , \( 21638158 a + 164791327\bigr] \) |
${y}^2+{x}{y}={x}^3+\left(-w+1\right){x}^2+\left(40005w+304695\right){x}+21638158w+164791327$ |
18.3-f1 |
18.3-f |
$2$ |
$5$ |
\(\Q(\sqrt{58}) \) |
$2$ |
$[2, 0]$ |
18.3 |
\( 2 \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{6} \) |
$2.80350$ |
$(2,a), (3,a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B |
$1$ |
\( 2^{3} \) |
$1$ |
$7.987152497$ |
4.195058012 |
\( -\frac{1030301}{16} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( 17 a - 109\) , \( 66 a - 485\bigr] \) |
${y}^2+{x}{y}={x}^3+w{x}^2+\left(17w-109\right){x}+66w-485$ |
18.3-f2 |
18.3-f |
$2$ |
$5$ |
\(\Q(\sqrt{58}) \) |
$2$ |
$[2, 0]$ |
18.3 |
\( 2 \cdot 3^{2} \) |
\( 2^{40} \cdot 3^{6} \) |
$2.80350$ |
$(2,a), (3,a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B |
$1$ |
\( 2^{3} \cdot 5 \) |
$1$ |
$1.597430499$ |
4.195058012 |
\( \frac{237176659}{1048576} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( -103 a + 806\) , \( -3804 a + 28990\bigr] \) |
${y}^2+{x}{y}={x}^3+w{x}^2+\left(-103w+806\right){x}-3804w+28990$ |
*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.