| 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 |
| 28672.5-a1 |
28672.5-a |
$4$ |
$10$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.5 |
\( 2^{12} \cdot 7 \) |
\( 2^{29} \cdot 7^{2} \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \) |
$0.998327441$ |
$1.394083610$ |
4.208262259 |
\( \frac{1143001}{28} a - \frac{2178651}{14} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -12 a - 52\) , \( 76 a + 128\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-12a-52\right){x}+76a+128$ |
| 28672.5-a2 |
28672.5-a |
$4$ |
$10$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.5 |
\( 2^{12} \cdot 7 \) |
\( 2^{37} \cdot 7^{10} \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \) |
$4.991637207$ |
$0.278816722$ |
4.208262259 |
\( \frac{243980943049}{17210368} a - \frac{103121045163}{8605184} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -92 a + 1068\) , \( 9324 a - 3136\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-92a+1068\right){x}+9324a-3136$ |
| 28672.5-a3 |
28672.5-a |
$4$ |
$10$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.5 |
\( 2^{12} \cdot 7 \) |
\( 2^{25} \cdot 7 \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \) |
$0.499163720$ |
$2.788167220$ |
4.208262259 |
\( \frac{5363}{112} a + \frac{23735}{56} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -2 a - 2\) , \( 4\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-2a-2\right){x}+4$ |
| 28672.5-a4 |
28672.5-a |
$4$ |
$10$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.5 |
\( 2^{12} \cdot 7 \) |
\( 2^{41} \cdot 7^{5} \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \) |
$2.495818603$ |
$0.557633444$ |
4.208262259 |
\( -\frac{581506766557}{359661568} a + \frac{327209683751}{179830784} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -82 a + 158\) , \( -64 a - 796\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-82a+158\right){x}-64a-796$ |
| 28672.5-b1 |
28672.5-b |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.5 |
\( 2^{12} \cdot 7 \) |
\( 2^{17} \cdot 7^{4} \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.733894296$ |
2.066629834 |
\( -\frac{3728}{49} a + \frac{1056}{49} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -3\) , \( -3 a + 5\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}-3{x}-3a+5$ |
| 28672.5-b2 |
28672.5-b |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.5 |
\( 2^{12} \cdot 7 \) |
\( 2^{19} \cdot 7^{2} \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.733894296$ |
2.066629834 |
\( -\frac{225856}{7} a + \frac{105664}{7} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 3 a - 14\) , \( -2 a + 20\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(3a-14\right){x}-2a+20$ |
| 28672.5-c1 |
28672.5-c |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.5 |
\( 2^{12} \cdot 7 \) |
\( 2^{23} \cdot 7 \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.949735186$ |
$3.128064916$ |
4.491477793 |
\( \frac{1072}{7} a + \frac{2208}{7} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 2 a - 1\) , \( 3 a - 1\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(2a-1\right){x}+3a-1$ |
| 28672.5-c2 |
28672.5-c |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.5 |
\( 2^{12} \cdot 7 \) |
\( 2^{19} \cdot 7^{2} \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.474867593$ |
$3.128064916$ |
4.491477793 |
\( -\frac{9244}{7} a + 5848 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -2 a + 6\) , \( 4 a + 4\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-2a+6\right){x}+4a+4$ |
| 28672.5-d1 |
28672.5-d |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.5 |
\( 2^{12} \cdot 7 \) |
\( 2^{21} \cdot 7^{6} \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Cn |
$1$ |
\( 2^{3} \) |
$1$ |
$1.562354823$ |
2.362058470 |
\( \frac{12393}{343} a - \frac{64854}{343} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -5 a - 4\) , \( 26 a - 4\bigr] \) |
${y}^2={x}^{3}+\left(-5a-4\right){x}+26a-4$ |
| 28672.5-d2 |
28672.5-d |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.5 |
\( 2^{12} \cdot 7 \) |
\( 2^{27} \cdot 7^{3} \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Cn |
$1$ |
\( 2^{3} \) |
$1$ |
$1.562354823$ |
2.362058470 |
\( -\frac{608715}{49} a + \frac{447714}{49} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -23 a + 2\) , \( 50 a - 44\bigr] \) |
${y}^2={x}^{3}+\left(-23a+2\right){x}+50a-44$ |
| 28672.5-e1 |
28672.5-e |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.5 |
\( 2^{12} \cdot 7 \) |
\( 2^{28} \cdot 7^{2} \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.067882687$ |
1.614486868 |
\( \frac{23725299}{896} a - \frac{2152841545}{448} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 120 a + 1\) , \( -149 a - 841\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(120a+1\right){x}-149a-841$ |
| 28672.5-e2 |
28672.5-e |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.5 |
\( 2^{12} \cdot 7 \) |
\( 2^{41} \cdot 7 \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.067882687$ |
1.614486868 |
\( -\frac{182016677}{114688} a + \frac{87433471}{57344} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -4 a + 44\) , \( -56 a - 24\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-4a+44\right){x}-56a-24$ |
| 28672.5-f1 |
28672.5-f |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.5 |
\( 2^{12} \cdot 7 \) |
\( 2^{20} \cdot 7^{2} \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.290751244$ |
$2.736244025$ |
4.811133086 |
\( -\frac{11418}{7} a - 16636 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -8 a + 1\) , \( 9 a - 15\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-8a+1\right){x}+9a-15$ |
| 28672.5-f2 |
28672.5-f |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.5 |
\( 2^{12} \cdot 7 \) |
\( 2^{25} \cdot 7 \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.581502488$ |
$2.736244025$ |
4.811133086 |
\( -\frac{4532}{7} a - \frac{520}{7} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 4 a - 4\) , \( -4 a\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(4a-4\right){x}-4a$ |
| 28672.5-g1 |
28672.5-g |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.5 |
\( 2^{12} \cdot 7 \) |
\( 2^{23} \cdot 7^{3} \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.824201334$ |
$2.063563427$ |
5.142710798 |
\( \frac{1104701}{196} a - \frac{241863}{98} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 10 a - 14\) , \( -16 a + 20\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(10a-14\right){x}-16a+20$ |
| 28672.5-g2 |
28672.5-g |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.5 |
\( 2^{12} \cdot 7 \) |
\( 2^{28} \cdot 7^{6} \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.648402668$ |
$1.031781713$ |
5.142710798 |
\( -\frac{31083}{98} a - \frac{60265}{343} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -20 a - 4\) , \( -84 a\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-20a-4\right){x}-84a$ |
| 28672.5-h1 |
28672.5-h |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.5 |
\( 2^{12} \cdot 7 \) |
\( 2^{26} \cdot 7^{2} \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.736289018$ |
$1.934816705$ |
4.307538015 |
\( -\frac{11418}{7} a - 16636 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 9 a + 13\) , \( 21 a - 35\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(9a+13\right){x}+21a-35$ |
| 28672.5-h2 |
28672.5-h |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.5 |
\( 2^{12} \cdot 7 \) |
\( 2^{19} \cdot 7 \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.368144509$ |
$3.869633410$ |
4.307538015 |
\( -\frac{4532}{7} a - \frac{520}{7} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -a + 3\) , \( -a - 1\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-a+3\right){x}-a-1$ |
| 28672.5-i1 |
28672.5-i |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.5 |
\( 2^{12} \cdot 7 \) |
\( 2^{34} \cdot 7^{2} \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.755107089$ |
2.283229226 |
\( \frac{23725299}{896} a - \frac{2152841545}{448} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -119 a - 243\) , \( -1169 a - 1141\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-119a-243\right){x}-1169a-1141$ |
| 28672.5-i2 |
28672.5-i |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.5 |
\( 2^{12} \cdot 7 \) |
\( 2^{35} \cdot 7 \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.510214179$ |
2.283229226 |
\( -\frac{182016677}{114688} a + \frac{87433471}{57344} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -9 a - 13\) , \( -11 a - 23\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-9a-13\right){x}-11a-23$ |
| 28672.5-j1 |
28672.5-j |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.5 |
\( 2^{12} \cdot 7 \) |
\( 2^{29} \cdot 7^{3} \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.369869896$ |
$1.459159692$ |
4.895691373 |
\( \frac{1104701}{196} a - \frac{241863}{98} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -22 a + 7\) , \( -51 a + 79\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-22a+7\right){x}-51a+79$ |
| 28672.5-j2 |
28672.5-j |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.5 |
\( 2^{12} \cdot 7 \) |
\( 2^{22} \cdot 7^{6} \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.184934948$ |
$1.459159692$ |
4.895691373 |
\( -\frac{31083}{98} a - \frac{60265}{343} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 11 a - 9\) , \( -21 a - 21\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(11a-9\right){x}-21a-21$ |
| 28672.5-k1 |
28672.5-k |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.5 |
\( 2^{12} \cdot 7 \) |
\( 2^{27} \cdot 7^{6} \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Cn |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.480774292$ |
$1.104751690$ |
4.818014847 |
\( \frac{12393}{343} a - \frac{64854}{343} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( a + 18\) , \( 74 a - 60\bigr] \) |
${y}^2={x}^{3}+\left(a+18\right){x}+74a-60$ |
| 28672.5-k2 |
28672.5-k |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.5 |
\( 2^{12} \cdot 7 \) |
\( 2^{21} \cdot 7^{3} \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Cn |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.240387146$ |
$2.209503381$ |
4.818014847 |
\( -\frac{608715}{49} a + \frac{447714}{49} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 11 a - 12\) , \( 18 a - 4\bigr] \) |
${y}^2={x}^{3}+\left(11a-12\right){x}+18a-4$ |
| 28672.5-l1 |
28672.5-l |
$4$ |
$10$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.5 |
\( 2^{12} \cdot 7 \) |
\( 2^{23} \cdot 7^{2} \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.971531948$ |
2.980676135 |
\( \frac{1143001}{28} a - \frac{2178651}{14} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 19 a + 7\) , \( 3 a + 67\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(19a+7\right){x}+3a+67$ |
| 28672.5-l2 |
28672.5-l |
$4$ |
$10$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.5 |
\( 2^{12} \cdot 7 \) |
\( 2^{31} \cdot 7^{10} \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \cdot 5 \) |
$1$ |
$0.394306389$ |
2.980676135 |
\( \frac{243980943049}{17210368} a - \frac{103121045163}{8605184} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -221 a - 313\) , \( 2723 a + 1155\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-221a-313\right){x}+2723a+1155$ |
| 28672.5-l3 |
28672.5-l |
$4$ |
$10$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.5 |
\( 2^{12} \cdot 7 \) |
\( 2^{31} \cdot 7 \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.971531948$ |
2.980676135 |
\( \frac{5363}{112} a + \frac{23735}{56} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 2 a + 7\) , \( 5 a + 15\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(2a+7\right){x}+5a+15$ |
| 28672.5-l4 |
28672.5-l |
$4$ |
$10$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.5 |
\( 2^{12} \cdot 7 \) |
\( 2^{47} \cdot 7^{5} \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \cdot 5 \) |
$1$ |
$0.394306389$ |
2.980676135 |
\( -\frac{581506766557}{359661568} a + \frac{327209683751}{179830784} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 242 a - 153\) , \( -747 a - 1617\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(242a-153\right){x}-747a-1617$ |
| 28672.5-m1 |
28672.5-m |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.5 |
\( 2^{12} \cdot 7 \) |
\( 2^{23} \cdot 7^{4} \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.933155196$ |
2.922655939 |
\( -\frac{3728}{49} a + \frac{1056}{49} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -3 a + 5\) , \( -7 a + 21\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-3a+5\right){x}-7a+21$ |
| 28672.5-m2 |
28672.5-m |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.5 |
\( 2^{12} \cdot 7 \) |
\( 2^{13} \cdot 7^{2} \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.866310392$ |
2.922655939 |
\( -\frac{225856}{7} a + \frac{105664}{7} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 2 a + 5\) , \( -3 a + 7\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(2a+5\right){x}-3a+7$ |
| 28672.5-n1 |
28672.5-n |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.5 |
\( 2^{12} \cdot 7 \) |
\( 2^{17} \cdot 7 \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$4.423751828$ |
3.344042057 |
\( \frac{1072}{7} a + \frac{2208}{7} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 1\) , \( a - 1\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+{x}+a-1$ |
| 28672.5-n2 |
28672.5-n |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.5 |
\( 2^{12} \cdot 7 \) |
\( 2^{25} \cdot 7^{2} \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.211875914$ |
3.344042057 |
\( -\frac{9244}{7} a + 5848 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 10 a - 9\) , \( 7 a + 9\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(10a-9\right){x}+7a+9$ |
*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.
