| 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 |
| 86.4-a1 |
86.4-a |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
86.4 |
\( 2 \cdot 43 \) |
\( 2^{15} \cdot 43^{3} \) |
$0.71997$ |
$(-a+1), (2a+5)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 3 \) |
$1$ |
$2.148115240$ |
0.541274163 |
\( -\frac{6249441045295}{2605285376} a + \frac{5506866419901}{1302642688} \) |
\( \bigl[a\) , \( a + 1\) , \( 1\) , \( 4 a + 9\) , \( 17 a - 13\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(4a+9\right){x}+17a-13$ |
| 2752.14-b1 |
2752.14-b |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
2752.14 |
\( 2^{6} \cdot 43 \) |
\( 2^{33} \cdot 43^{3} \) |
$1.71238$ |
$(-a+1), (2a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs |
$1$ |
\( 2^{2} \) |
$0.481611283$ |
$0.759473426$ |
2.211974923 |
\( -\frac{6249441045295}{2605285376} a + \frac{5506866419901}{1302642688} \) |
\( \bigl[0\) , \( -a + 1\) , \( a + 1\) , \( -43 a + 105\) , \( 89 a + 249\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-43a+105\right){x}+89a+249$ |
| 5504.4-g1 |
5504.4-g |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
5504.4 |
\( 2^{7} \cdot 43 \) |
\( 2^{21} \cdot 43^{3} \) |
$2.03637$ |
$(a), (-a+1), (2a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs |
$1$ |
\( 3^{2} \cdot 5 \) |
$0.044845183$ |
$1.518946853$ |
4.634275720 |
\( -\frac{6249441045295}{2605285376} a + \frac{5506866419901}{1302642688} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( 6 a - 27\) , \( 11 a - 44\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(6a-27\right){x}+11a-44$ |
| 6966.4-a1 |
6966.4-a |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6966.4 |
\( 2 \cdot 3^{4} \cdot 43 \) |
\( 2^{15} \cdot 3^{12} \cdot 43^{3} \) |
$2.15990$ |
$(-a+1), (2a+5), (3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \cdot 3^{2} \cdot 5 \) |
$0.359137410$ |
$0.716038413$ |
3.887836029 |
\( -\frac{6249441045295}{2605285376} a + \frac{5506866419901}{1302642688} \) |
\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( 32 a + 91\) , \( -337 a + 272\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(32a+91\right){x}-337a+272$ |
| 11008.10-b2 |
11008.10-b |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
11008.10 |
\( 2^{8} \cdot 43 \) |
\( 2^{39} \cdot 43^{3} \) |
$2.42167$ |
$(a), (-a+1), (2a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs |
$1$ |
\( 2^{2} \) |
$1.260395327$ |
$0.537028810$ |
4.093316556 |
\( -\frac{6249441045295}{2605285376} a + \frac{5506866419901}{1302642688} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 58 a + 159\) , \( -595 a + 727\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(58a+159\right){x}-595a+727$ |
| 29584.15-a2 |
29584.15-a |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
29584.15 |
\( 2^{4} \cdot 43^{2} \) |
\( 2^{27} \cdot 43^{9} \) |
$3.10064$ |
$(-a+1), (2a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs |
$1$ |
\( 2^{3} \) |
$2.226459655$ |
$0.163792251$ |
4.410716468 |
\( -\frac{6249441045295}{2605285376} a + \frac{5506866419901}{1302642688} \) |
\( \bigl[0\) , \( a + 1\) , \( a + 1\) , \( 766 a - 2309\) , \( 20390 a - 32744\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(766a-2309\right){x}+20390a-32744$ |
| 33712.10-c2 |
33712.10-c |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
33712.10 |
\( 2^{4} \cdot 7^{2} \cdot 43 \) |
\( 2^{27} \cdot 7^{6} \cdot 43^{3} \) |
$3.20357$ |
$(-a+1), (-2a+1), (2a+5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$0.405955622$ |
1.841241634 |
\( -\frac{6249441045295}{2605285376} a + \frac{5506866419901}{1302642688} \) |
\( \bigl[0\) , \( -a - 1\) , \( a + 1\) , \( -258 a + 219\) , \( 1049 a - 2609\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-258a+219\right){x}+1049a-2609$ |
| 44032.10-f2 |
44032.10-f |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
44032.10 |
\( 2^{10} \cdot 43 \) |
\( 2^{33} \cdot 43^{3} \) |
$3.42476$ |
$(a), (-a+1), (2a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs |
$1$ |
\( 2 \) |
$1.848110344$ |
$0.759473426$ |
4.244059340 |
\( -\frac{6249441045295}{2605285376} a + \frac{5506866419901}{1302642688} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -68 a - 12\) , \( -234 a + 50\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-68a-12\right){x}-234a+50$ |
| 44032.14-d2 |
44032.14-d |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
44032.14 |
\( 2^{10} \cdot 43 \) |
\( 2^{45} \cdot 43^{3} \) |
$3.42476$ |
$(a), (-a+1), (2a+5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$0.379736713$ |
1.722323840 |
\( -\frac{6249441045295}{2605285376} a + \frac{5506866419901}{1302642688} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -273 a - 46\) , \( -2191 a + 946\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-273a-46\right){x}-2191a+946$ |
*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.
