| 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 |
| 7936.2-a1 |
7936.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
7936.2 |
\( 2^{8} \cdot 31 \) |
\( 2^{26} \cdot 31^{3} \) |
$1.46083$ |
$(6a-5), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B[2] |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.038512273$ |
$1.259510110$ |
1.344254264 |
\( \frac{10618695}{29791} a - \frac{124425801}{59582} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -31 a + 25\) , \( -39 a + 112\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-31a+25\right){x}-39a+112$ |
| 7936.2-a2 |
7936.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
7936.2 |
\( 2^{8} \cdot 31 \) |
\( 2^{30} \cdot 31 \) |
$1.46083$ |
$(6a-5), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B[2] |
$1$ |
\( 2^{2} \) |
$0.115536819$ |
$1.259510110$ |
1.344254264 |
\( -\frac{44272737}{124} a + \frac{99194139}{248} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 66 a - 97\) , \( 321 a - 353\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(66a-97\right){x}+321a-353$ |
| 7936.2-b1 |
7936.2-b |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
7936.2 |
\( 2^{8} \cdot 31 \) |
\( 2^{22} \cdot 31 \) |
$1.46083$ |
$(6a-5), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$0.077516098$ |
$2.810548978$ |
2.012530258 |
\( \frac{20086}{31} a - \frac{69202}{31} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 5 a + 1\) , \( a - 6\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(5a+1\right){x}+a-6$ |
| 7936.2-c1 |
7936.2-c |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
7936.2 |
\( 2^{8} \cdot 31 \) |
\( 2^{22} \cdot 31 \) |
$1.46083$ |
$(6a-5), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$0.092041987$ |
$2.810548978$ |
2.389662118 |
\( \frac{20086}{31} a - \frac{69202}{31} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 5 a + 1\) , \( -a + 6\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(5a+1\right){x}-a+6$ |
| 7936.2-d1 |
7936.2-d |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
7936.2 |
\( 2^{8} \cdot 31 \) |
\( 2^{74} \cdot 31 \) |
$1.46083$ |
$(6a-5), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.4.2 |
$1$ |
\( 2^{2} \) |
$2.882361124$ |
$0.092107946$ |
2.452476457 |
\( \frac{936087656892551}{1040187392} a - \frac{833285178768245}{1040187392} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -20800 a + 12008\) , \( -651200 a + 1075524\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-20800a+12008\right){x}-651200a+1075524$ |
| 7936.2-d2 |
7936.2-d |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
7936.2 |
\( 2^{8} \cdot 31 \) |
\( 2^{26} \cdot 31 \) |
$1.46083$ |
$(6a-5), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.4.1 |
$1$ |
\( 2^{2} \) |
$0.115294444$ |
$2.302698662$ |
2.452476457 |
\( \frac{24551}{62} a + \frac{66955}{62} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 8\) , \( 4\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+8{x}+4$ |
| 7936.2-d3 |
7936.2-d |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
7936.2 |
\( 2^{8} \cdot 31 \) |
\( 2^{34} \cdot 31^{5} \) |
$1.46083$ |
$(6a-5), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5Cs.4.1 |
$1$ |
\( 2^{2} \) |
$0.576472224$ |
$0.460539732$ |
2.452476457 |
\( -\frac{511363962461}{916132832} a + \frac{764718499383}{458066416} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 240 a - 152\) , \( -128 a - 732\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(240a-152\right){x}-128a-732$ |
| 7936.2-e1 |
7936.2-e |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
7936.2 |
\( 2^{8} \cdot 31 \) |
\( 2^{26} \cdot 31^{3} \) |
$1.46083$ |
$(6a-5), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B[2] |
$1$ |
\( 2 \) |
$1$ |
$1.259510110$ |
2.908714005 |
\( \frac{10618695}{29791} a - \frac{124425801}{59582} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -31 a + 25\) , \( 39 a - 112\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-31a+25\right){x}+39a-112$ |
| 7936.2-e2 |
7936.2-e |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
7936.2 |
\( 2^{8} \cdot 31 \) |
\( 2^{30} \cdot 31 \) |
$1.46083$ |
$(6a-5), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B[2] |
$1$ |
\( 2 \) |
$1$ |
$1.259510110$ |
2.908714005 |
\( -\frac{44272737}{124} a + \frac{99194139}{248} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 66 a - 97\) , \( -321 a + 353\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(66a-97\right){x}-321a+353$ |
*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.
