The results below are complete, since the LMFDB contains all elliptic curves with conductor norm at most 1000 over imaginary quadratic fields with absolute discriminant 91
Note: The completeness Only modular elliptic curves are included
| 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 |
| 448.1-a1 |
448.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-91}) \) |
$2$ |
$[0, 1]$ |
448.1 |
\( 2^{6} \cdot 7 \) |
\( 2^{20} \cdot 7^{2} \) |
$3.92174$ |
$(7,a+3), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$2.026676007$ |
$3.197869643$ |
2.717592766 |
\( -\frac{4}{7} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 0\) , \( -4\bigr] \) |
${y}^2={x}^3-{x}^2-4$ |
| 448.1-a2 |
448.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-91}) \) |
$2$ |
$[0, 1]$ |
448.1 |
\( 2^{6} \cdot 7 \) |
\( 2^{22} \cdot 7^{4} \) |
$3.92174$ |
$(7,a+3), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$4.053352015$ |
$1.598934821$ |
2.717592766 |
\( \frac{3543122}{49} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -40\) , \( -84\bigr] \) |
${y}^2={x}^3-{x}^2-40{x}-84$ |
| 448.1-b1 |
448.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-91}) \) |
$2$ |
$[0, 1]$ |
448.1 |
\( 2^{6} \cdot 7 \) |
\( 2^{16} \cdot 7^{14} \) |
$3.92174$ |
$(7,a+3), (2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.891959002$ |
$4.016295718$ |
1.593113446 |
\( \frac{432}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 49\) , \( -686\bigr] \) |
${y}^2={x}^3+49{x}-686$ |
| 448.1-b2 |
448.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-91}) \) |
$2$ |
$[0, 1]$ |
448.1 |
\( 2^{6} \cdot 7 \) |
\( 2^{22} \cdot 7^{20} \) |
$3.92174$ |
$(7,a+3), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.891959002$ |
$1.004073929$ |
1.593113446 |
\( \frac{11090466}{2401} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -2891\) , \( 47334\bigr] \) |
${y}^2={x}^3-2891{x}+47334$ |
| 448.1-b3 |
448.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-91}) \) |
$2$ |
$[0, 1]$ |
448.1 |
\( 2^{6} \cdot 7 \) |
\( 2^{20} \cdot 7^{16} \) |
$3.92174$ |
$(7,a+3), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$3.783918005$ |
$2.008147859$ |
1.593113446 |
\( \frac{740772}{49} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -931\) , \( -10290\bigr] \) |
${y}^2={x}^3-931{x}-10290$ |
| 448.1-b4 |
448.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-91}) \) |
$2$ |
$[0, 1]$ |
448.1 |
\( 2^{6} \cdot 7 \) |
\( 2^{22} \cdot 7^{14} \) |
$3.92174$ |
$(7,a+3), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$7.567836011$ |
$1.004073929$ |
1.593113446 |
\( \frac{1443468546}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -14651\) , \( -682570\bigr] \) |
${y}^2={x}^3-14651{x}-682570$ |
| 448.1-c1 |
448.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-91}) \) |
$2$ |
$[0, 1]$ |
448.1 |
\( 2^{6} \cdot 7 \) |
\( 2^{16} \cdot 7^{2} \) |
$3.92174$ |
$(7,a+3), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$9$ |
\( 2^{3} \) |
$1$ |
$4.016295718$ |
3.789199711 |
\( \frac{432}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 1\) , \( 2\bigr] \) |
${y}^2={x}^3+{x}+2$ |
| 448.1-c2 |
448.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-91}) \) |
$2$ |
$[0, 1]$ |
448.1 |
\( 2^{6} \cdot 7 \) |
\( 2^{22} \cdot 7^{8} \) |
$3.92174$ |
$(7,a+3), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$36$ |
\( 2 \) |
$1$ |
$1.004073929$ |
3.789199711 |
\( \frac{11090466}{2401} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -59\) , \( -138\bigr] \) |
${y}^2={x}^3-59{x}-138$ |
| 448.1-c3 |
448.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-91}) \) |
$2$ |
$[0, 1]$ |
448.1 |
\( 2^{6} \cdot 7 \) |
\( 2^{20} \cdot 7^{4} \) |
$3.92174$ |
$(7,a+3), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$36$ |
\( 2^{2} \) |
$1$ |
$2.008147859$ |
3.789199711 |
\( \frac{740772}{49} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -19\) , \( 30\bigr] \) |
${y}^2={x}^3-19{x}+30$ |
| 448.1-c4 |
448.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-91}) \) |
$2$ |
$[0, 1]$ |
448.1 |
\( 2^{6} \cdot 7 \) |
\( 2^{22} \cdot 7^{2} \) |
$3.92174$ |
$(7,a+3), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$36$ |
\( 2 \) |
$1$ |
$1.004073929$ |
3.789199711 |
\( \frac{1443468546}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -299\) , \( 1990\bigr] \) |
${y}^2={x}^3-299{x}+1990$ |
| 448.1-d1 |
448.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{-91}) \) |
$2$ |
$[0, 1]$ |
448.1 |
\( 2^{6} \cdot 7 \) |
\( 2^{20} \cdot 7^{14} \) |
$3.92174$ |
$(7,a+3), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$9$ |
\( 2^{2} \) |
$1$ |
$3.197869643$ |
6.034100862 |
\( -\frac{4}{7} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -16\) , \( 1392\bigr] \) |
${y}^2={x}^3+{x}^2-16{x}+1392$ |
| 448.1-d2 |
448.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{-91}) \) |
$2$ |
$[0, 1]$ |
448.1 |
\( 2^{6} \cdot 7 \) |
\( 2^{22} \cdot 7^{16} \) |
$3.92174$ |
$(7,a+3), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$36$ |
\( 2 \) |
$1$ |
$1.598934821$ |
6.034100862 |
\( \frac{3543122}{49} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -1976\) , \( 32752\bigr] \) |
${y}^2={x}^3+{x}^2-1976{x}+32752$ |
*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.
