| 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 |
| 97216.2-a1 |
97216.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
97216.2 |
\( 2^{6} \cdot 7^{2} \cdot 31 \) |
\( 2^{20} \cdot 7^{3} \cdot 31^{3} \) |
$2.73296$ |
$(-3a+1), (6a-5), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.460165277$ |
$0.858016543$ |
2.735458468 |
\( -\frac{1019278796}{29791} a - \frac{2968797888}{29791} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -16 a + 160\) , \( -784 a + 272\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-16a+160\right){x}-784a+272$ |
| 97216.2-a2 |
97216.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
97216.2 |
\( 2^{6} \cdot 7^{2} \cdot 31 \) |
\( 2^{22} \cdot 7^{3} \cdot 31^{6} \) |
$2.73296$ |
$(-3a+1), (6a-5), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.920330554$ |
$0.429008271$ |
2.735458468 |
\( \frac{245418516722}{887503681} a + \frac{479382157402}{887503681} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 104 a + 120\) , \( -592 a - 912\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(104a+120\right){x}-592a-912$ |
| 97216.2-b1 |
97216.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
97216.2 |
\( 2^{6} \cdot 7^{2} \cdot 31 \) |
\( 2^{22} \cdot 7^{8} \cdot 31^{2} \) |
$2.73296$ |
$(-3a+1), (6a-5), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.419856335$ |
$0.510276134$ |
3.346409001 |
\( \frac{1312084358}{47089} a - \frac{569421536}{47089} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 371 a - 205\) , \( 2153 a + 273\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(371a-205\right){x}+2153a+273$ |
| 97216.2-b2 |
97216.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
97216.2 |
\( 2^{6} \cdot 7^{2} \cdot 31 \) |
\( 2^{20} \cdot 7^{7} \cdot 31 \) |
$2.73296$ |
$(-3a+1), (6a-5), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.709928167$ |
$1.020552268$ |
3.346409001 |
\( -\frac{458588}{217} a + \frac{581628}{217} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 51 a - 5\) , \( 49 a - 127\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(51a-5\right){x}+49a-127$ |
| 97216.2-c1 |
97216.2-c |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
97216.2 |
\( 2^{6} \cdot 7^{2} \cdot 31 \) |
\( 2^{22} \cdot 7^{8} \cdot 31 \) |
$2.73296$ |
$(-3a+1), (6a-5), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$0.639147202$ |
1.476047237 |
\( -\frac{48720628}{1519} a - \frac{49631490}{1519} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 245 a - 235\) , \( 1753 a - 742\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(245a-235\right){x}+1753a-742$ |
| 97216.2-d1 |
97216.2-d |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
97216.2 |
\( 2^{6} \cdot 7^{2} \cdot 31 \) |
\( 2^{22} \cdot 7^{8} \cdot 31 \) |
$2.73296$ |
$(-3a+1), (6a-5), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$0.748400086$ |
1.728355966 |
\( -\frac{1612250}{1519} a - \frac{5108500}{1519} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 62 a + 53\) , \( 401 a - 534\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(62a+53\right){x}+401a-534$ |
| 97216.2-e1 |
97216.2-e |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
97216.2 |
\( 2^{6} \cdot 7^{2} \cdot 31 \) |
\( 2^{20} \cdot 7^{10} \cdot 31^{5} \) |
$2.73296$ |
$(-3a+1), (6a-5), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$0.203365697$ |
2.348264803 |
\( \frac{25563474932}{28629151} a - \frac{22884782364}{28629151} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -232 a + 984\) , \( -18832 a + 10476\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-232a+984\right){x}-18832a+10476$ |
| 97216.2-f1 |
97216.2-f |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
97216.2 |
\( 2^{6} \cdot 7^{2} \cdot 31 \) |
\( 2^{22} \cdot 7^{7} \cdot 31^{4} \) |
$2.73296$ |
$(-3a+1), (6a-5), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$4.145396938$ |
$0.328300459$ |
3.142946415 |
\( \frac{256820381838}{6464647} a - \frac{25590802500}{6464647} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -95 a + 893\) , \( -10575 a + 4548\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-95a+893\right){x}-10575a+4548$ |
| 97216.2-f2 |
97216.2-f |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
97216.2 |
\( 2^{6} \cdot 7^{2} \cdot 31 \) |
\( 2^{16} \cdot 7^{7} \cdot 31 \) |
$2.73296$ |
$(-3a+1), (6a-5), (2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.036349234$ |
$1.313201837$ |
3.142946415 |
\( \frac{180144}{217} a + \frac{164160}{217} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 5 a - 27\) , \( 21 a + 8\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(5a-27\right){x}+21a+8$ |
| 97216.2-f3 |
97216.2-f |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
97216.2 |
\( 2^{6} \cdot 7^{2} \cdot 31 \) |
\( 2^{20} \cdot 7^{8} \cdot 31^{2} \) |
$2.73296$ |
$(-3a+1), (6a-5), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$2.072698469$ |
$0.656600918$ |
3.142946415 |
\( -\frac{59793228}{47089} a + \frac{122058252}{47089} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -55 a + 133\) , \( 193 a + 268\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-55a+133\right){x}+193a+268$ |
| 97216.2-f4 |
97216.2-f |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
97216.2 |
\( 2^{6} \cdot 7^{2} \cdot 31 \) |
\( 2^{22} \cdot 7^{10} \cdot 31 \) |
$2.73296$ |
$(-3a+1), (6a-5), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$4.145396938$ |
$0.328300459$ |
3.142946415 |
\( -\frac{232338494718}{74431} a + \frac{105295935636}{74431} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -975 a + 1933\) , \( 21329 a + 9108\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-975a+1933\right){x}+21329a+9108$ |
| 97216.2-g1 |
97216.2-g |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
97216.2 |
\( 2^{6} \cdot 7^{2} \cdot 31 \) |
\( 2^{16} \cdot 7^{9} \cdot 31^{2} \) |
$2.73296$ |
$(-3a+1), (6a-5), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.684626419$ |
1.581076991 |
\( \frac{3766176}{961} a - \frac{1859760}{961} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -87 a - 43\) , \( -493 a + 140\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-87a-43\right){x}-493a+140$ |
| 97216.2-g2 |
97216.2-g |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
97216.2 |
\( 2^{6} \cdot 7^{2} \cdot 31 \) |
\( 2^{8} \cdot 7^{9} \cdot 31 \) |
$2.73296$ |
$(-3a+1), (6a-5), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.369252839$ |
1.581076991 |
\( -\frac{331776}{31} a + \frac{55296}{31} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 3 a - 38\) , \( -4 a + 110\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(3a-38\right){x}-4a+110$ |
| 97216.2-h1 |
97216.2-h |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
97216.2 |
\( 2^{6} \cdot 7^{2} \cdot 31 \) |
\( 2^{20} \cdot 7^{8} \cdot 31 \) |
$2.73296$ |
$(-3a+1), (6a-5), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1.271841012$ |
$0.856818177$ |
5.033277287 |
\( -\frac{63212}{31} a + \frac{126248}{31} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 27 a + 59\) , \( -215 a + 185\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(27a+59\right){x}-215a+185$ |
| 97216.2-i1 |
97216.2-i |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
97216.2 |
\( 2^{6} \cdot 7^{2} \cdot 31 \) |
\( 2^{22} \cdot 7^{6} \cdot 31 \) |
$2.73296$ |
$(-3a+1), (6a-5), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1.022286856$ |
$1.062287663$ |
5.015846931 |
\( \frac{20086}{31} a - \frac{69202}{31} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -24 a + 48\) , \( 112 a + 48\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-24a+48\right){x}+112a+48$ |
| 97216.2-j1 |
97216.2-j |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
97216.2 |
\( 2^{6} \cdot 7^{2} \cdot 31 \) |
\( 2^{16} \cdot 7^{4} \cdot 31 \) |
$2.73296$ |
$(-3a+1), (6a-5), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$0.292653267$ |
$2.039496322$ |
5.513605125 |
\( -\frac{77808}{31} a + \frac{162016}{31} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -4 a - 12\) , \( 20\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-4a-12\right){x}+20$ |
| 97216.2-k1 |
97216.2-k |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
97216.2 |
\( 2^{6} \cdot 7^{2} \cdot 31 \) |
\( 2^{22} \cdot 7^{9} \cdot 31^{2} \) |
$2.73296$ |
$(-3a+1), (6a-5), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$6.524413830$ |
$0.379553664$ |
5.718920412 |
\( \frac{118936308}{961} a - \frac{149100406}{961} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 840 a - 760\) , \( -9824 a + 3964\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(840a-760\right){x}-9824a+3964$ |
| 97216.2-k2 |
97216.2-k |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
97216.2 |
\( 2^{6} \cdot 7^{2} \cdot 31 \) |
\( 2^{20} \cdot 7^{9} \cdot 31 \) |
$2.73296$ |
$(-3a+1), (6a-5), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$3.262206915$ |
$0.759107329$ |
5.718920412 |
\( -\frac{8544}{31} a + \frac{35276}{31} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 80 a - 40\) , \( -96 a + 236\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(80a-40\right){x}-96a+236$ |
*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.
