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 |
4356.5-a1 |
4356.5-a |
$4$ |
$6$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4356.5 |
\( 2^{2} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{6} \cdot 3^{4} \cdot 11^{12} \) |
$1.92070$ |
$(a), (-a+1), (-2a+3), (2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \) |
$1$ |
$0.623134288$ |
0.942090491 |
\( -\frac{7357983625}{127552392} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -41\) , \( -556\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-41{x}-556$ |
4356.5-a2 |
4356.5-a |
$4$ |
$6$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4356.5 |
\( 2^{2} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{2} \cdot 3^{12} \cdot 11^{4} \) |
$1.92070$ |
$(a), (-a+1), (-2a+3), (2a+1), (3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$1.869402865$ |
0.942090491 |
\( \frac{9938375}{176418} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 4\) , \( 20\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+4{x}+20$ |
4356.5-a3 |
4356.5-a |
$4$ |
$6$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4356.5 |
\( 2^{2} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{4} \cdot 3^{6} \cdot 11^{2} \) |
$1.92070$ |
$(a), (-a+1), (-2a+3), (2a+1), (3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$3.738805730$ |
0.942090491 |
\( \frac{18609625}{1188} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -6\) , \( 4\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-6{x}+4$ |
4356.5-a4 |
4356.5-a |
$4$ |
$6$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4356.5 |
\( 2^{2} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{12} \cdot 3^{2} \cdot 11^{6} \) |
$1.92070$ |
$(a), (-a+1), (-2a+3), (2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$1.246268576$ |
0.942090491 |
\( \frac{57736239625}{255552} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -81\) , \( -284\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-81{x}-284$ |
4356.5-b1 |
4356.5-b |
$4$ |
$6$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4356.5 |
\( 2^{2} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{10} \cdot 3^{12} \cdot 11^{8} \) |
$1.92070$ |
$(a), (-a+1), (-2a+3), (2a+1), (3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3^{3} \) |
$1$ |
$0.523029338$ |
2.372238099 |
\( \frac{229027231511}{680279424} a - \frac{24638577262535}{165307900032} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -79 a + 79\) , \( -325 a - 685\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-79a+79\right){x}-325a-685$ |
4356.5-b2 |
4356.5-b |
$4$ |
$6$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4356.5 |
\( 2^{2} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{20} \cdot 3^{6} \cdot 11^{4} \) |
$1.92070$ |
$(a), (-a+1), (-2a+3), (2a+1), (3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{3} \) |
$1$ |
$1.046058676$ |
2.372238099 |
\( -\frac{2492457457997}{588791808} a + \frac{3282842124127}{588791808} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( 41 a - 1\) , \( -13 a - 125\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(41a-1\right){x}-13a-125$ |
4356.5-b3 |
4356.5-b |
$4$ |
$6$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4356.5 |
\( 2^{2} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{44} \cdot 3^{2} \cdot 11^{4} \) |
$1.92070$ |
$(a), (-a+1), (-2a+3), (2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$1$ |
$0.348686225$ |
2.372238099 |
\( \frac{105273133194758264123}{17561399718838272} a + \frac{342157997809516499975}{17561399718838272} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -424 a + 614\) , \( -1060 a - 6260\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-424a+614\right){x}-1060a-6260$ |
4356.5-b4 |
4356.5-b |
$4$ |
$6$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4356.5 |
\( 2^{2} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{22} \cdot 3^{4} \cdot 11^{8} \) |
$1.92070$ |
$(a), (-a+1), (-2a+3), (2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{3} \) |
$1$ |
$0.174343112$ |
2.372238099 |
\( \frac{968213635965123841917}{3715232694272} a + \frac{9325769488561763242777}{33437094248448} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -6694 a + 9754\) , \( -54874 a - 409456\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-6694a+9754\right){x}-54874a-409456$ |
4356.5-c1 |
4356.5-c |
$4$ |
$6$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4356.5 |
\( 2^{2} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{10} \cdot 3^{12} \cdot 11^{8} \) |
$1.92070$ |
$(a), (-a+1), (-2a+3), (2a+1), (3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3^{3} \) |
$1$ |
$0.523029338$ |
2.372238099 |
\( -\frac{229027231511}{680279424} a + \frac{15507519997319}{82653950016} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( 79 a\) , \( 325 a - 1010\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+79a{x}+325a-1010$ |
4356.5-c2 |
4356.5-c |
$4$ |
$6$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4356.5 |
\( 2^{2} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{20} \cdot 3^{6} \cdot 11^{4} \) |
$1.92070$ |
$(a), (-a+1), (-2a+3), (2a+1), (3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{3} \) |
$1$ |
$1.046058676$ |
2.372238099 |
\( \frac{2492457457997}{588791808} a + \frac{395192333065}{294395904} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( -41 a + 40\) , \( 13 a - 138\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(-41a+40\right){x}+13a-138$ |
4356.5-c3 |
4356.5-c |
$4$ |
$6$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4356.5 |
\( 2^{2} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{44} \cdot 3^{2} \cdot 11^{4} \) |
$1.92070$ |
$(a), (-a+1), (-2a+3), (2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$1$ |
$0.348686225$ |
2.372238099 |
\( -\frac{105273133194758264123}{17561399718838272} a + \frac{223715565502137382049}{8780699859419136} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( 424 a + 190\) , \( 1060 a - 7320\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(424a+190\right){x}+1060a-7320$ |
4356.5-c4 |
4356.5-c |
$4$ |
$6$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4356.5 |
\( 2^{2} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{22} \cdot 3^{4} \cdot 11^{8} \) |
$1.92070$ |
$(a), (-a+1), (-2a+3), (2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{3} \) |
$1$ |
$0.174343112$ |
2.372238099 |
\( -\frac{968213635965123841917}{3715232694272} a + \frac{9019846106123938910015}{16718547124224} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( 6694 a + 3060\) , \( 54874 a - 464330\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(6694a+3060\right){x}+54874a-464330$ |
4356.5-d1 |
4356.5-d |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4356.5 |
\( 2^{2} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{2} \cdot 3^{8} \cdot 11^{8} \) |
$1.92070$ |
$(a), (-a+1), (-2a+3), (2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.209138112$ |
3.656089994 |
\( -\frac{192100033}{2371842} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -12\) , \( -81\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-12{x}-81$ |
4356.5-d2 |
4356.5-d |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4356.5 |
\( 2^{2} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{8} \cdot 3^{2} \cdot 11^{2} \) |
$1.92070$ |
$(a), (-a+1), (-2a+3), (2a+1), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$4.836552448$ |
3.656089994 |
\( \frac{912673}{528} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -2\) , \( -1\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-2{x}-1$ |
4356.5-d3 |
4356.5-d |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4356.5 |
\( 2^{2} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{4} \cdot 3^{4} \cdot 11^{4} \) |
$1.92070$ |
$(a), (-a+1), (-2a+3), (2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$2.418276224$ |
3.656089994 |
\( \frac{1180932193}{4356} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -22\) , \( -49\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-22{x}-49$ |
4356.5-d4 |
4356.5-d |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4356.5 |
\( 2^{2} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{2} \cdot 3^{2} \cdot 11^{2} \) |
$1.92070$ |
$(a), (-a+1), (-2a+3), (2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$16$ |
\( 1 \) |
$1$ |
$1.209138112$ |
3.656089994 |
\( \frac{4824238966273}{66} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -352\) , \( -2689\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-352{x}-2689$ |
4356.5-e1 |
4356.5-e |
$4$ |
$10$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4356.5 |
\( 2^{2} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{2} \cdot 3^{4} \cdot 11^{20} \) |
$1.92070$ |
$(a), (-a+1), (-2a+3), (2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$1$ |
\( 2^{3} \cdot 5^{2} \) |
$1$ |
$0.112045110$ |
4.234907127 |
\( -\frac{112427521449300721}{466873642818} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -10055\) , \( -390309\bigr] \) |
${y}^2+{x}{y}={x}^{3}-10055{x}-390309$ |
4356.5-e2 |
4356.5-e |
$4$ |
$10$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4356.5 |
\( 2^{2} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{10} \cdot 3^{20} \cdot 11^{4} \) |
$1.92070$ |
$(a), (-a+1), (-2a+3), (2a+1), (3)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 2^{3} \cdot 5^{3} \) |
$1$ |
$0.560225554$ |
4.234907127 |
\( \frac{168105213359}{228637728} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( 115\) , \( 561\bigr] \) |
${y}^2+{x}{y}={x}^{3}+115{x}+561$ |
4356.5-e3 |
4356.5-e |
$4$ |
$10$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4356.5 |
\( 2^{2} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{20} \cdot 3^{10} \cdot 11^{2} \) |
$1.92070$ |
$(a), (-a+1), (-2a+3), (2a+1), (3)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 2^{2} \cdot 5^{3} \) |
$1$ |
$1.120451108$ |
4.234907127 |
\( \frac{10091699281}{2737152} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -45\) , \( 81\bigr] \) |
${y}^2+{x}{y}={x}^{3}-45{x}+81$ |
4356.5-e4 |
4356.5-e |
$4$ |
$10$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4356.5 |
\( 2^{2} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{4} \cdot 3^{2} \cdot 11^{10} \) |
$1.92070$ |
$(a), (-a+1), (-2a+3), (2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$1$ |
\( 2^{2} \cdot 5^{2} \) |
$1$ |
$0.224090221$ |
4.234907127 |
\( \frac{112763292123580561}{1932612} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -10065\) , \( -389499\bigr] \) |
${y}^2+{x}{y}={x}^{3}-10065{x}-389499$ |
*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.