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 |
340.1-a1 |
340.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
340.1 |
\( 2^{2} \cdot 5 \cdot 17 \) |
\( 2^{4} \cdot 5^{3} \cdot 17^{6} \) |
$0.76743$ |
$(a+1), (-a-2), (a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$1.693569039$ |
0.846784519 |
\( \frac{8285953568288}{3017196125} a + \frac{8530762181584}{3017196125} \) |
\( \bigl[i + 1\) , \( i + 1\) , \( i + 1\) , \( 7 i - 19\) , \( -17 i + 18\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(i+1\right){x}^{2}+\left(7i-19\right){x}-17i+18$ |
5780.1-a1 |
5780.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
5780.1 |
\( 2^{2} \cdot 5 \cdot 17^{2} \) |
\( 2^{4} \cdot 5^{3} \cdot 17^{12} \) |
$1.55830$ |
$(a+1), (-a-2), (a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$0.410750825$ |
1.232252476 |
\( \frac{8285953568288}{3017196125} a + \frac{8530762181584}{3017196125} \) |
\( \bigl[i + 1\) , \( 1\) , \( 0\) , \( 44 i + 335\) , \( 1972 i - 709\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+{x}^{2}+\left(44i+335\right){x}+1972i-709$ |
6800.1-b1 |
6800.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
6800.1 |
\( 2^{4} \cdot 5^{2} \cdot 17 \) |
\( 2^{4} \cdot 5^{9} \cdot 17^{6} \) |
$1.62292$ |
$(a+1), (-a-2), (a+4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1.645111751$ |
$0.757387099$ |
2.491972834 |
\( \frac{8285953568288}{3017196125} a + \frac{8530762181584}{3017196125} \) |
\( \bigl[i + 1\) , \( -i + 1\) , \( 0\) , \( 53 i + 84\) , \( 165 i - 251\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(53i+84\right){x}+165i-251$ |
21760.1-m1 |
21760.1-m |
$4$ |
$6$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
21760.1 |
\( 2^{8} \cdot 5 \cdot 17 \) |
\( 2^{16} \cdot 5^{3} \cdot 17^{6} \) |
$2.17062$ |
$(a+1), (-a-2), (a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$0.846784519$ |
2.540353559 |
\( \frac{8285953568288}{3017196125} a + \frac{8530762181584}{3017196125} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 28 i - 74\) , \( 86 i - 248\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(28i-74\right){x}+86i-248$ |
27540.1-a1 |
27540.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
27540.1 |
\( 2^{2} \cdot 3^{4} \cdot 5 \cdot 17 \) |
\( 2^{4} \cdot 3^{12} \cdot 5^{3} \cdot 17^{6} \) |
$2.30229$ |
$(a+1), (-a-2), (a+4), (3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{3} \) |
$1$ |
$0.564523013$ |
1.693569039 |
\( \frac{8285953568288}{3017196125} a + \frac{8530762181584}{3017196125} \) |
\( \bigl[i + 1\) , \( i\) , \( 0\) , \( 63 i - 168\) , \( 175 i - 785\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(63i-168\right){x}+175i-785$ |
34000.5-g1 |
34000.5-g |
$4$ |
$6$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
34000.5 |
\( 2^{4} \cdot 5^{3} \cdot 17 \) |
\( 2^{4} \cdot 5^{9} \cdot 17^{6} \) |
$2.42682$ |
$(a+1), (-a-2), (2a+1), (a+4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$0.271449282$ |
$0.757387099$ |
3.700659321 |
\( \frac{8285953568288}{3017196125} a + \frac{8530762181584}{3017196125} \) |
\( \bigl[i + 1\) , \( -i - 1\) , \( i + 1\) , \( -96 i + 28\) , \( -23 i + 301\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(-96i+28\right){x}-23i+301$ |
42500.5-c1 |
42500.5-c |
$4$ |
$6$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
42500.5 |
\( 2^{2} \cdot 5^{4} \cdot 17 \) |
\( 2^{4} \cdot 5^{15} \cdot 17^{6} \) |
$2.56605$ |
$(a+1), (-a-2), (2a+1), (a+4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$0.180962091$ |
$0.338713807$ |
4.413193851 |
\( \frac{8285953568288}{3017196125} a + \frac{8530762181584}{3017196125} \) |
\( \bigl[i + 1\) , \( i + 1\) , \( 0\) , \( 176 i - 465\) , \( 1024 i - 3731\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(i+1\right){x}^{2}+\left(176i-465\right){x}+1024i-3731$ |
87040.1-i1 |
87040.1-i |
$4$ |
$6$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
87040.1 |
\( 2^{10} \cdot 5 \cdot 17 \) |
\( 2^{22} \cdot 5^{3} \cdot 17^{6} \) |
$3.06972$ |
$(a+1), (-a-2), (a+4)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.424610328$ |
$0.598767076$ |
6.101824432 |
\( \frac{8285953568288}{3017196125} a + \frac{8530762181584}{3017196125} \) |
\( \bigl[0\) , \( -i + 1\) , \( 0\) , \( 148 i + 56\) , \( 324 i + 668\bigr] \) |
${y}^2={x}^{3}+\left(-i+1\right){x}^{2}+\left(148i+56\right){x}+324i+668$ |
87040.1-x1 |
87040.1-x |
$4$ |
$6$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
87040.1 |
\( 2^{10} \cdot 5 \cdot 17 \) |
\( 2^{22} \cdot 5^{3} \cdot 17^{6} \) |
$3.06972$ |
$(a+1), (-a-2), (a+4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$0.440042061$ |
$0.598767076$ |
4.742688577 |
\( \frac{8285953568288}{3017196125} a + \frac{8530762181584}{3017196125} \) |
\( \bigl[0\) , \( -i - 1\) , \( 0\) , \( -148 i - 56\) , \( 668 i - 324\bigr] \) |
${y}^2={x}^{3}+\left(-i-1\right){x}^{2}+\left(-148i-56\right){x}+668i-324$ |
98260.3-d1 |
98260.3-d |
$4$ |
$6$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
98260.3 |
\( 2^{2} \cdot 5 \cdot 17^{3} \) |
\( 2^{4} \cdot 5^{3} \cdot 17^{12} \) |
$3.16419$ |
$(a+1), (-a-2), (a+4), (a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$0.629830757$ |
$0.410750825$ |
4.656663064 |
\( \frac{8285953568288}{3017196125} a + \frac{8530762181584}{3017196125} \) |
\( \bigl[i + 1\) , \( -1\) , \( i + 1\) , \( -255 i + 223\) , \( 1122 i + 1778\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}-{x}^{2}+\left(-255i+223\right){x}+1122i+1778$ |
*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.