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 |
14400.4-a1 |
14400.4-a |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
14400.4 |
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{12} \cdot 3^{4} \cdot 5^{2} \) |
$2.58987$ |
$(a), (-a+1), (3), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.359738906$ |
$3.273708555$ |
3.560970616 |
\( -\frac{25168}{15} a - \frac{452704}{45} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -5 a + 3\) , \( 2 a - 6\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-5a+3\right){x}+2a-6$ |
14400.4-a2 |
14400.4-a |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
14400.4 |
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{12} \cdot 3^{2} \cdot 5^{4} \) |
$2.58987$ |
$(a), (-a+1), (3), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.179869453$ |
$3.273708555$ |
3.560970616 |
\( \frac{25648}{25} a - \frac{106288}{75} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -2 a\) , \( a - 2\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}-2a{x}+a-2$ |
14400.4-b1 |
14400.4-b |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
14400.4 |
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{12} \cdot 3^{4} \cdot 5^{2} \) |
$2.58987$ |
$(a), (-a+1), (3), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.359738906$ |
$3.273708555$ |
3.560970616 |
\( \frac{25168}{15} a - \frac{528208}{45} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 5 a - 2\) , \( -2 a - 4\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(5a-2\right){x}-2a-4$ |
14400.4-b2 |
14400.4-b |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
14400.4 |
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{12} \cdot 3^{2} \cdot 5^{4} \) |
$2.58987$ |
$(a), (-a+1), (3), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.179869453$ |
$3.273708555$ |
3.560970616 |
\( -\frac{25648}{25} a - \frac{29344}{75} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 4 a - 3\) , \( -4 a + 2\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(4a-3\right){x}-4a+2$ |
14400.4-c1 |
14400.4-c |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
14400.4 |
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{22} \cdot 3^{2} \cdot 5^{16} \) |
$2.58987$ |
$(a), (-a+1), (3), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$3.177609075$ |
$0.382893755$ |
3.678914691 |
\( -\frac{27995042}{1171875} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -80\) , \( -2400\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-80{x}-2400$ |
14400.4-c2 |
14400.4-c |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
14400.4 |
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{20} \cdot 3^{16} \cdot 5^{2} \) |
$2.58987$ |
$(a), (-a+1), (3), (5)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1.588804537$ |
$0.765787510$ |
3.678914691 |
\( \frac{54607676}{32805} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 80\) , \( 80\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+80{x}+80$ |
14400.4-c3 |
14400.4-c |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
14400.4 |
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{16} \cdot 3^{8} \cdot 5^{4} \) |
$2.58987$ |
$(a), (-a+1), (3), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$0.794402268$ |
$1.531575020$ |
3.678914691 |
\( \frac{3631696}{2025} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -20\) , \( 0\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-20{x}$ |
14400.4-c4 |
14400.4-c |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
14400.4 |
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{20} \cdot 3^{4} \cdot 5^{8} \) |
$2.58987$ |
$(a), (-a+1), (3), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1.588804537$ |
$0.765787510$ |
3.678914691 |
\( \frac{868327204}{5625} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -200\) , \( -1152\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-200{x}-1152$ |
14400.4-c5 |
14400.4-c |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
14400.4 |
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{4} \cdot 5^{2} \) |
$2.58987$ |
$(a), (-a+1), (3), (5)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.588804537$ |
$3.063150040$ |
3.678914691 |
\( \frac{24918016}{45} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -15\) , \( 18\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-15{x}+18$ |
14400.4-c6 |
14400.4-c |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
14400.4 |
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{22} \cdot 3^{2} \cdot 5^{4} \) |
$2.58987$ |
$(a), (-a+1), (3), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2 \) |
$3.177609075$ |
$0.382893755$ |
3.678914691 |
\( \frac{1770025017602}{75} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -3200\) , \( -70752\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-3200{x}-70752$ |
14400.4-d1 |
14400.4-d |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
14400.4 |
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{16} \cdot 3^{2} \cdot 5^{2} \) |
$2.58987$ |
$(a), (-a+1), (3), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.885340762$ |
$3.481586885$ |
4.660136837 |
\( \frac{21296}{15} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 4\) , \( 0\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+4{x}$ |
14400.4-d2 |
14400.4-d |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
14400.4 |
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{20} \cdot 3^{4} \cdot 5^{4} \) |
$2.58987$ |
$(a), (-a+1), (3), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1.770681524$ |
$1.740793442$ |
4.660136837 |
\( \frac{470596}{225} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -16\) , \( -16\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-16{x}-16$ |
14400.4-d3 |
14400.4-d |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
14400.4 |
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{22} \cdot 3^{2} \cdot 5^{8} \) |
$2.58987$ |
$(a), (-a+1), (3), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$3.541363048$ |
$0.870396721$ |
4.660136837 |
\( \frac{136835858}{1875} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -136\) , \( 560\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-136{x}+560$ |
14400.4-d4 |
14400.4-d |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
14400.4 |
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{22} \cdot 3^{8} \cdot 5^{2} \) |
$2.58987$ |
$(a), (-a+1), (3), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$3.541363048$ |
$0.870396721$ |
4.660136837 |
\( \frac{546718898}{405} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -216\) , \( -1296\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-216{x}-1296$ |
*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.