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 |
2.1-a1 |
2.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{114}) \) |
$2$ |
$[2, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{3} \) |
$2.26923$ |
$(-3a-32)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3Nn |
$16$ |
\( 3 \) |
$5.234562170$ |
$0.872145222$ |
5.130952434 |
\( -\frac{216595158866073603}{4} a + 578150865056023272 \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 65568 a - 700075\) , \( 29846182 a - 318670021\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(65568a-700075\right){x}+29846182a-318670021$ |
2.1-a2 |
2.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{114}) \) |
$2$ |
$[2, 0]$ |
2.1 |
\( 2 \) |
\( 2^{12} \) |
$2.26923$ |
$(-3a-32)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3Nn |
$1$ |
\( 2^{2} \cdot 3 \) |
$5.234562170$ |
$13.95432355$ |
5.130952434 |
\( \frac{2146689}{64} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 258 a - 2755\) , \( 7114 a - 75957\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(258a-2755\right){x}+7114a-75957$ |
2.1-a3 |
2.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{114}) \) |
$2$ |
$[2, 0]$ |
2.1 |
\( 2 \) |
\( 2^{6} \) |
$2.26923$ |
$(-3a-32)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2Cs, 3Nn |
$4$ |
\( 2 \cdot 3 \) |
$10.46912434$ |
$3.488580888$ |
5.130952434 |
\( \frac{8602523649}{8} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 4098 a - 43755\) , \( 465578 a - 4971013\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(4098a-43755\right){x}+465578a-4971013$ |
2.1-a4 |
2.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{114}) \) |
$2$ |
$[2, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{3} \) |
$2.26923$ |
$(-3a-32)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3Nn |
$4$ |
\( 3 \) |
$20.93824868$ |
$0.872145222$ |
5.130952434 |
\( \frac{216595158866073603}{4} a + 578150865056023272 \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 4068 a - 43435\) , \( 472750 a - 5047589\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(4068a-43435\right){x}+472750a-5047589$ |
2.1-b1 |
2.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{114}) \) |
$2$ |
$[2, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{3} \cdot 3^{12} \) |
$2.26923$ |
$(-3a-32)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3Nn |
$4$ |
\( 1 \) |
$1$ |
$19.10792981$ |
0.894810797 |
\( -\frac{216595158866073603}{4} a + 578150865056023272 \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 590112 a - 6300672\) , \( -806437026 a + 8610391232\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(590112a-6300672\right){x}-806437026a+8610391232$ |
2.1-b2 |
2.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{114}) \) |
$2$ |
$[2, 0]$ |
2.1 |
\( 2 \) |
\( 2^{12} \cdot 3^{12} \) |
$2.26923$ |
$(-3a-32)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3Nn |
$1$ |
\( 2 \) |
$1$ |
$38.21585963$ |
0.894810797 |
\( \frac{2146689}{64} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 2322 a - 24792\) , \( -194400 a + 2075624\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(2322a-24792\right){x}-194400a+2075624$ |
2.1-b3 |
2.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{114}) \) |
$2$ |
$[2, 0]$ |
2.1 |
\( 2 \) |
\( 2^{6} \cdot 3^{12} \) |
$2.26923$ |
$(-3a-32)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2Cs, 3Nn |
$4$ |
\( 2 \) |
$1$ |
$38.21585963$ |
0.894810797 |
\( \frac{8602523649}{8} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 36882 a - 393792\) , \( -12607488 a + 134611136\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(36882a-393792\right){x}-12607488a+134611136$ |
2.1-b4 |
2.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{114}) \) |
$2$ |
$[2, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{3} \cdot 3^{12} \) |
$2.26923$ |
$(-3a-32)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3Nn |
$4$ |
\( 1 \) |
$1$ |
$19.10792981$ |
0.894810797 |
\( \frac{216595158866073603}{4} a + 578150865056023272 \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 36612 a - 390912\) , \( -12800862 a + 136675808\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(36612a-390912\right){x}-12800862a+136675808$ |
2.1-c1 |
2.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{114}) \) |
$2$ |
$[2, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{3} \cdot 3^{12} \) |
$2.26923$ |
$(-3a-32)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3Nn |
$4$ |
\( 1 \) |
$1$ |
$19.10792981$ |
0.894810797 |
\( -\frac{216595158866073603}{4} a + 578150865056023272 \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -36612 a - 390912\) , \( 12800862 a + 136675808\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-36612a-390912\right){x}+12800862a+136675808$ |
2.1-c2 |
2.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{114}) \) |
$2$ |
$[2, 0]$ |
2.1 |
\( 2 \) |
\( 2^{12} \cdot 3^{12} \) |
$2.26923$ |
$(-3a-32)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3Nn |
$1$ |
\( 2 \) |
$1$ |
$38.21585963$ |
0.894810797 |
\( \frac{2146689}{64} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -2322 a - 24792\) , \( 194400 a + 2075624\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-2322a-24792\right){x}+194400a+2075624$ |
2.1-c3 |
2.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{114}) \) |
$2$ |
$[2, 0]$ |
2.1 |
\( 2 \) |
\( 2^{6} \cdot 3^{12} \) |
$2.26923$ |
$(-3a-32)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2Cs, 3Nn |
$4$ |
\( 2 \) |
$1$ |
$38.21585963$ |
0.894810797 |
\( \frac{8602523649}{8} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -36882 a - 393792\) , \( 12607488 a + 134611136\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-36882a-393792\right){x}+12607488a+134611136$ |
2.1-c4 |
2.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{114}) \) |
$2$ |
$[2, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{3} \cdot 3^{12} \) |
$2.26923$ |
$(-3a-32)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3Nn |
$4$ |
\( 1 \) |
$1$ |
$19.10792981$ |
0.894810797 |
\( \frac{216595158866073603}{4} a + 578150865056023272 \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -590112 a - 6300672\) , \( 806437026 a + 8610391232\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-590112a-6300672\right){x}+806437026a+8610391232$ |
2.1-d1 |
2.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{114}) \) |
$2$ |
$[2, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{3} \) |
$2.26923$ |
$(-3a-32)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3Nn |
$4$ |
\( 3 \) |
$20.93824868$ |
$0.872145222$ |
5.130952434 |
\( -\frac{216595158866073603}{4} a + 578150865056023272 \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -4068 a - 43435\) , \( -472750 a - 5047589\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-4068a-43435\right){x}-472750a-5047589$ |
2.1-d2 |
2.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{114}) \) |
$2$ |
$[2, 0]$ |
2.1 |
\( 2 \) |
\( 2^{12} \) |
$2.26923$ |
$(-3a-32)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3Nn |
$1$ |
\( 2^{2} \cdot 3 \) |
$5.234562170$ |
$13.95432355$ |
5.130952434 |
\( \frac{2146689}{64} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -258 a - 2755\) , \( -7114 a - 75957\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-258a-2755\right){x}-7114a-75957$ |
2.1-d3 |
2.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{114}) \) |
$2$ |
$[2, 0]$ |
2.1 |
\( 2 \) |
\( 2^{6} \) |
$2.26923$ |
$(-3a-32)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2Cs, 3Nn |
$4$ |
\( 2 \cdot 3 \) |
$10.46912434$ |
$3.488580888$ |
5.130952434 |
\( \frac{8602523649}{8} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -4098 a - 43755\) , \( -465578 a - 4971013\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-4098a-43755\right){x}-465578a-4971013$ |
2.1-d4 |
2.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{114}) \) |
$2$ |
$[2, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{3} \) |
$2.26923$ |
$(-3a-32)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3Nn |
$16$ |
\( 3 \) |
$5.234562170$ |
$0.872145222$ |
5.130952434 |
\( \frac{216595158866073603}{4} a + 578150865056023272 \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -65568 a - 700075\) , \( -29846182 a - 318670021\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-65568a-700075\right){x}-29846182a-318670021$ |
*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.