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 |
1.1-a1 |
1.1-a |
$8$ |
$42$ |
\(\Q(\sqrt{2}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$3.57436$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
✓ |
$2, 3, 7$ |
2B, 3B, 7B.1.3 |
$49$ |
\( 1 \) |
$1$ |
$0.925503519$ |
0.283435452 |
\( -4572291148814851641920 a^{3} + 10462525154672292268320 a^{2} + 3492919624948937785472 a - 7992658002021083838208 \) |
\( \bigl[\frac{1}{2} a^{3} - a\) , \( -a - 1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a - 1\) , \( \frac{85}{2} a^{3} + \frac{51}{2} a^{2} - 284 a - 304\) , \( \frac{951}{2} a^{3} + \frac{589}{2} a^{2} - 2911 a - 2650\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-a\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-2a-1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(\frac{85}{2}a^{3}+\frac{51}{2}a^{2}-284a-304\right){x}+\frac{951}{2}a^{3}+\frac{589}{2}a^{2}-2911a-2650$ |
1.1-a2 |
1.1-a |
$8$ |
$42$ |
\(\Q(\sqrt{2}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$3.57436$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
✓ |
$2, 3, 7$ |
2B, 3B, 7B.1.3 |
$49$ |
\( 1 \) |
$1$ |
$0.925503519$ |
0.283435452 |
\( 4572291148814851641920 a^{3} + 10462525154672292268320 a^{2} - 3492919624948937785472 a - 7992658002021083838208 \) |
\( \bigl[\frac{1}{2} a^{3} - a\) , \( a - 1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a - 1\) , \( -43 a^{3} + \frac{51}{2} a^{2} + 284 a - 304\) , \( -\frac{951}{2} a^{3} + \frac{589}{2} a^{2} + 2910 a - 2650\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-a\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-2a-1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-43a^{3}+\frac{51}{2}a^{2}+284a-304\right){x}-\frac{951}{2}a^{3}+\frac{589}{2}a^{2}+2910a-2650$ |
1.1-a3 |
1.1-a |
$8$ |
$42$ |
\(\Q(\sqrt{2}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$3.57436$ |
$\textsf{none}$ |
0 |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
✓ |
$2, 3, 7$ |
2B, 3B, 7B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$2222.133950$ |
0.283435452 |
\( 820352 a^{3} - 717600 a^{2} - 4294784 a + 3756992 \) |
\( \bigl[\frac{1}{2} a^{3} - a\) , \( \frac{1}{2} a^{3} - 2 a\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - a\) , \( \frac{1}{2} a^{2} + a - 1\) , \( 0\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-a\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-a\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-2a\right){x}^{2}+\left(\frac{1}{2}a^{2}+a-1\right){x}$ |
1.1-a4 |
1.1-a |
$8$ |
$42$ |
\(\Q(\sqrt{2}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$3.57436$ |
$\textsf{none}$ |
0 |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
✓ |
$2, 3, 7$ |
2B, 3B, 7B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$2222.133950$ |
0.283435452 |
\( -820352 a^{3} - 717600 a^{2} + 4294784 a + 3756992 \) |
\( \bigl[\frac{1}{2} a^{3} - a\) , \( -\frac{1}{2} a^{3} + 2 a\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - a\) , \( -a^{3} + \frac{1}{2} a^{2} - 1\) , \( -a^{3} + a\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-a\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-a\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+2a\right){x}^{2}+\left(-a^{3}+\frac{1}{2}a^{2}-1\right){x}-a^{3}+a$ |
1.1-a5 |
1.1-a |
$8$ |
$42$ |
\(\Q(\sqrt{2}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$3.57436$ |
$\textsf{none}$ |
0 |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
✓ |
$2, 3, 7$ |
2B, 3B, 7B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$2222.133950$ |
0.283435452 |
\( 313664 a^{3} + 717600 a^{2} - 241280 a - 548608 \) |
\( \bigl[a\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a - 1\) , \( \frac{1}{2} a^{2} + a - 1\) , \( \frac{1}{2} a^{3} - a^{2} + 1\) , \( \frac{1}{2} a^{3} - \frac{3}{2} a^{2} + 1\bigr] \) |
${y}^2+a{x}{y}+\left(\frac{1}{2}a^{2}+a-1\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-2a-1\right){x}^{2}+\left(\frac{1}{2}a^{3}-a^{2}+1\right){x}+\frac{1}{2}a^{3}-\frac{3}{2}a^{2}+1$ |
1.1-a6 |
1.1-a |
$8$ |
$42$ |
\(\Q(\sqrt{2}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$3.57436$ |
$\textsf{none}$ |
0 |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
✓ |
$2, 3, 7$ |
2B, 3B, 7B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$2222.133950$ |
0.283435452 |
\( -313664 a^{3} + 717600 a^{2} + 241280 a - 548608 \) |
\( \bigl[a\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + 2 a - 1\) , \( \frac{1}{2} a^{2} + a - 1\) , \( -a^{3} - a^{2} + a + 1\) , \( -a^{3} - \frac{3}{2} a^{2} + a + 1\bigr] \) |
${y}^2+a{x}{y}+\left(\frac{1}{2}a^{2}+a-1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+2a-1\right){x}^{2}+\left(-a^{3}-a^{2}+a+1\right){x}-a^{3}-\frac{3}{2}a^{2}+a+1$ |
1.1-a7 |
1.1-a |
$8$ |
$42$ |
\(\Q(\sqrt{2}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$3.57436$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
✓ |
$2, 3, 7$ |
2B, 3B, 7B.1.3 |
$49$ |
\( 1 \) |
$1$ |
$0.925503519$ |
0.283435452 |
\( 11970413633970086033024 a^{3} - 10462525154672292268320 a^{2} - 62677899506190812914304 a + 54782492926012669771712 \) |
\( \bigl[a\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 3 a\) , \( \frac{1}{2} a^{2} + a\) , \( \frac{25}{2} a^{3} - 25 a^{2} - 164 a - 151\) , \( -28 a^{3} - 421 a^{2} - 984 a - 681\bigr] \) |
${y}^2+a{x}{y}+\left(\frac{1}{2}a^{2}+a\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-3a\right){x}^{2}+\left(\frac{25}{2}a^{3}-25a^{2}-164a-151\right){x}-28a^{3}-421a^{2}-984a-681$ |
1.1-a8 |
1.1-a |
$8$ |
$42$ |
\(\Q(\sqrt{2}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$3.57436$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
✓ |
$2, 3, 7$ |
2B, 3B, 7B.1.3 |
$49$ |
\( 1 \) |
$1$ |
$0.925503519$ |
0.283435452 |
\( -11970413633970086033024 a^{3} - 10462525154672292268320 a^{2} + 62677899506190812914304 a + 54782492926012669771712 \) |
\( \bigl[a\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + 3 a\) , \( \frac{1}{2} a^{2} + a\) , \( -13 a^{3} - 25 a^{2} + 164 a - 151\) , \( \frac{55}{2} a^{3} - 421 a^{2} + 984 a - 681\bigr] \) |
${y}^2+a{x}{y}+\left(\frac{1}{2}a^{2}+a\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+3a\right){x}^{2}+\left(-13a^{3}-25a^{2}+164a-151\right){x}+\frac{55}{2}a^{3}-421a^{2}+984a-681$ |
*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.