| 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 |
| 35.1-a1 |
35.1-a |
$4$ |
$6$ |
3.3.1825.1 |
$3$ |
$[3, 0]$ |
35.1 |
\( 5 \cdot 7 \) |
\( 5^{3} \cdot 7^{12} \) |
$6.90422$ |
$(a-2), (-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$4.697805787$ |
$24.42639829$ |
4.029158180 |
\( -\frac{5523209449580259866763}{69206436005} a^{2} + \frac{761127012824843830457}{69206436005} a + \frac{44841915529379799234402}{69206436005} \) |
\( \bigl[a\) , \( a + 1\) , \( a^{2} - 6\) , \( 17 a - 68\) , \( -33 a^{2} + 24 a + 124\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-6\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(17a-68\right){x}-33a^{2}+24a+124$ |
| 35.1-a2 |
35.1-a |
$4$ |
$6$ |
3.3.1825.1 |
$3$ |
$[3, 0]$ |
35.1 |
\( 5 \cdot 7 \) |
\( 5 \cdot 7^{4} \) |
$6.90422$ |
$(a-2), (-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1.565935262$ |
$73.27919487$ |
4.029158180 |
\( \frac{759176618264}{12005} a^{2} - \frac{2854803868001}{12005} a + \frac{1897150792291}{12005} \) |
\( \bigl[a\) , \( a + 1\) , \( a^{2} - 6\) , \( -5 a^{2} + 17 a - 8\) , \( -17 a^{2} + 67 a - 52\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-6\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-5a^{2}+17a-8\right){x}-17a^{2}+67a-52$ |
| 35.1-a3 |
35.1-a |
$4$ |
$6$ |
3.3.1825.1 |
$3$ |
$[3, 0]$ |
35.1 |
\( 5 \cdot 7 \) |
\( 5^{2} \cdot 7^{2} \) |
$6.90422$ |
$(a-2), (-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$0.782967631$ |
$73.27919487$ |
4.029158180 |
\( -\frac{74247}{49} a^{2} + \frac{1682594}{245} a - \frac{1130363}{245} \) |
\( \bigl[a\) , \( a + 1\) , \( a^{2} - 6\) , \( 2 a + 2\) , \( a^{2} + 2 a - 9\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-6\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(2a+2\right){x}+a^{2}+2a-9$ |
| 35.1-a4 |
35.1-a |
$4$ |
$6$ |
3.3.1825.1 |
$3$ |
$[3, 0]$ |
35.1 |
\( 5 \cdot 7 \) |
\( 5^{6} \cdot 7^{6} \) |
$6.90422$ |
$(a-2), (-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$2.348902893$ |
$24.42639829$ |
4.029158180 |
\( \frac{2499774334544}{2941225} a^{2} + \frac{4172403380589}{2941225} a - \frac{1545634061053}{588245} \) |
\( \bigl[a\) , \( a + 1\) , \( a^{2} - 6\) , \( -8 a + 7\) , \( -8 a^{2} - 11 a + 9\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-6\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-8a+7\right){x}-8a^{2}-11a+9$ |
| 35.1-b1 |
35.1-b |
$4$ |
$6$ |
3.3.1825.1 |
$3$ |
$[3, 0]$ |
35.1 |
\( 5 \cdot 7 \) |
\( 5^{3} \cdot 7^{12} \) |
$6.90422$ |
$(a-2), (-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$6.303107341$ |
0.442633748 |
\( -\frac{5523209449580259866763}{69206436005} a^{2} + \frac{761127012824843830457}{69206436005} a + \frac{44841915529379799234402}{69206436005} \) |
\( \bigl[a^{2} - 6\) , \( 0\) , \( a^{2} - 6\) , \( 399 a^{2} - 55 a - 3249\) , \( 9368 a^{2} - 1293 a - 76062\bigr] \) |
${y}^2+\left(a^{2}-6\right){x}{y}+\left(a^{2}-6\right){y}={x}^{3}+\left(399a^{2}-55a-3249\right){x}+9368a^{2}-1293a-76062$ |
| 35.1-b2 |
35.1-b |
$4$ |
$6$ |
3.3.1825.1 |
$3$ |
$[3, 0]$ |
35.1 |
\( 5 \cdot 7 \) |
\( 5^{6} \cdot 7^{6} \) |
$6.90422$ |
$(a-2), (-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$6.303107341$ |
0.442633748 |
\( \frac{2499774334544}{2941225} a^{2} + \frac{4172403380589}{2941225} a - \frac{1545634061053}{588245} \) |
\( \bigl[a^{2} - 6\) , \( 0\) , \( a^{2} - 6\) , \( 24 a^{2} - 5 a - 199\) , \( 188 a^{2} - 28 a - 1532\bigr] \) |
${y}^2+\left(a^{2}-6\right){x}{y}+\left(a^{2}-6\right){y}={x}^{3}+\left(24a^{2}-5a-199\right){x}+188a^{2}-28a-1532$ |
| 35.1-b3 |
35.1-b |
$4$ |
$6$ |
3.3.1825.1 |
$3$ |
$[3, 0]$ |
35.1 |
\( 5 \cdot 7 \) |
\( 5 \cdot 7^{4} \) |
$6.90422$ |
$(a-2), (-a)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$170.1838982$ |
0.442633748 |
\( \frac{759176618264}{12005} a^{2} - \frac{2854803868001}{12005} a + \frac{1897150792291}{12005} \) |
\( \bigl[a^{2} - 6\) , \( 0\) , \( a^{2} - 6\) , \( 4 a^{2} - 39\) , \( 22 a^{2} - 4 a - 177\bigr] \) |
${y}^2+\left(a^{2}-6\right){x}{y}+\left(a^{2}-6\right){y}={x}^{3}+\left(4a^{2}-39\right){x}+22a^{2}-4a-177$ |
| 35.1-b4 |
35.1-b |
$4$ |
$6$ |
3.3.1825.1 |
$3$ |
$[3, 0]$ |
35.1 |
\( 5 \cdot 7 \) |
\( 5^{2} \cdot 7^{2} \) |
$6.90422$ |
$(a-2), (-a)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$170.1838982$ |
0.442633748 |
\( -\frac{74247}{49} a^{2} + \frac{1682594}{245} a - \frac{1130363}{245} \) |
\( \bigl[a^{2} - 6\) , \( 0\) , \( a^{2} - 6\) , \( -a^{2} + 6\) , \( -a^{2} + 7\bigr] \) |
${y}^2+\left(a^{2}-6\right){x}{y}+\left(a^{2}-6\right){y}={x}^{3}+\left(-a^{2}+6\right){x}-a^{2}+7$ |
*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.
