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 |
700.2-a1 |
700.2-a |
$6$ |
$18$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
700.2 |
\( 2^{2} \cdot 5^{2} \cdot 7 \) |
\( 2^{15} \cdot 5^{2} \cdot 7^{2} \) |
$1.21608$ |
$(a), (-a+1), (-2a+1), (5)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$2.024054762$ |
1.530041583 |
\( \frac{13113497519}{17920} a - \frac{3547675441}{8960} \) |
\( \bigl[1\) , \( 1\) , \( a\) , \( -29 a + 9\) , \( 46 a - 73\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-29a+9\right){x}+46a-73$ |
700.2-a2 |
700.2-a |
$6$ |
$18$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
700.2 |
\( 2^{2} \cdot 5^{2} \cdot 7 \) |
\( 2^{15} \cdot 5^{12} \cdot 7^{3} \) |
$1.21608$ |
$(a), (-a+1), (-2a+1), (5)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{2} \cdot 3^{3} \) |
$1$ |
$0.674684920$ |
1.530041583 |
\( -\frac{185012985079}{78400000} a - \frac{376583187511}{392000000} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -4 a + 123\) , \( 396 a - 51\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-4a+123\right){x}+396a-51$ |
700.2-a3 |
700.2-a |
$6$ |
$18$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
700.2 |
\( 2^{2} \cdot 5^{2} \cdot 7 \) |
\( 2^{21} \cdot 5^{6} \cdot 7^{6} \) |
$1.21608$ |
$(a), (-a+1), (-2a+1), (5)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{2} \cdot 3^{3} \) |
$1$ |
$0.674684920$ |
1.530041583 |
\( \frac{9103345957169}{11239424000} a - \frac{2655632525181}{1605632000} \) |
\( \bigl[1\) , \( 1\) , \( a\) , \( -34 a + 104\) , \( 321 a + 134\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-34a+104\right){x}+321a+134$ |
700.2-a4 |
700.2-a |
$6$ |
$18$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
700.2 |
\( 2^{2} \cdot 5^{2} \cdot 7 \) |
\( 2^{21} \cdot 5^{4} \cdot 7 \) |
$1.21608$ |
$(a), (-a+1), (-2a+1), (5)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$2.024054762$ |
1.530041583 |
\( \frac{3747996503}{9175040} a + \frac{31247605623}{22937600} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( a - 12\) , \( a - 10\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(a-12\right){x}+a-10$ |
700.2-a5 |
700.2-a |
$6$ |
$18$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
700.2 |
\( 2^{2} \cdot 5^{2} \cdot 7 \) |
\( 2^{55} \cdot 5^{2} \cdot 7^{2} \) |
$1.21608$ |
$(a), (-a+1), (-2a+1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$1$ |
$0.224894973$ |
1.530041583 |
\( -\frac{41282203518025836237719}{630503947831869440} a + \frac{37460205421439226610825}{126100789566373888} \) |
\( \bigl[1\) , \( 1\) , \( a\) , \( 1891 a - 421\) , \( 17926 a + 35379\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(1891a-421\right){x}+17926a+35379$ |
700.2-a6 |
700.2-a |
$6$ |
$18$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
700.2 |
\( 2^{2} \cdot 5^{2} \cdot 7 \) |
\( 2^{29} \cdot 5^{4} \cdot 7 \) |
$1.21608$ |
$(a), (-a+1), (-2a+1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$1$ |
$0.224894973$ |
1.530041583 |
\( -\frac{810722517917135481181}{23488102400} a + \frac{1861013035614760768527}{23488102400} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -629 a + 10498\) , \( 294721 a - 96726\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-629a+10498\right){x}+294721a-96726$ |
700.2-b1 |
700.2-b |
$6$ |
$18$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
700.2 |
\( 2^{2} \cdot 5^{2} \cdot 7 \) |
\( 2^{15} \cdot 5^{2} \cdot 7^{2} \) |
$1.21608$ |
$(a), (-a+1), (-2a+1), (5)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$2.024054762$ |
1.530041583 |
\( -\frac{13113497519}{17920} a + \frac{6018146637}{17920} \) |
\( \bigl[1\) , \( 1\) , \( a + 1\) , \( 28 a - 20\) , \( -47 a - 27\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(28a-20\right){x}-47a-27$ |
700.2-b2 |
700.2-b |
$6$ |
$18$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
700.2 |
\( 2^{2} \cdot 5^{2} \cdot 7 \) |
\( 2^{15} \cdot 5^{12} \cdot 7^{3} \) |
$1.21608$ |
$(a), (-a+1), (-2a+1), (5)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{2} \cdot 3^{3} \) |
$1$ |
$0.674684920$ |
1.530041583 |
\( \frac{185012985079}{78400000} a - \frac{650824056453}{196000000} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( 4 a + 119\) , \( -396 a + 345\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(4a+119\right){x}-396a+345$ |
700.2-b3 |
700.2-b |
$6$ |
$18$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
700.2 |
\( 2^{2} \cdot 5^{2} \cdot 7 \) |
\( 2^{21} \cdot 5^{6} \cdot 7^{6} \) |
$1.21608$ |
$(a), (-a+1), (-2a+1), (5)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{2} \cdot 3^{3} \) |
$1$ |
$0.674684920$ |
1.530041583 |
\( -\frac{9103345957169}{11239424000} a - \frac{4743040859549}{5619712000} \) |
\( \bigl[1\) , \( 1\) , \( a + 1\) , \( 33 a + 70\) , \( -322 a + 455\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(33a+70\right){x}-322a+455$ |
700.2-b4 |
700.2-b |
$6$ |
$18$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
700.2 |
\( 2^{2} \cdot 5^{2} \cdot 7 \) |
\( 2^{21} \cdot 5^{4} \cdot 7 \) |
$1.21608$ |
$(a), (-a+1), (-2a+1), (5)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$2.024054762$ |
1.530041583 |
\( -\frac{3747996503}{9175040} a + \frac{81235193761}{45875200} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( -a - 11\) , \( -a - 9\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(-a-11\right){x}-a-9$ |
700.2-b5 |
700.2-b |
$6$ |
$18$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
700.2 |
\( 2^{2} \cdot 5^{2} \cdot 7 \) |
\( 2^{55} \cdot 5^{2} \cdot 7^{2} \) |
$1.21608$ |
$(a), (-a+1), (-2a+1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$1$ |
$0.224894973$ |
1.530041583 |
\( \frac{41282203518025836237719}{630503947831869440} a + \frac{73009411794585148408203}{315251973915934720} \) |
\( \bigl[1\) , \( 1\) , \( a + 1\) , \( -1892 a + 1470\) , \( -17927 a + 53305\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-1892a+1470\right){x}-17927a+53305$ |
700.2-b6 |
700.2-b |
$6$ |
$18$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
700.2 |
\( 2^{2} \cdot 5^{2} \cdot 7 \) |
\( 2^{29} \cdot 5^{4} \cdot 7 \) |
$1.21608$ |
$(a), (-a+1), (-2a+1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$1$ |
$0.224894973$ |
1.530041583 |
\( \frac{810722517917135481181}{23488102400} a + \frac{525145258848812643673}{11744051200} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( 629 a + 9869\) , \( -294721 a + 197995\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(629a+9869\right){x}-294721a+197995$ |
700.2-c1 |
700.2-c |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
700.2 |
\( 2^{2} \cdot 5^{2} \cdot 7 \) |
\( 2^{10} \cdot 5^{2} \cdot 7 \) |
$1.21608$ |
$(a), (-a+1), (-2a+1), (5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$3.699948933$ |
2.796898497 |
\( -\frac{385902711}{8960} a - \frac{1290916467}{8960} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 6 a - 7\) , \( 6 a - 1\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(6a-7\right){x}+6a-1$ |
700.2-c2 |
700.2-c |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
700.2 |
\( 2^{2} \cdot 5^{2} \cdot 7 \) |
\( 2^{10} \cdot 5^{2} \cdot 7 \) |
$1.21608$ |
$(a), (-a+1), (-2a+1), (5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$3.699948933$ |
2.796898497 |
\( \frac{385902711}{8960} a - \frac{838409589}{4480} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -6 a - 1\) , \( -6 a + 5\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-6a-1\right){x}-6a+5$ |
700.2-c3 |
700.2-c |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
700.2 |
\( 2^{2} \cdot 5^{2} \cdot 7 \) |
\( 2^{8} \cdot 5^{4} \cdot 7^{2} \) |
$1.21608$ |
$(a), (-a+1), (-2a+1), (5)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$3.699948933$ |
2.796898497 |
\( \frac{1367631}{2800} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 2\) , \( -3\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+2{x}-3$ |
700.2-c4 |
700.2-c |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
700.2 |
\( 2^{2} \cdot 5^{2} \cdot 7 \) |
\( 2^{4} \cdot 5^{8} \cdot 7^{4} \) |
$1.21608$ |
$(a), (-a+1), (-2a+1), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.849974466$ |
2.796898497 |
\( \frac{611960049}{122500} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -18\) , \( -19\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-18{x}-19$ |
700.2-c5 |
700.2-c |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
700.2 |
\( 2^{2} \cdot 5^{2} \cdot 7 \) |
\( 2^{2} \cdot 5^{16} \cdot 7^{2} \) |
$1.21608$ |
$(a), (-a+1), (-2a+1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.924987233$ |
2.796898497 |
\( \frac{74565301329}{5468750} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -88\) , \( 317\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-88{x}+317$ |
700.2-c6 |
700.2-c |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
700.2 |
\( 2^{2} \cdot 5^{2} \cdot 7 \) |
\( 2^{2} \cdot 5^{4} \cdot 7^{8} \) |
$1.21608$ |
$(a), (-a+1), (-2a+1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$0.924987233$ |
2.796898497 |
\( \frac{2121328796049}{120050} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -268\) , \( -1619\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-268{x}-1619$ |
*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.