| 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 |
| 14400.1-a1 |
14400.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
14400.1 |
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{16} \cdot 3^{12} \cdot 5^{4} \) |
$2.58987$ |
$(a), (3), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.134291398$ |
$1.081426142$ |
2.634737040 |
\( -\frac{343139}{6075} a + \frac{1391954}{18225} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -2 a + 16\) , \( 17 a + 90\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2a+16\right){x}+17a+90$ |
| 14400.1-a2 |
14400.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
14400.1 |
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{14} \cdot 3^{6} \cdot 5^{2} \) |
$2.58987$ |
$(a), (3), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.268582796$ |
$2.162852284$ |
2.634737040 |
\( -\frac{6507349}{135} a + \frac{3273806}{135} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 13 a + 6\) , \( -8 a + 48\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(13a+6\right){x}-8a+48$ |
| 14400.1-b1 |
14400.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
14400.1 |
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{16} \cdot 3^{2} \cdot 5^{8} \) |
$2.58987$ |
$(a), (3), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.261832364$ |
1.907711219 |
\( \frac{73891081}{1875} a - \frac{37962002}{1875} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 45 a - 32\) , \( 129 a + 17\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(45a-32\right){x}+129a+17$ |
| 14400.1-b2 |
14400.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
14400.1 |
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{14} \cdot 3^{4} \cdot 5^{4} \) |
$2.58987$ |
$(a), (3), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$2.523664729$ |
1.907711219 |
\( \frac{5159}{75} a - \frac{3598}{225} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -2\) , \( 3 a + 5\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-2{x}+3a+5$ |
| 14400.1-b3 |
14400.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
14400.1 |
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{10} \cdot 3^{8} \cdot 5^{2} \) |
$2.58987$ |
$(a), (3), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.523664729$ |
1.907711219 |
\( -\frac{819929}{135} a + \frac{6035234}{405} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 5 a + 6\) , \( -4 a + 8\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(5a+6\right){x}-4a+8$ |
| 14400.1-b4 |
14400.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
14400.1 |
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{16} \cdot 3^{2} \cdot 5^{2} \) |
$2.58987$ |
$(a), (3), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.523664729$ |
1.907711219 |
\( -\frac{1997369}{15} a + \frac{2728978}{15} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 13 a - 12\) , \( 17 a + 1\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(13a-12\right){x}+17a+1$ |
| 14400.1-c1 |
14400.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
14400.1 |
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{22} \cdot 3^{8} \cdot 5^{8} \) |
$2.58987$ |
$(a), (3), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.592420197$ |
0.895655150 |
\( \frac{427962719}{270000} a - \frac{4540203359}{810000} \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( -82 a + 171\) , \( -355 a - 573\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(-82a+171\right){x}-355a-573$ |
| 14400.1-c2 |
14400.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
14400.1 |
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{34} \cdot 3^{2} \cdot 5^{2} \) |
$2.58987$ |
$(a), (3), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.184840394$ |
0.895655150 |
\( \frac{283009199}{327680} a - \frac{2474048159}{983040} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -22 a - 8\) , \( -69 a + 46\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-22a-8\right){x}-69a+46$ |
| 14400.1-c3 |
14400.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
14400.1 |
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{26} \cdot 3^{4} \cdot 5^{4} \) |
$2.58987$ |
$(a), (3), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$1.184840394$ |
0.895655150 |
\( -\frac{26440799}{19200} a - \frac{112620977}{57600} \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( -27 a + 1\) , \( -86 a + 85\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(-27a+1\right){x}-86a+85$ |
| 14400.1-c4 |
14400.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
14400.1 |
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{22} \cdot 3^{2} \cdot 5^{2} \) |
$2.58987$ |
$(a), (3), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.184840394$ |
0.895655150 |
\( \frac{746269231}{80} a + \frac{746269649}{240} \) |
\( \bigl[a\) , \( a - 1\) , \( a\) , \( 25 a - 168\) , \( -262 a + 891\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(25a-168\right){x}-262a+891$ |
| 14400.1-d1 |
14400.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
14400.1 |
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{18} \cdot 3^{32} \cdot 5^{2} \) |
$2.58987$ |
$(a), (3), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$15.27600809$ |
$0.197609980$ |
4.563832806 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( -550 a - 221\) , \( -14407 a + 5499\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(-550a-221\right){x}-14407a+5499$ |
| 14400.1-d2 |
14400.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
14400.1 |
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{18} \cdot 3^{2} \cdot 5^{2} \) |
$2.58987$ |
$(a), (3), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.954750506$ |
$3.161759683$ |
4.563832806 |
\( -\frac{1}{15} \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( -1\) , \( 3 a - 1\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}-{x}+3a-1$ |
| 14400.1-d3 |
14400.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
14400.1 |
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{18} \cdot 3^{4} \cdot 5^{16} \) |
$2.58987$ |
$(a), (3), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.909501012$ |
$0.395219960$ |
4.563832806 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( 175 a + 69\) , \( -648 a + 97\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(175a+69\right){x}-648a+97$ |
| 14400.1-d4 |
14400.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
14400.1 |
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{18} \cdot 3^{8} \cdot 5^{8} \) |
$2.58987$ |
$(a), (3), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$3.819002024$ |
$0.790439920$ |
4.563832806 |
\( \frac{111284641}{50625} \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( -50 a - 21\) , \( -117 a + 79\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(-50a-21\right){x}-117a+79$ |
| 14400.1-d5 |
14400.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
14400.1 |
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{18} \cdot 3^{4} \cdot 5^{4} \) |
$2.58987$ |
$(a), (3), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1.909501012$ |
$1.580879841$ |
4.563832806 |
\( \frac{13997521}{225} \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( -25 a - 11\) , \( 62 a - 3\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(-25a-11\right){x}+62a-3$ |
| 14400.1-d6 |
14400.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
14400.1 |
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{18} \cdot 3^{16} \cdot 5^{4} \) |
$2.58987$ |
$(a), (3), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$7.638004048$ |
$0.395219960$ |
4.563832806 |
\( \frac{272223782641}{164025} \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( -675 a - 271\) , \( -10542 a + 4229\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(-675a-271\right){x}-10542a+4229$ |
| 14400.1-d7 |
14400.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
14400.1 |
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{18} \cdot 3^{2} \cdot 5^{2} \) |
$2.58987$ |
$(a), (3), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$3.819002024$ |
$0.790439920$ |
4.563832806 |
\( \frac{56667352321}{15} \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( -400 a - 161\) , \( 4517 a - 1293\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(-400a-161\right){x}+4517a-1293$ |
| 14400.1-d8 |
14400.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
14400.1 |
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{18} \cdot 3^{8} \cdot 5^{2} \) |
$2.58987$ |
$(a), (3), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$15.27600809$ |
$0.197609980$ |
4.563832806 |
\( \frac{1114544804970241}{405} \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( -10800 a - 4321\) , \( -661377 a + 241559\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(-10800a-4321\right){x}-661377a+241559$ |
| 14400.1-e1 |
14400.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
14400.1 |
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{16} \cdot 3^{4} \cdot 5^{4} \) |
$2.58987$ |
$(a), (3), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.962573393$ |
2.967132073 |
\( \frac{803941}{75} a - \frac{1619806}{225} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -15 a + 12\) , \( -12 a + 31\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-15a+12\right){x}-12a+31$ |
| 14400.1-e2 |
14400.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
14400.1 |
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{14} \cdot 3^{2} \cdot 5^{2} \) |
$2.58987$ |
$(a), (3), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.925146786$ |
2.967132073 |
\( -\frac{349}{15} a - \frac{4354}{15} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 2\) , \( -2 a + 3\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+2{x}-2a+3$ |
*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.
