| 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-a2 |
1.1-a |
$2$ |
$5$ |
\(\Q(\sqrt{-111}) \) |
$2$ |
$[0, 1]$ |
1.1 |
\( 1 \) |
\( 7^{12} \) |
$0.94146$ |
$\textsf{none}$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
✓ |
$3, 5$ |
3Cn, 5B |
$1$ |
\( 1 \) |
$1.027862956$ |
$2.635686227$ |
1.028554772 |
\( 38477541376 \) |
\( \bigl[0\) , \( -a + 1\) , \( 1\) , \( -563 a - 1486\) , \( -14287 a + 263\bigr] \) |
${y}^2+{y}={x}^3+\left(-a+1\right){x}^2+\left(-563a-1486\right){x}-14287a+263$ |
| 1.1-b2 |
1.1-b |
$2$ |
$5$ |
\(\Q(\sqrt{-111}) \) |
$2$ |
$[0, 1]$ |
1.1 |
\( 1 \) |
\( 7^{12} \) |
$0.94146$ |
$\textsf{none}$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
✓ |
$3, 5$ |
3Cn, 5B |
$1$ |
\( 1 \) |
$1.027862956$ |
$2.635686227$ |
1.028554772 |
\( 38477541376 \) |
\( \bigl[0\) , \( a\) , \( 1\) , \( 563 a - 2049\) , \( 14287 a - 14024\bigr] \) |
${y}^2+{y}={x}^3+a{x}^2+\left(563a-2049\right){x}+14287a-14024$ |
| 144.1-a2 |
144.1-a |
$2$ |
$5$ |
\(\Q(\sqrt{-111}) \) |
$2$ |
$[0, 1]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{6} \) |
$3.26130$ |
$(2,a), (3,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 5$ |
3Cn, 5B |
$1$ |
\( 1 \) |
$11.10985461$ |
$1.521714153$ |
3.209297383 |
\( 38477541376 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 3367\) , \( -15457 a + 6045\bigr] \) |
${y}^2={x}^3+\left(-a-1\right){x}^2+\left(a+3367\right){x}-15457a+6045$ |
| 144.1-d2 |
144.1-d |
$2$ |
$5$ |
\(\Q(\sqrt{-111}) \) |
$2$ |
$[0, 1]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{6} \cdot 5^{12} \) |
$3.26130$ |
$(2,a), (3,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 5$ |
3Cn, 5B |
$1$ |
\( 1 \) |
$24.11724345$ |
$1.521714153$ |
6.966734397 |
\( 38477541376 \) |
\( \bigl[0\) , \( -a - 1\) , \( a\) , \( 3588 a + 7587\) , \( 16016 a + 1195021\bigr] \) |
${y}^2+a{y}={x}^3+\left(-a-1\right){x}^2+\left(3588a+7587\right){x}+16016a+1195021$ |
| 144.5-a2 |
144.5-a |
$2$ |
$5$ |
\(\Q(\sqrt{-111}) \) |
$2$ |
$[0, 1]$ |
144.5 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{6} \) |
$3.26130$ |
$(2,a+1), (3,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 5$ |
3Cn, 5B |
$1$ |
\( 1 \) |
$11.10985461$ |
$1.521714153$ |
3.209297383 |
\( 38477541376 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 3367\) , \( 15457 a - 6045\bigr] \) |
${y}^2={x}^3+\left(a+1\right){x}^2+\left(a+3367\right){x}+15457a-6045$ |
| 144.5-d2 |
144.5-d |
$2$ |
$5$ |
\(\Q(\sqrt{-111}) \) |
$2$ |
$[0, 1]$ |
144.5 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{6} \cdot 5^{12} \) |
$3.26130$ |
$(2,a+1), (3,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 5$ |
3Cn, 5B |
$1$ |
\( 1 \) |
$24.11724345$ |
$1.521714153$ |
6.966734397 |
\( 38477541376 \) |
\( \bigl[0\) , \( a + 1\) , \( a + 1\) , \( -3586 a + 11174\) , \( -19604 a + 1222211\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^3+\left(a+1\right){x}^2+\left(-3586a+11174\right){x}-19604a+1222211$ |
| 256.5-a2 |
256.5-a |
$2$ |
$5$ |
\(\Q(\sqrt{-111}) \) |
$2$ |
$[0, 1]$ |
256.5 |
\( 2^{8} \) |
\( 2^{24} \cdot 7^{12} \) |
$3.76582$ |
$(2,a), (2,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 5$ |
3Cn, 5B |
$1$ |
\( 1 \) |
$32.02370302$ |
$1.317843113$ |
8.011314248 |
\( 38477541376 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -9003 a - 23641\) , \( 938063 a - 292683\bigr] \) |
${y}^2={x}^3+\left(a-1\right){x}^2+\left(-9003a-23641\right){x}+938063a-292683$ |
| 256.5-b2 |
256.5-b |
$2$ |
$5$ |
\(\Q(\sqrt{-111}) \) |
$2$ |
$[0, 1]$ |
256.5 |
\( 2^{8} \) |
\( 2^{24} \cdot 7^{12} \) |
$3.76582$ |
$(2,a), (2,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 5$ |
3Cn, 5B |
$1$ |
\( 1 \) |
$32.02370302$ |
$1.317843113$ |
8.011314248 |
\( 38477541376 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 9003 a - 32644\) , \( -938063 a + 645380\bigr] \) |
${y}^2={x}^3-a{x}^2+\left(9003a-32644\right){x}-938063a+645380$ |
| 441.1-a2 |
441.1-a |
$2$ |
$5$ |
\(\Q(\sqrt{-111}) \) |
$2$ |
$[0, 1]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{6} \cdot 5^{12} \cdot 7^{6} \) |
$4.31429$ |
$(3,a+1), (7,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 5$ |
3Cn, 5B |
$1$ |
\( 1 \) |
$6.490282766$ |
$1.150307775$ |
1.417249068 |
\( 38477541376 \) |
\( \bigl[0\) , \( a + 1\) , \( 1\) , \( 6753 a - 13302\) , \( 481998 a + 698324\bigr] \) |
${y}^2+{y}={x}^3+\left(a+1\right){x}^2+\left(6753a-13302\right){x}+481998a+698324$ |
| 441.1-d2 |
441.1-d |
$2$ |
$5$ |
\(\Q(\sqrt{-111}) \) |
$2$ |
$[0, 1]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( 2^{12} \cdot 3^{6} \cdot 7^{6} \) |
$4.31429$ |
$(3,a+1), (7,a)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 5$ |
3Cn, 5B |
|
\( 1 \) |
$1$ |
$1.150307775$ |
26.48431954 |
\( 38477541376 \) |
\( \bigl[0\) , \( a + 1\) , \( a\) , \( 212 a - 5917\) , \( 7464 a - 176373\bigr] \) |
${y}^2+a{y}={x}^3+\left(a+1\right){x}^2+\left(212a-5917\right){x}+7464a-176373$ |
| 441.3-a2 |
441.3-a |
$2$ |
$5$ |
\(\Q(\sqrt{-111}) \) |
$2$ |
$[0, 1]$ |
441.3 |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{6} \cdot 5^{12} \cdot 7^{6} \) |
$4.31429$ |
$(3,a+1), (7,a+6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 5$ |
3Cn, 5B |
$1$ |
\( 1 \) |
$6.490282766$ |
$1.150307775$ |
1.417249068 |
\( 38477541376 \) |
\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( -6751 a - 6550\) , \( -475246 a + 1186872\bigr] \) |
${y}^2+{y}={x}^3+\left(-a-1\right){x}^2+\left(-6751a-6550\right){x}-475246a+1186872$ |
| 441.3-d2 |
441.3-d |
$2$ |
$5$ |
\(\Q(\sqrt{-111}) \) |
$2$ |
$[0, 1]$ |
441.3 |
\( 3^{2} \cdot 7^{2} \) |
\( 2^{12} \cdot 3^{6} \cdot 7^{6} \) |
$4.31429$ |
$(3,a+1), (7,a+6)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 5$ |
3Cn, 5B |
|
\( 1 \) |
$1$ |
$1.150307775$ |
26.48431954 |
\( 38477541376 \) |
\( \bigl[0\) , \( -a - 1\) , \( a + 1\) , \( -210 a - 5706\) , \( -7254 a - 163203\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^3+\left(-a-1\right){x}^2+\left(-210a-5706\right){x}-7254a-163203$ |
| 625.3-a2 |
625.3-a |
$2$ |
$5$ |
\(\Q(\sqrt{-111}) \) |
$2$ |
$[0, 1]$ |
625.3 |
\( 5^{4} \) |
\( 5^{12} \cdot 7^{12} \) |
$4.70728$ |
$(5,a+1), (5,a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 5$ |
3Cn, 5B |
$1$ |
\( 2^{2} \) |
$11.76437019$ |
$1.054274491$ |
9.417830684 |
\( 38477541376 \) |
\( \bigl[0\) , \( a - 1\) , \( 1\) , \( -14067 a - 36934\) , \( -1859851 a + 894746\bigr] \) |
${y}^2+{y}={x}^3+\left(a-1\right){x}^2+\left(-14067a-36934\right){x}-1859851a+894746$ |
| 625.3-d2 |
625.3-d |
$2$ |
$5$ |
\(\Q(\sqrt{-111}) \) |
$2$ |
$[0, 1]$ |
625.3 |
\( 5^{4} \) |
\( 5^{12} \cdot 7^{12} \) |
$4.70728$ |
$(5,a+1), (5,a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 5$ |
3Cn, 5B |
$1$ |
\( 2^{2} \) |
$11.76437019$ |
$1.054274491$ |
9.417830684 |
\( 38477541376 \) |
\( \bigl[0\) , \( -a\) , \( 1\) , \( 14067 a - 51001\) , \( 1859851 a - 965105\bigr] \) |
${y}^2+{y}={x}^3-a{x}^2+\left(14067a-51001\right){x}+1859851a-965105$ |
| 784.1-a2 |
784.1-a |
$2$ |
$5$ |
\(\Q(\sqrt{-111}) \) |
$2$ |
$[0, 1]$ |
784.1 |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{12} \cdot 7^{18} \) |
$4.98172$ |
$(2,a), (7,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 5$ |
3Cn, 5B |
$1$ |
\( 1 \) |
$24.67886797$ |
$0.996195756$ |
4.667006741 |
\( 38477541376 \) |
\( \bigl[0\) , \( a - 1\) , \( a\) , \( -17232 a + 41347\) , \( -562313 a + 11566577\bigr] \) |
${y}^2+a{y}={x}^3+\left(a-1\right){x}^2+\left(-17232a+41347\right){x}-562313a+11566577$ |
| 784.1-b2 |
784.1-b |
$2$ |
$5$ |
\(\Q(\sqrt{-111}) \) |
$2$ |
$[0, 1]$ |
784.1 |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{12} \cdot 7^{18} \) |
$4.98172$ |
$(2,a), (7,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 5$ |
3Cn, 5B |
$1$ |
\( 1 \) |
$27.57398019$ |
$0.996195756$ |
5.214499773 |
\( 38477541376 \) |
\( \bigl[0\) , \( 1\) , \( a\) , \( 13715 a + 57111\) , \( 655242 a - 11323145\bigr] \) |
${y}^2+a{y}={x}^3+{x}^2+\left(13715a+57111\right){x}+655242a-11323145$ |
| 784.13-a2 |
784.13-a |
$2$ |
$5$ |
\(\Q(\sqrt{-111}) \) |
$2$ |
$[0, 1]$ |
784.13 |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{12} \cdot 7^{6} \) |
$4.98172$ |
$(2,a+1), (7,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 5$ |
3Cn, 5B |
$1$ |
\( 1 \) |
$8.576503935$ |
$0.996195756$ |
1.621897800 |
\( 38477541376 \) |
\( \bigl[0\) , \( a\) , \( a + 1\) , \( 352 a + 483\) , \( -1400 a - 34890\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^3+a{x}^2+\left(352a+483\right){x}-1400a-34890$ |
| 784.13-d2 |
784.13-d |
$2$ |
$5$ |
\(\Q(\sqrt{-111}) \) |
$2$ |
$[0, 1]$ |
784.13 |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{12} \cdot 3^{12} \cdot 7^{6} \) |
$4.98172$ |
$(2,a+1), (7,a)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 5$ |
3Cn, 5B |
|
\( 1 \) |
$1$ |
$0.996195756$ |
16.32001708 |
\( 38477541376 \) |
\( \bigl[0\) , \( 0\) , \( a + 1\) , \( 3165 a + 4431\) , \( 45348 a + 853571\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^3+\left(3165a+4431\right){x}+45348a+853571$ |
| 784.15-a2 |
784.15-a |
$2$ |
$5$ |
\(\Q(\sqrt{-111}) \) |
$2$ |
$[0, 1]$ |
784.15 |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{12} \cdot 7^{18} \) |
$4.98172$ |
$(2,a+1), (7,a+6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 5$ |
3Cn, 5B |
$1$ |
\( 1 \) |
$24.67886797$ |
$0.996195756$ |
4.667006741 |
\( 38477541376 \) |
\( \bigl[0\) , \( -a\) , \( a + 1\) , \( 17232 a + 24115\) , \( 562312 a + 11004264\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^3-a{x}^2+\left(17232a+24115\right){x}+562312a+11004264$ |
| 784.15-b2 |
784.15-b |
$2$ |
$5$ |
\(\Q(\sqrt{-111}) \) |
$2$ |
$[0, 1]$ |
784.15 |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{12} \cdot 7^{18} \) |
$4.98172$ |
$(2,a+1), (7,a+6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 5$ |
3Cn, 5B |
$1$ |
\( 1 \) |
$27.57398019$ |
$0.996195756$ |
5.214499773 |
\( 38477541376 \) |
\( \bigl[0\) , \( 1\) , \( a + 1\) , \( -13715 a + 70826\) , \( -655243 a - 10667903\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^3+{x}^2+\left(-13715a+70826\right){x}-655243a-10667903$ |
| 784.3-a2 |
784.3-a |
$2$ |
$5$ |
\(\Q(\sqrt{-111}) \) |
$2$ |
$[0, 1]$ |
784.3 |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{12} \cdot 7^{6} \) |
$4.98172$ |
$(2,a), (7,a+6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 5$ |
3Cn, 5B |
$1$ |
\( 1 \) |
$8.576503935$ |
$0.996195756$ |
1.621897800 |
\( 38477541376 \) |
\( \bigl[0\) , \( -a + 1\) , \( a\) , \( -352 a + 835\) , \( 1399 a - 36289\bigr] \) |
${y}^2+a{y}={x}^3+\left(-a+1\right){x}^2+\left(-352a+835\right){x}+1399a-36289$ |
| 784.3-d2 |
784.3-d |
$2$ |
$5$ |
\(\Q(\sqrt{-111}) \) |
$2$ |
$[0, 1]$ |
784.3 |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{12} \cdot 3^{12} \cdot 7^{6} \) |
$4.98172$ |
$(2,a), (7,a+6)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 5$ |
3Cn, 5B |
|
\( 1 \) |
$1$ |
$0.996195756$ |
16.32001708 |
\( 38477541376 \) |
\( \bigl[0\) , \( 0\) , \( a\) , \( -3165 a + 7596\) , \( -45349 a + 898920\bigr] \) |
${y}^2+a{y}={x}^3+\left(-3165a+7596\right){x}-45349a+898920$ |
*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.
