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 |
123904.1-a1 |
123904.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
123904.1 |
\( 2^{10} \cdot 11^{2} \) |
\( 2^{24} \cdot 11^{2} \) |
$2.90383$ |
$(2), (11)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$0.300686726$ |
$2.139025749$ |
2.970705695 |
\( -\frac{82944}{11} a + \frac{41472}{11} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -7 a + 16\) , \( -14 a - 1\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-7a+16\right){x}-14a-1$ |
123904.1-b1 |
123904.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
123904.1 |
\( 2^{10} \cdot 11^{2} \) |
\( 2^{24} \cdot 11^{6} \) |
$2.90383$ |
$(2), (11)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3Nn[2] |
$1$ |
\( 2 \cdot 3 \) |
$0.113810843$ |
$1.057465715$ |
1.667633279 |
\( \frac{13824}{1331} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -8 a\) , \( 112\bigr] \) |
${y}^2={x}^{3}-8a{x}+112$ |
123904.1-c1 |
123904.1-c |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
123904.1 |
\( 2^{10} \cdot 11^{2} \) |
\( 2^{24} \cdot 11^{2} \) |
$2.90383$ |
$(2), (11)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$0.300686726$ |
$2.139025749$ |
2.970705695 |
\( \frac{82944}{11} a - \frac{41472}{11} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 9 a - 16\) , \( 14 a - 15\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(9a-16\right){x}+14a-15$ |
123904.1-d1 |
123904.1-d |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
123904.1 |
\( 2^{10} \cdot 11^{2} \) |
\( 2^{24} \cdot 11^{2} \) |
$2.90383$ |
$(2), (11)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
|
|
$1$ |
\( 2 \) |
$0.206774281$ |
$1.661708817$ |
1.587014170 |
\( -\frac{2515456}{11} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 45 a\) , \( 133\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+45a{x}+133$ |
123904.1-e1 |
123904.1-e |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
123904.1 |
\( 2^{10} \cdot 11^{2} \) |
\( 2^{24} \cdot 11^{2} \) |
$2.90383$ |
$(2), (11)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$1.208486268$ |
2.790879488 |
\( \frac{8303616}{11} a + \frac{67599872}{11} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 136 a - 141\) , \( 680 a - 347\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(136a-141\right){x}+680a-347$ |
123904.1-f1 |
123904.1-f |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
123904.1 |
\( 2^{10} \cdot 11^{2} \) |
\( 2^{24} \cdot 11^{2} \) |
$2.90383$ |
$(2), (11)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$1.208486268$ |
2.790879488 |
\( -\frac{8303616}{11} a + \frac{75903488}{11} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -5 a + 141\) , \( -680 a + 333\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-5a+141\right){x}-680a+333$ |
123904.1-g1 |
123904.1-g |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
123904.1 |
\( 2^{10} \cdot 11^{2} \) |
\( 2^{24} \cdot 11^{2} \) |
$2.90383$ |
$(2), (11)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
|
|
$1$ |
\( 2 \) |
$0.412611165$ |
$2.347750992$ |
4.474271860 |
\( \frac{512}{11} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -3 a\) , \( -11\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}-3a{x}-11$ |
123904.1-h1 |
123904.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
123904.1 |
\( 2^{10} \cdot 11^{2} \) |
\( 2^{18} \cdot 11^{4} \) |
$2.90383$ |
$(2), (11)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.469985615$ |
$2.205099606$ |
3.742921037 |
\( \frac{74088}{121} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a - 7\) , \( 9 a - 8\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a-7\right){x}+9a-8$ |
123904.1-h2 |
123904.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
123904.1 |
\( 2^{10} \cdot 11^{2} \) |
\( 2^{12} \cdot 11^{2} \) |
$2.90383$ |
$(2), (11)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.734992807$ |
$4.410199213$ |
3.742921037 |
\( \frac{46656}{11} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 3\) , \( 3 a\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a+3\right){x}+3a$ |
123904.1-i1 |
123904.1-i |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
123904.1 |
\( 2^{10} \cdot 11^{2} \) |
\( 2^{24} \cdot 11^{4} \) |
$2.90383$ |
$(2), (11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.543417037$ |
1.782184484 |
\( \frac{216000}{121} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -19 a\) , \( -6 a + 3\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}-19a{x}-6a+3$ |
123904.1-i2 |
123904.1-i |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
123904.1 |
\( 2^{10} \cdot 11^{2} \) |
\( 2^{12} \cdot 11^{2} \) |
$2.90383$ |
$(2), (11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$3.086834075$ |
1.782184484 |
\( \frac{5832000}{11} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -14 a\) , \( 16 a - 8\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}-14a{x}+16a-8$ |
123904.1-j1 |
123904.1-j |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
123904.1 |
\( 2^{10} \cdot 11^{2} \) |
\( 2^{18} \cdot 11^{12} \) |
$2.90383$ |
$(2), (11)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Nn[2] |
$1$ |
\( 2 \cdot 3 \) |
$3.018431820$ |
$0.399464569$ |
4.176863274 |
\( -\frac{17535471192}{1771561} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -433 a\) , \( 4340 a - 2170\bigr] \) |
${y}^2={x}^{3}-433a{x}+4340a-2170$ |
123904.1-j2 |
123904.1-j |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
123904.1 |
\( 2^{10} \cdot 11^{2} \) |
\( 2^{12} \cdot 11^{6} \) |
$2.90383$ |
$(2), (11)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Nn[2] |
$1$ |
\( 2 \cdot 3 \) |
$1.509215910$ |
$0.798929139$ |
4.176863274 |
\( \frac{150229394496}{1331} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -443 a\) , \( 4144 a - 2072\bigr] \) |
${y}^2={x}^{3}-443a{x}+4144a-2072$ |
123904.1-k1 |
123904.1-k |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
123904.1 |
\( 2^{10} \cdot 11^{2} \) |
\( 2^{18} \cdot 11^{12} \) |
$2.90383$ |
$(2), (11)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Nn[2] |
$1$ |
\( 2 \cdot 3 \) |
$3.018431820$ |
$0.399464569$ |
4.176863274 |
\( -\frac{17535471192}{1771561} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 433 a - 433\) , \( -4340 a + 2170\bigr] \) |
${y}^2={x}^{3}+\left(433a-433\right){x}-4340a+2170$ |
123904.1-k2 |
123904.1-k |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
123904.1 |
\( 2^{10} \cdot 11^{2} \) |
\( 2^{12} \cdot 11^{6} \) |
$2.90383$ |
$(2), (11)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Nn[2] |
$1$ |
\( 2 \cdot 3 \) |
$1.509215910$ |
$0.798929139$ |
4.176863274 |
\( \frac{150229394496}{1331} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 443 a - 443\) , \( -4144 a + 2072\bigr] \) |
${y}^2={x}^{3}+\left(443a-443\right){x}-4144a+2072$ |
123904.1-l1 |
123904.1-l |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
123904.1 |
\( 2^{10} \cdot 11^{2} \) |
\( 2^{24} \cdot 11^{4} \) |
$2.90383$ |
$(2), (11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.543417037$ |
1.782184484 |
\( \frac{216000}{121} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -19 a\) , \( 6 a - 3\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}-19a{x}+6a-3$ |
123904.1-l2 |
123904.1-l |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
123904.1 |
\( 2^{10} \cdot 11^{2} \) |
\( 2^{12} \cdot 11^{2} \) |
$2.90383$ |
$(2), (11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$3.086834075$ |
1.782184484 |
\( \frac{5832000}{11} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -14 a\) , \( -16 a + 8\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}-14a{x}-16a+8$ |
123904.1-m1 |
123904.1-m |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
123904.1 |
\( 2^{10} \cdot 11^{2} \) |
\( 2^{18} \cdot 11^{4} \) |
$2.90383$ |
$(2), (11)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.469985615$ |
$2.205099606$ |
3.742921037 |
\( \frac{74088}{121} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a - 7\) , \( -9 a + 8\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(a-7\right){x}-9a+8$ |
123904.1-m2 |
123904.1-m |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
123904.1 |
\( 2^{10} \cdot 11^{2} \) |
\( 2^{12} \cdot 11^{2} \) |
$2.90383$ |
$(2), (11)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.734992807$ |
$4.410199213$ |
3.742921037 |
\( \frac{46656}{11} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 3\) , \( -3 a\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+3\right){x}-3a$ |
123904.1-n1 |
123904.1-n |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
123904.1 |
\( 2^{10} \cdot 11^{2} \) |
\( 2^{24} \cdot 11^{2} \) |
$2.90383$ |
$(2), (11)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
|
|
$1$ |
\( 2 \) |
$0.308894972$ |
$2.347750992$ |
3.349594481 |
\( \frac{512}{11} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 3\) , \( 11\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+3{x}+11$ |
123904.1-o1 |
123904.1-o |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
123904.1 |
\( 2^{10} \cdot 11^{2} \) |
\( 2^{24} \cdot 11^{2} \) |
$2.90383$ |
$(2), (11)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$0.718571393$ |
$1.208486268$ |
4.010892324 |
\( -\frac{8303616}{11} a + \frac{75903488}{11} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -136 a - 5\) , \( 680 a - 333\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-136a-5\right){x}+680a-333$ |
123904.1-p1 |
123904.1-p |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
123904.1 |
\( 2^{10} \cdot 11^{2} \) |
\( 2^{24} \cdot 11^{2} \) |
$2.90383$ |
$(2), (11)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$0.718571393$ |
$1.208486268$ |
4.010892324 |
\( \frac{8303616}{11} a + \frac{67599872}{11} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 5 a + 136\) , \( -680 a + 347\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(5a+136\right){x}-680a+347$ |
123904.1-q1 |
123904.1-q |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
123904.1 |
\( 2^{10} \cdot 11^{2} \) |
\( 2^{24} \cdot 11^{2} \) |
$2.90383$ |
$(2), (11)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
|
|
$1$ |
\( 2 \) |
$0.843949982$ |
$1.661708817$ |
6.477404111 |
\( -\frac{2515456}{11} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -45\) , \( -133\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-45{x}-133$ |
123904.1-r1 |
123904.1-r |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
123904.1 |
\( 2^{10} \cdot 11^{2} \) |
\( 2^{24} \cdot 11^{2} \) |
$2.90383$ |
$(2), (11)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$2.139025749$ |
4.939868369 |
\( \frac{82944}{11} a - \frac{41472}{11} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 9 a - 16\) , \( -14 a + 15\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(9a-16\right){x}-14a+15$ |
123904.1-s1 |
123904.1-s |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
123904.1 |
\( 2^{10} \cdot 11^{2} \) |
\( 2^{24} \cdot 11^{6} \) |
$2.90383$ |
$(2), (11)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3Nn[2] |
$1$ |
\( 2 \cdot 3 \) |
$0.502931376$ |
$1.057465715$ |
7.369289890 |
\( \frac{13824}{1331} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 8\) , \( -112\bigr] \) |
${y}^2={x}^{3}+8{x}-112$ |
123904.1-t1 |
123904.1-t |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
123904.1 |
\( 2^{10} \cdot 11^{2} \) |
\( 2^{24} \cdot 11^{2} \) |
$2.90383$ |
$(2), (11)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$2.139025749$ |
4.939868369 |
\( -\frac{82944}{11} a + \frac{41472}{11} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 17 a - 8\) , \( 6 a + 17\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(17a-8\right){x}+6a+17$ |
*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.