| 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 |
| 13520.6-a1 |
13520.6-a |
$4$ |
$10$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
13520.6 |
\( 2^{4} \cdot 5 \cdot 13^{2} \) |
\( 2^{13} \cdot 5^{10} \cdot 13^{9} \) |
$1.92714$ |
$(a+1), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.222869319$ |
0.891477279 |
\( -\frac{80398914857}{19531250} a - \frac{197826917099}{19531250} \) |
\( \bigl[i + 1\) , \( -i - 1\) , \( 0\) , \( 604 i - 1288\) , \( 13984 i - 16632\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(604i-1288\right){x}+13984i-16632$ |
| 13520.6-a2 |
13520.6-a |
$4$ |
$10$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
13520.6 |
\( 2^{4} \cdot 5 \cdot 13^{2} \) |
\( 2^{14} \cdot 5^{5} \cdot 13^{9} \) |
$1.92714$ |
$(a+1), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.445738639$ |
0.891477279 |
\( \frac{10462207}{6250} a - \frac{2706038}{3125} \) |
\( \bigl[i + 1\) , \( -i - 1\) , \( 0\) , \( -136 i - 188\) , \( 1704 i + 672\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(-136i-188\right){x}+1704i+672$ |
| 13520.6-a3 |
13520.6-a |
$4$ |
$10$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
13520.6 |
\( 2^{4} \cdot 5 \cdot 13^{2} \) |
\( 2^{22} \cdot 5 \cdot 13^{9} \) |
$1.92714$ |
$(a+1), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.445738639$ |
0.891477279 |
\( -\frac{523313}{160} a + \frac{424661}{40} \) |
\( \bigl[i + 1\) , \( -i + 1\) , \( i + 1\) , \( -201 i + 302\) , \( 1396 i + 1989\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(-201i+302\right){x}+1396i+1989$ |
| 13520.6-a4 |
13520.6-a |
$4$ |
$10$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
13520.6 |
\( 2^{4} \cdot 5 \cdot 13^{2} \) |
\( 2^{17} \cdot 5^{2} \cdot 13^{9} \) |
$1.92714$ |
$(a+1), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.222869319$ |
0.891477279 |
\( -\frac{12916359143}{200} a + \frac{17274394699}{200} \) |
\( \bigl[i + 1\) , \( -i + 1\) , \( i + 1\) , \( -3161 i + 4702\) , \( 101764 i + 128309\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(-3161i+4702\right){x}+101764i+128309$ |
| 13520.6-b1 |
13520.6-b |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
13520.6 |
\( 2^{4} \cdot 5 \cdot 13^{2} \) |
\( 2^{8} \cdot 5^{2} \cdot 13^{8} \) |
$1.92714$ |
$(a+1), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$1.054021929$ |
1.054021929 |
\( -\frac{8646624}{4225} a - \frac{66027268}{4225} \) |
\( \bigl[i + 1\) , \( -i - 1\) , \( 0\) , \( -66 i - 18\) , \( -190 i + 80\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(-66i-18\right){x}-190i+80$ |
| 13520.6-b2 |
13520.6-b |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
13520.6 |
\( 2^{4} \cdot 5 \cdot 13^{2} \) |
\( 2^{11} \cdot 5^{2} \cdot 13^{14} \) |
$1.92714$ |
$(a+1), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.263505482$ |
1.054021929 |
\( \frac{94078100761841}{20393268025} a - \frac{11284537597913}{20393268025} \) |
\( \bigl[i + 1\) , \( -i - 1\) , \( 0\) , \( 774 i + 332\) , \( 3058 i + 9320\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(774i+332\right){x}+3058i+9320$ |
| 13520.6-b3 |
13520.6-b |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
13520.6 |
\( 2^{4} \cdot 5 \cdot 13^{2} \) |
\( 2^{10} \cdot 5^{4} \cdot 13^{10} \) |
$1.92714$ |
$(a+1), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$0.527010964$ |
1.054021929 |
\( -\frac{15461171586}{17850625} a - \frac{9080741152}{17850625} \) |
\( \bigl[i + 1\) , \( -i - 1\) , \( 0\) , \( -16 i - 138\) , \( -126 i + 1008\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(-16i-138\right){x}-126i+1008$ |
| 13520.6-b4 |
13520.6-b |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
13520.6 |
\( 2^{4} \cdot 5 \cdot 13^{2} \) |
\( 2^{4} \cdot 5 \cdot 13^{7} \) |
$1.92714$ |
$(a+1), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$2.108043858$ |
1.054021929 |
\( \frac{75008}{65} a - \frac{29104}{65} \) |
\( \bigl[i + 1\) , \( -i - 1\) , \( 0\) , \( -6 i + 7\) , \( -10 i - 14\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(-6i+7\right){x}-10i-14$ |
| 13520.6-b5 |
13520.6-b |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
13520.6 |
\( 2^{4} \cdot 5 \cdot 13^{2} \) |
\( 2^{11} \cdot 5^{8} \cdot 13^{8} \) |
$1.92714$ |
$(a+1), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.263505482$ |
1.054021929 |
\( \frac{143087370512191}{66015625} a + \frac{29292377558137}{66015625} \) |
\( \bigl[i + 1\) , \( -i - 1\) , \( 0\) , \( -6 i - 2528\) , \( 626 i + 49768\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(-6i-2528\right){x}+626i+49768$ |
| 13520.6-b6 |
13520.6-b |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
13520.6 |
\( 2^{4} \cdot 5 \cdot 13^{2} \) |
\( 2^{10} \cdot 5 \cdot 13^{7} \) |
$1.92714$ |
$(a+1), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.527010964$ |
1.054021929 |
\( \frac{4355686402}{65} a + \frac{17124606704}{65} \) |
\( \bigl[i + 1\) , \( -i - 1\) , \( 0\) , \( -1076 i - 298\) , \( -12934 i + 5248\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(-1076i-298\right){x}-12934i+5248$ |
| 13520.6-c1 |
13520.6-c |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
13520.6 |
\( 2^{4} \cdot 5 \cdot 13^{2} \) |
\( 2^{30} \cdot 5^{9} \cdot 13^{7} \) |
$1.92714$ |
$(a+1), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$0.133228779$ |
2.398118025 |
\( -\frac{276861163011391}{13000000000} a - \frac{33515586556057}{812500000} \) |
\( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( 4206 i - 3289\) , \( 149030 i - 31276\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(4206i-3289\right){x}+149030i-31276$ |
| 13520.6-c2 |
13520.6-c |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
13520.6 |
\( 2^{4} \cdot 5 \cdot 13^{2} \) |
\( 2^{18} \cdot 5^{3} \cdot 13^{9} \) |
$1.92714$ |
$(a+1), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.399686337$ |
2.398118025 |
\( \frac{37525044319}{2197000} a - \frac{7169596274}{274625} \) |
\( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( -34 i - 549\) , \( 438 i + 5056\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(-34i-549\right){x}+438i+5056$ |
| 13520.6-c3 |
13520.6-c |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
13520.6 |
\( 2^{4} \cdot 5 \cdot 13^{2} \) |
\( 2^{15} \cdot 5^{6} \cdot 13^{12} \) |
$1.92714$ |
$(a+1), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$0.199843168$ |
2.398118025 |
\( \frac{133816114442969}{301675562500} a - \frac{19082395919017}{301675562500} \) |
\( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( -714 i - 269\) , \( -11042 i + 12328\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(-714i-269\right){x}-11042i+12328$ |
| 13520.6-c4 |
13520.6-c |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
13520.6 |
\( 2^{4} \cdot 5 \cdot 13^{2} \) |
\( 2^{21} \cdot 5^{18} \cdot 13^{8} \) |
$1.92714$ |
$(a+1), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$1$ |
$0.066614389$ |
2.398118025 |
\( -\frac{8418015312387897223}{20629882812500000} a + \frac{2783266907131437289}{20629882812500000} \) |
\( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( 6446 i + 2151\) , \( 208998 i - 367724\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(6446i+2151\right){x}+208998i-367724$ |
| 13520.6-c5 |
13520.6-c |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
13520.6 |
\( 2^{4} \cdot 5 \cdot 13^{2} \) |
\( 2^{14} \cdot 5 \cdot 13^{7} \) |
$1.92714$ |
$(a+1), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.199059012$ |
2.398118025 |
\( \frac{31409}{130} a + \frac{101344}{65} \) |
\( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( 6 i + 31\) , \( -2 i + 28\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(6i+31\right){x}-2i+28$ |
| 13520.6-c6 |
13520.6-c |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
13520.6 |
\( 2^{4} \cdot 5 \cdot 13^{2} \) |
\( 2^{13} \cdot 5^{2} \cdot 13^{8} \) |
$1.92714$ |
$(a+1), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.599529506$ |
2.398118025 |
\( \frac{4406742137}{8450} a + \frac{1310300809}{8450} \) |
\( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( 146 i + 371\) , \( -2526 i + 1624\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(146i+371\right){x}-2526i+1624$ |
| 13520.6-d1 |
13520.6-d |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
13520.6 |
\( 2^{4} \cdot 5 \cdot 13^{2} \) |
\( 2^{4} \cdot 5 \cdot 13^{3} \) |
$1.92714$ |
$(a+1), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$5.029222351$ |
2.514611175 |
\( -\frac{256}{5} a + \frac{8048}{5} \) |
\( \bigl[i + 1\) , \( -i + 1\) , \( 0\) , \( -2 i + 1\) , \( -i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(-2i+1\right){x}-i$ |
| 13520.6-d2 |
13520.6-d |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
13520.6 |
\( 2^{4} \cdot 5 \cdot 13^{2} \) |
\( 2^{8} \cdot 5^{2} \cdot 13^{3} \) |
$1.92714$ |
$(a+1), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.514611175$ |
2.514611175 |
\( \frac{4439964}{25} a + \frac{3656648}{25} \) |
\( \bigl[i + 1\) , \( -i + 1\) , \( 0\) , \( -17 i + 11\) , \( -10 i - 33\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(-17i+11\right){x}-10i-33$ |
*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.
