| 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 |
| 1875.1-a1 |
1875.1-a |
$2$ |
$5$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1875.1 |
\( 3 \cdot 5^{4} \) |
\( 3^{2} \cdot 5^{8} \) |
$2.03695$ |
$(a), (5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$5$ |
5B.1.3 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$1.967118283$ |
3.407148812 |
\( -\frac{102400}{3} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -8\) , \( -7\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}-8{x}-7$ |
| 1875.1-a2 |
1875.1-a |
$2$ |
$5$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1875.1 |
\( 3 \cdot 5^{4} \) |
\( 3^{10} \cdot 5^{16} \) |
$2.03695$ |
$(a), (5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$5$ |
5B.1.4 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$1.967118283$ |
3.407148812 |
\( \frac{20480}{243} \) |
\( \bigl[0\) , \( a - 1\) , \( a\) , \( -2334 a + 4043\) , \( -354472 a + 613963\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-2334a+4043\right){x}-354472a+613963$ |
| 1875.1-b1 |
1875.1-b |
$2$ |
$5$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1875.1 |
\( 3 \cdot 5^{4} \) |
\( 3^{2} \cdot 5^{20} \) |
$2.03695$ |
$(a), (5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$5$ |
5B.4.2 |
$1$ |
\( 2 \) |
$1$ |
$4.360907218$ |
2.517770956 |
\( -\frac{102400}{3} \) |
\( \bigl[0\) , \( -1\) , \( a\) , \( -208\) , \( 1255\bigr] \) |
${y}^2+a{y}={x}^{3}-{x}^{2}-208{x}+1255$ |
| 1875.1-b2 |
1875.1-b |
$2$ |
$5$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1875.1 |
\( 3 \cdot 5^{4} \) |
\( 3^{10} \cdot 5^{4} \) |
$2.03695$ |
$(a), (5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$5$ |
5B.4.1 |
$1$ |
\( 2 \) |
$1$ |
$4.360907218$ |
2.517770956 |
\( \frac{20480}{243} \) |
\( \bigl[0\) , \( a - 1\) , \( 1\) , \( -94 a + 163\) , \( 2938 a - 5089\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-94a+163\right){x}+2938a-5089$ |
| 1875.1-c1 |
1875.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1875.1 |
\( 3 \cdot 5^{4} \) |
\( 3^{32} \cdot 5^{14} \) |
$2.03695$ |
$(a), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$0.509597846$ |
1.176865815 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -2752\) , \( 104476\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-2752{x}+104476$ |
| 1875.1-c2 |
1875.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1875.1 |
\( 3 \cdot 5^{4} \) |
\( 3^{2} \cdot 5^{14} \) |
$2.03695$ |
$(a), (5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$2.038391385$ |
1.176865815 |
\( -\frac{1}{15} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -2\) , \( -24\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-2{x}-24$ |
| 1875.1-c3 |
1875.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1875.1 |
\( 3 \cdot 5^{4} \) |
\( 3^{4} \cdot 5^{28} \) |
$2.03695$ |
$(a), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$0.509597846$ |
1.176865815 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 873\) , \( 5226\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+873{x}+5226$ |
| 1875.1-c4 |
1875.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1875.1 |
\( 3 \cdot 5^{4} \) |
\( 3^{8} \cdot 5^{20} \) |
$2.03695$ |
$(a), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$1$ |
$2.038391385$ |
1.176865815 |
\( \frac{111284641}{50625} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -252\) , \( 726\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-252{x}+726$ |
| 1875.1-c5 |
1875.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1875.1 |
\( 3 \cdot 5^{4} \) |
\( 3^{4} \cdot 5^{16} \) |
$2.03695$ |
$(a), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$1$ |
$2.038391385$ |
1.176865815 |
\( \frac{13997521}{225} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -127\) , \( -524\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-127{x}-524$ |
| 1875.1-c6 |
1875.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1875.1 |
\( 3 \cdot 5^{4} \) |
\( 3^{16} \cdot 5^{16} \) |
$2.03695$ |
$(a), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$1$ |
$2.038391385$ |
1.176865815 |
\( \frac{272223782641}{164025} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -3377\) , \( 75726\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-3377{x}+75726$ |
| 1875.1-c7 |
1875.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1875.1 |
\( 3 \cdot 5^{4} \) |
\( 3^{2} \cdot 5^{14} \) |
$2.03695$ |
$(a), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$0.509597846$ |
1.176865815 |
\( \frac{56667352321}{15} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -2002\) , \( -34274\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-2002{x}-34274$ |
| 1875.1-c8 |
1875.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1875.1 |
\( 3 \cdot 5^{4} \) |
\( 3^{8} \cdot 5^{14} \) |
$2.03695$ |
$(a), (5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$2.038391385$ |
1.176865815 |
\( \frac{1114544804970241}{405} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -54002\) , \( 4834476\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-54002{x}+4834476$ |
| 1875.1-d1 |
1875.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1875.1 |
\( 3 \cdot 5^{4} \) |
\( 3^{32} \cdot 5^{14} \) |
$2.03695$ |
$(a), (5)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$9.603901418$ |
$0.098084444$ |
4.350880830 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2751\) , \( -104477\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-2751{x}-104477$ |
| 1875.1-d2 |
1875.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1875.1 |
\( 3 \cdot 5^{4} \) |
\( 3^{2} \cdot 5^{14} \) |
$2.03695$ |
$(a), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.600243838$ |
$6.277404423$ |
4.350880830 |
\( -\frac{1}{15} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( 23\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}+23$ |
| 1875.1-d3 |
1875.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1875.1 |
\( 3 \cdot 5^{4} \) |
\( 3^{4} \cdot 5^{28} \) |
$2.03695$ |
$(a), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$4.801950709$ |
$0.392337776$ |
4.350880830 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 874\) , \( -5227\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+874{x}-5227$ |
| 1875.1-d4 |
1875.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1875.1 |
\( 3 \cdot 5^{4} \) |
\( 3^{8} \cdot 5^{20} \) |
$2.03695$ |
$(a), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$2.400975354$ |
$1.569351105$ |
4.350880830 |
\( \frac{111284641}{50625} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -251\) , \( -727\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-251{x}-727$ |
| 1875.1-d5 |
1875.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1875.1 |
\( 3 \cdot 5^{4} \) |
\( 3^{4} \cdot 5^{16} \) |
$2.03695$ |
$(a), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1.200487677$ |
$6.277404423$ |
4.350880830 |
\( \frac{13997521}{225} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -126\) , \( 523\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-126{x}+523$ |
| 1875.1-d6 |
1875.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1875.1 |
\( 3 \cdot 5^{4} \) |
\( 3^{16} \cdot 5^{16} \) |
$2.03695$ |
$(a), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$4.801950709$ |
$0.392337776$ |
4.350880830 |
\( \frac{272223782641}{164025} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -3376\) , \( -75727\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-3376{x}-75727$ |
| 1875.1-d7 |
1875.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1875.1 |
\( 3 \cdot 5^{4} \) |
\( 3^{2} \cdot 5^{14} \) |
$2.03695$ |
$(a), (5)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$2.400975354$ |
$6.277404423$ |
4.350880830 |
\( \frac{56667352321}{15} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2001\) , \( 34273\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-2001{x}+34273$ |
| 1875.1-d8 |
1875.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1875.1 |
\( 3 \cdot 5^{4} \) |
\( 3^{8} \cdot 5^{14} \) |
$2.03695$ |
$(a), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$9.603901418$ |
$0.098084444$ |
4.350880830 |
\( \frac{1114544804970241}{405} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -54001\) , \( -4834477\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-54001{x}-4834477$ |
| 1875.1-e1 |
1875.1-e |
$2$ |
$5$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1875.1 |
\( 3 \cdot 5^{4} \) |
\( 3^{2} \cdot 5^{20} \) |
$2.03695$ |
$(a), (5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$5$ |
5B.1.2 |
$1$ |
\( 2 \) |
$4.591654055$ |
$0.393423656$ |
2.085926488 |
\( -\frac{102400}{3} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -208\) , \( -1256\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}-208{x}-1256$ |
| 1875.1-e2 |
1875.1-e |
$2$ |
$5$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1875.1 |
\( 3 \cdot 5^{4} \) |
\( 3^{10} \cdot 5^{4} \) |
$2.03695$ |
$(a), (5)$ |
$1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$5$ |
5B.1.1 |
$1$ |
\( 2 \cdot 5 \) |
$0.918330811$ |
$9.835591419$ |
2.085926488 |
\( \frac{20480}{243} \) |
\( \bigl[0\) , \( -a + 1\) , \( a\) , \( -94 a + 163\) , \( -2938 a + 5088\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-94a+163\right){x}-2938a+5088$ |
| 1875.1-f1 |
1875.1-f |
$2$ |
$5$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1875.1 |
\( 3 \cdot 5^{4} \) |
\( 3^{2} \cdot 5^{8} \) |
$2.03695$ |
$(a), (5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$5$ |
5B.4.2 |
$1$ |
\( 2 \cdot 3 \) |
$0.025588090$ |
$21.80453609$ |
1.932748529 |
\( -\frac{102400}{3} \) |
\( \bigl[0\) , \( 1\) , \( a\) , \( -8\) , \( 6\bigr] \) |
${y}^2+a{y}={x}^{3}+{x}^{2}-8{x}+6$ |
| 1875.1-f2 |
1875.1-f |
$2$ |
$5$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1875.1 |
\( 3 \cdot 5^{4} \) |
\( 3^{10} \cdot 5^{16} \) |
$2.03695$ |
$(a), (5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$5$ |
5B.4.1 |
$1$ |
\( 2 \cdot 3 \cdot 5 \) |
$0.127940452$ |
$0.872181443$ |
1.932748529 |
\( \frac{20480}{243} \) |
\( \bigl[0\) , \( -a + 1\) , \( 1\) , \( -2334 a + 4043\) , \( 354472 a - 613964\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2334a+4043\right){x}+354472a-613964$ |
*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.
