| 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 |
| 30625.2-a1 |
30625.2-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
30625.2 |
\( 5^{4} \cdot 7^{2} \) |
\( 5^{30} \cdot 7^{2} \) |
$2.04747$ |
$(-3a+1), (3a-2), (5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B[2] |
$1$ |
\( 2^{2} \) |
$0.833160004$ |
$0.154995040$ |
1.192904208 |
\( -\frac{250523582464}{13671875} \) |
\( \bigl[0\) , \( a\) , \( 1\) , \( -3283 a + 3283\) , \( -74657\bigr] \) |
${y}^2+{y}={x}^{3}+a{x}^{2}+\left(-3283a+3283\right){x}-74657$ |
| 30625.3-d1 |
30625.3-d |
$3$ |
$9$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
30625.3 |
\( 5^{4} \cdot 7^{2} \) |
\( 5^{30} \cdot 7^{2} \) |
$2.36422$ |
$(-a-2), (2a+1), (7)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B |
$1$ |
\( 2^{4} \) |
$0.403835458$ |
$0.154995040$ |
4.005919565 |
\( -\frac{250523582464}{13671875} \) |
\( \bigl[0\) , \( 1\) , \( i\) , \( -3283\) , \( 74657\bigr] \) |
${y}^2+i{y}={x}^{3}+{x}^{2}-3283{x}+74657$ |
| 4375.1-b1 |
4375.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4375.1 |
\( 5^{4} \cdot 7 \) |
\( 5^{30} \cdot 7^{2} \) |
$1.92279$ |
$(-2a+1), (5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B |
$1$ |
\( 2^{3} \) |
$0.833160004$ |
$0.154995040$ |
1.561878237 |
\( -\frac{250523582464}{13671875} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -3283\) , \( -74657\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}-3283{x}-74657$ |
| 30625.1-b1 |
30625.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
30625.1 |
\( 5^{4} \cdot 7^{2} \) |
\( 5^{30} \cdot 7^{2} \) |
$3.34351$ |
$(5), (7)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$2.180275799$ |
$0.154995040$ |
3.823263413 |
\( -\frac{250523582464}{13671875} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -3283\) , \( -74657\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}-3283{x}-74657$ |
| 30625.3-c1 |
30625.3-c |
$3$ |
$9$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
30625.3 |
\( 5^{4} \cdot 7^{2} \) |
\( 5^{30} \cdot 7^{2} \) |
$3.92061$ |
$(-a-1), (a-2), (7)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B |
$1$ |
\( 2^{4} \) |
$0.623447633$ |
$0.154995040$ |
3.729335107 |
\( -\frac{250523582464}{13671875} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -3283\) , \( -74657\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}-3283{x}-74657$ |
| 245.1-a1 |
245.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{-15}) \) |
$2$ |
$[0, 1]$ |
245.1 |
\( 5 \cdot 7^{2} \) |
\( 2^{12} \cdot 5^{18} \cdot 7^{2} \) |
$1.36923$ |
$(5,a+2), (7)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$0.833160004$ |
$0.774975202$ |
1.333707449 |
\( -\frac{250523582464}{13671875} \) |
\( \bigl[0\) , \( -a + 1\) , \( a + 1\) , \( 131 a + 393\) , \( -1950 a + 4549\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^3+\left(-a+1\right){x}^2+\left(131a+393\right){x}-1950a+4549$ |
| 245.2-a1 |
245.2-a |
$3$ |
$9$ |
\(\Q(\sqrt{-5}) \) |
$2$ |
$[0, 1]$ |
245.2 |
\( 5 \cdot 7^{2} \) |
\( 5^{18} \cdot 7^{2} \) |
$1.58105$ |
$(-a), (7,a+3), (7,a+4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs |
$1$ |
\( 2 \) |
$0.833160004$ |
$0.774975202$ |
1.155024532 |
\( -\frac{250523582464}{13671875} \) |
\( \bigl[0\) , \( -1\) , \( a\) , \( -131\) , \( 651\bigr] \) |
${y}^2+a{y}={x}^3-{x}^2-131{x}+651$ |
| 35.1-a1 |
35.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{-35}) \) |
$2$ |
$[0, 1]$ |
35.1 |
\( 5 \cdot 7 \) |
\( 3^{12} \cdot 5^{18} \cdot 7^{2} \) |
$1.28585$ |
$(5,a+2), (7,a+3)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cn, 3Cs |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$0.034009387$ |
$0.774975202$ |
1.283054450 |
\( -\frac{250523582464}{13671875} \) |
\( \bigl[0\) , \( a - 1\) , \( 1\) , \( 131 a + 1048\) , \( 5198 a - 11046\bigr] \) |
${y}^2+{y}={x}^3+\left(a-1\right){x}^2+\left(131a+1048\right){x}+5198a-11046$ |
| 245.2-b1 |
245.2-b |
$3$ |
$9$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
245.2 |
\( 5 \cdot 7^{2} \) |
\( 2^{12} \cdot 5^{18} \cdot 7^{2} \) |
$2.23594$ |
$(5,a), (7,a+2), (7,a+5)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs |
$1$ |
\( 2 \cdot 3^{2} \) |
$0.210279443$ |
$0.774975202$ |
3.710369166 |
\( -\frac{250523582464}{13671875} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -525\) , \( 4673\bigr] \) |
${y}^2={x}^3+{x}^2-525{x}+4673$ |
| 245.2-a1 |
245.2-a |
$3$ |
$9$ |
\(\Q(\sqrt{-55}) \) |
$2$ |
$[0, 1]$ |
245.2 |
\( 5 \cdot 7^{2} \) |
\( 5^{30} \cdot 7^{2} \) |
$2.62187$ |
$(5,a+2), (7,a), (7,a+6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs |
$1$ |
\( 2 \) |
$0.833160004$ |
$0.774975202$ |
0.696505999 |
\( -\frac{250523582464}{13671875} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -3283\) , \( -74657\bigr] \) |
${y}^2+{y}={x}^3-{x}^2-3283{x}-74657$ |
| 245.1-a1 |
245.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{-95}) \) |
$2$ |
$[0, 1]$ |
245.1 |
\( 5 \cdot 7^{2} \) |
\( 5^{30} \cdot 7^{2} \) |
$3.44581$ |
$(5,a+2), (7)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs |
$1$ |
\( 2 \) |
$1.772797241$ |
$0.774975202$ |
2.255303809 |
\( -\frac{250523582464}{13671875} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -3283\) , \( -74657\bigr] \) |
${y}^2+{y}={x}^3-{x}^2-3283{x}-74657$ |
| 245.2-b1 |
245.2-b |
$3$ |
$9$ |
\(\Q(\sqrt{-115}) \) |
$2$ |
$[0, 1]$ |
245.2 |
\( 5 \cdot 7^{2} \) |
\( 5^{30} \cdot 7^{2} \) |
$3.79122$ |
$(5,a+2), (7,a+2), (7,a+4)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs |
$1$ |
\( 2 \cdot 3^{2} \) |
$0.520367244$ |
$0.774975202$ |
5.415160449 |
\( -\frac{250523582464}{13671875} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -3283\) , \( -74657\bigr] \) |
${y}^2+{y}={x}^3-{x}^2-3283{x}-74657$ |
| 245.1-a1 |
245.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
245.1 |
\( 5 \cdot 7^{2} \) |
\( 5^{30} \cdot 7^{2} \) |
$3.87276$ |
$(5,a), (7)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs |
$1$ |
\( 2 \) |
$3.959398052$ |
$0.774975202$ |
4.481736622 |
\( -\frac{250523582464}{13671875} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -3283\) , \( -74657\bigr] \) |
${y}^2+{y}={x}^3-{x}^2-3283{x}-74657$ |
| 35.1-c1 |
35.1-c |
$3$ |
$9$ |
\(\Q(\sqrt{-70}) \) |
$2$ |
$[0, 1]$ |
35.1 |
\( 5 \cdot 7 \) |
\( 5^{30} \cdot 7^{2} \) |
$3.63693$ |
$(5,a), (7,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs |
$4$ |
\( 2^{2} \) |
$0.833160004$ |
$0.774975202$ |
2.469546328 |
\( -\frac{250523582464}{13671875} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -3283\) , \( -74657\bigr] \) |
${y}^2+{y}={x}^3-{x}^2-3283{x}-74657$ |
| 35.1-a1 |
35.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{-105}) \) |
$2$ |
$[0, 1]$ |
35.1 |
\( 5 \cdot 7 \) |
\( 5^{30} \cdot 7^{2} \) |
$4.45431$ |
$(5,a), (7,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs |
$1$ |
\( 2^{2} \) |
$0.833160004$ |
$0.774975202$ |
0.504094033 |
\( -\frac{250523582464}{13671875} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -3283\) , \( -74657\bigr] \) |
${y}^2+{y}={x}^3-{x}^2-3283{x}-74657$ |
| 35.1-a1 |
35.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{-455}) \) |
$2$ |
$[0, 1]$ |
35.1 |
\( 5 \cdot 7 \) |
\( 5^{30} \cdot 7^{2} \) |
$4.63619$ |
$(5,a+2), (7,a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs |
$1$ |
\( 2^{2} \) |
$0.833160004$ |
$0.774975202$ |
0.484317881 |
\( -\frac{250523582464}{13671875} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -3283\) , \( -74657\bigr] \) |
${y}^2+{y}={x}^3-{x}^2-3283{x}-74657$ |
| 35.1-a1 |
35.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{-595}) \) |
$2$ |
$[0, 1]$ |
35.1 |
\( 5 \cdot 7 \) |
\( 5^{30} \cdot 7^{2} \) |
$5.30169$ |
$(5,a+2), (7,a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs |
$1$ |
\( 2^{2} \) |
$0.833160004$ |
$1.549950404$ |
0.423523701 |
\( -\frac{250523582464}{13671875} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -3283\) , \( -74657\bigr] \) |
${y}^2+{y}={x}^3-{x}^2-3283{x}-74657$ |
| 35.1-c1 |
35.1-c |
$3$ |
$9$ |
\(\Q(\sqrt{-210}) \) |
$2$ |
$[0, 1]$ |
35.1 |
\( 5 \cdot 7 \) |
\( 5^{30} \cdot 7^{2} \) |
$6.29934$ |
$(5,a), (7,a)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1.212647204$ |
$1.549950404$ |
9.338456947 |
\( -\frac{250523582464}{13671875} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -3283\) , \( -74657\bigr] \) |
${y}^2+{y}={x}^3-{x}^2-3283{x}-74657$ |
| 245.1-a1 |
245.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
245.1 |
\( 5 \cdot 7^{2} \) |
\( 5^{18} \cdot 7^{2} \) |
$0.79052$ |
$(-2a+1), (7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \) |
$0.833160004$ |
$0.494084210$ |
0.736384057 |
\( -\frac{250523582464}{13671875} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -131\) , \( -650\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}-131{x}-650$ |
| 245.1-b1 |
245.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
245.1 |
\( 5 \cdot 7^{2} \) |
\( 2^{12} \cdot 5^{18} \cdot 7^{2} \) |
$2.23594$ |
$(5,a), (7)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3^{2} \) |
$0.526463840$ |
$0.494084210$ |
2.961229198 |
\( -\frac{250523582464}{13671875} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -525\) , \( -4673\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-525{x}-4673$ |
| 35.1-a1 |
35.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
35.1 |
\( 5 \cdot 7 \) |
\( 5^{18} \cdot 7^{2} \) |
$2.22715$ |
$(2a-11), (7,a+3)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$3.380268306$ |
$0.494084210$ |
2.607819218 |
\( -\frac{250523582464}{13671875} \) |
\( \bigl[0\) , \( -a + 1\) , \( 1\) , \( -86155 a - 398325\) , \( -32460825 a - 150081819\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-86155a-398325\right){x}-32460825a-150081819$ |
| 245.1-a1 |
245.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{70 -14 \sqrt{5}})\) |
$4$ |
$[4, 0]$ |
245.1 |
\( 5 \cdot 7^{2} \) |
\( 5^{36} \cdot 7^{4} \) |
$13.91033$ |
$(3a^3+4a^2-17a-13), (-a^3-2a^2+5a+12)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.2 |
$81$ |
\( 2^{2} \) |
$0.833160004$ |
$0.244119206$ |
3.368079379 |
\( -\frac{250523582464}{13671875} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -131\) , \( -650\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}-131{x}-650$ |
*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.
