| 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 |
| 4375.1-b2 |
4375.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4375.1 |
\( 5^{4} \cdot 7 \) |
\( 5^{14} \cdot 7^{2} \) |
$1.92279$ |
$(-2a+1), (5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B |
$1$ |
\( 2^{3} \) |
$0.092573333$ |
$1.394955364$ |
1.561878237 |
\( -\frac{262144}{35} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -33\) , \( 93\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}-33{x}+93$ |
| 35.1-b2 |
35.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{-35}) \) |
$2$ |
$[0, 1]$ |
35.1 |
\( 5 \cdot 7 \) |
\( 5^{2} \cdot 7^{2} \) |
$1.28585$ |
$(5,a+2), (7,a+3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cn, 3Cs.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$6.974776820$ |
1.047957743 |
\( -\frac{262144}{35} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -1\) , \( 0\bigr] \) |
${y}^2+{y}={x}^3+{x}^2-{x}$ |
| 35.1-b2 |
35.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{-70}) \) |
$2$ |
$[0, 1]$ |
35.1 |
\( 5 \cdot 7 \) |
\( 2^{12} \cdot 5^{2} \cdot 7^{2} \) |
$3.63693$ |
$(5,a), (7,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs |
$1$ |
\( 2^{2} \) |
$0.631888037$ |
$6.974776820$ |
4.214163840 |
\( -\frac{262144}{35} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -5\) , \( 7\bigr] \) |
${y}^2={x}^3-{x}^2-5{x}+7$ |
| 35.1-g2 |
35.1-g |
$3$ |
$9$ |
\(\Q(\sqrt{-105}) \) |
$2$ |
$[0, 1]$ |
35.1 |
\( 5 \cdot 7 \) |
\( 3^{12} \cdot 5^{2} \cdot 7^{2} \) |
$4.45431$ |
$(5,a), (7,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$6.974776820$ |
2.722674083 |
\( -\frac{262144}{35} \) |
\( \bigl[0\) , \( 0\) , \( a\) , \( -12\) , \( 44\bigr] \) |
${y}^2+a{y}={x}^3-12{x}+44$ |
| 35.1-d2 |
35.1-d |
$3$ |
$9$ |
\(\Q(\sqrt{-455}) \) |
$2$ |
$[0, 1]$ |
35.1 |
\( 5 \cdot 7 \) |
\( 5^{2} \cdot 7^{2} \cdot 13^{12} \) |
$4.63619$ |
$(5,a+2), (7,a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$6.974776820$ |
2.615860645 |
\( -\frac{262144}{35} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -225\) , \( 1369\bigr] \) |
${y}^2+{y}={x}^3+{x}^2-225{x}+1369$ |
| 35.1-c2 |
35.1-c |
$3$ |
$9$ |
\(\Q(\sqrt{-595}) \) |
$2$ |
$[0, 1]$ |
35.1 |
\( 5 \cdot 7 \) |
\( 5^{2} \cdot 7^{2} \cdot 13^{12} \) |
$5.30169$ |
$(5,a+2), (7,a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$13.94955364$ |
2.287503776 |
\( -\frac{262144}{35} \) |
\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( -11 a + 128\) , \( 12 a + 598\bigr] \) |
${y}^2+{y}={x}^3+\left(-a-1\right){x}^2+\left(-11a+128\right){x}+12a+598$ |
| 35.1-e2 |
35.1-e |
$3$ |
$9$ |
\(\Q(\sqrt{-210}) \) |
$2$ |
$[0, 1]$ |
35.1 |
\( 5 \cdot 7 \) |
\( 5^{2} \cdot 7^{2} \cdot 41^{12} \) |
$6.29934$ |
$(5,a), (7,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs |
$1$ |
\( 2^{2} \) |
$1.682360458$ |
$13.94955364$ |
6.477832400 |
\( -\frac{262144}{35} \) |
\( \bigl[0\) , \( -a + 1\) , \( a + 1\) , \( 154 a - 71\) , \( 2272 a + 42865\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^3+\left(-a+1\right){x}^2+\left(154a-71\right){x}+2272a+42865$ |
| 35.1-b2 |
35.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
35.1 |
\( 5 \cdot 7 \) |
\( 2^{12} \cdot 5^{2} \cdot 7^{2} \) |
$2.22715$ |
$(2a-11), (7,a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$4.862220259$ |
1.898016442 |
\( -\frac{262144}{35} \) |
\( \bigl[0\) , \( 1\) , \( a\) , \( -124 a - 573\) , \( -1929 a - 8924\bigr] \) |
${y}^2+a{y}={x}^{3}+{x}^{2}+\left(-124a-573\right){x}-1929a-8924$ |
| 245.1-b2 |
245.1-b |
$3$ |
$9$ |
4.4.6125.1 |
$4$ |
$[4, 0]$ |
245.1 |
\( 5 \cdot 7^{2} \) |
\( 5^{4} \cdot 7^{4} \) |
$13.91033$ |
$(3a^3+4a^2-17a-13), (-a^3-2a^2+5a+12)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B |
$1$ |
\( 2^{3} \) |
$0.367377802$ |
$23.64118585$ |
3.551232451 |
\( -\frac{262144}{35} \) |
\( \bigl[0\) , \( a^{2} - a - 3\) , \( a^{3} + 2 a^{2} - 6 a - 8\) , \( 37 a^{3} + 48 a^{2} - 237 a - 198\) , \( 149 a^{3} + 183 a^{2} - 946 a - 757\bigr] \) |
${y}^2+\left(a^{3}+2a^{2}-6a-8\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(37a^{3}+48a^{2}-237a-198\right){x}+149a^{3}+183a^{2}-946a-757$ |
*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.
