| 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 |
| 7938.3-d3 |
7938.3-d |
$6$ |
$18$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
7938.3 |
\( 2 \cdot 3^{4} \cdot 7^{2} \) |
\( 2^{12} \cdot 3^{12} \cdot 7^{6} \) |
$2.38568$ |
$(a), (-a-1), (a-1), (7)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$1.108016383$ |
$0.875417135$ |
5.487015846 |
\( \frac{9938375}{21952} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 40\) , \( 155\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+40{x}+155$ |
| 784.2-e3 |
784.2-e |
$6$ |
$18$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
784.2 |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{36} \cdot 7^{6} \) |
$2.31645$ |
$(2,a), (a+1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$4.432065534$ |
$1.313125702$ |
4.751895113 |
\( \frac{9938375}{21952} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 72\) , \( 368\bigr] \) |
${y}^2={x}^3-{x}^2+72{x}+368$ |
| 784.1-b3 |
784.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
784.1 |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{24} \cdot 3^{12} \cdot 7^{6} \) |
$5.17974$ |
$(2,a), (7)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{2} \cdot 3 \) |
$3.035287098$ |
$1.313125702$ |
8.732260775 |
\( \frac{9938375}{21952} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 195\) , \( -1734\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+195{x}-1734$ |
| 14.1-a3 |
14.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-42}) \) |
$2$ |
$[0, 1]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{12} \cdot 7^{18} \) |
$2.24040$ |
$(2,a), (7,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{2} \) |
$4.432065534$ |
$2.626251405$ |
3.592095064 |
\( \frac{9938375}{21952} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( 220\) , \( 2192\bigr] \) |
${y}^2+{x}{y}={x}^3+{x}^2+220{x}+2192$ |
| 98.2-c3 |
98.2-c |
$6$ |
$18$ |
\(\Q(\sqrt{-66}) \) |
$2$ |
$[0, 1]$ |
98.2 |
\( 2 \cdot 7^{2} \) |
\( 2^{12} \cdot 7^{6} \cdot 11^{12} \) |
$4.56822$ |
$(2,a), (7,a+2), (7,a+5)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{2} \cdot 3 \) |
$2.797917772$ |
$2.626251405$ |
10.85376772 |
\( \frac{9938375}{21952} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( 542\) , \( 8196\bigr] \) |
${y}^2+{x}{y}={x}^3+542{x}+8196$ |
| 98.1-d3 |
98.1-d |
$6$ |
$18$ |
\(\Q(\sqrt{-114}) \) |
$2$ |
$[0, 1]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2^{12} \cdot 7^{6} \cdot 19^{12} \) |
$6.00382$ |
$(2,a), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$4.432065534$ |
$2.626251405$ |
19.62287108 |
\( \frac{9938375}{21952} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 1617\) , \( 42677\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2+1617{x}+42677$ |
| 98.2-a3 |
98.2-a |
$6$ |
$18$ |
\(\Q(\sqrt{-138}) \) |
$2$ |
$[0, 1]$ |
98.2 |
\( 2 \cdot 7^{2} \) |
\( 2^{12} \cdot 7^{6} \cdot 23^{12} \) |
$6.60564$ |
$(2,a), (7,a+3), (7,a+4)$ |
$3$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2 \) |
$12.36622502$ |
$5.252502811$ |
11.05844063 |
\( \frac{9938375}{21952} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 2369\) , \( 74706\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+2369{x}+74706$ |
| 98.1-b3 |
98.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{-186}) \) |
$2$ |
$[0, 1]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2^{12} \cdot 7^{6} \cdot 31^{12} \) |
$7.66887$ |
$(2,a), (7)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2 \cdot 3 \) |
$16.19340494$ |
$5.252502811$ |
18.70980462 |
\( \frac{9938375}{21952} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( 4305\) , \( 184229\bigr] \) |
${y}^2+{x}{y}={x}^3+{x}^2+4305{x}+184229$ |
| 14.1-e3 |
14.1-e |
$6$ |
$18$ |
\(\Q(\sqrt{-210}) \) |
$2$ |
$[0, 1]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{12} \cdot 7^{6} \cdot 41^{12} \) |
$5.00968$ |
$(2,a), (7,a)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{3} \cdot 3 \) |
$2.771885873$ |
$5.252502811$ |
12.05627755 |
\( \frac{9938375}{21952} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -537 a + 897\) , \( -11412 a - 285047\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3+\left(-537a+897\right){x}-11412a-285047$ |
| 98.1-g3 |
98.1-g |
$6$ |
$18$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2^{12} \cdot 7^{6} \) |
$1.37737$ |
$(-a+2), (7)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$4.432065534$ |
$3.925715946$ |
1.183854065 |
\( \frac{9938375}{21952} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 4\) , \( -6\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+4{x}-6$ |
*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.
