| 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 |
| 4.1-a1 |
4.1-a |
$2$ |
$5$ |
\(\Q(\sqrt{365}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{6} \cdot 5^{12} \) |
$2.41435$ |
$(2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$3, 5$ |
3Nn, 5B.1.4 |
$1$ |
\( 1 \) |
$1$ |
$54.80625484$ |
2.868690489 |
\( \frac{3307949}{8} \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( -1455 a - 13128\) , \( 77780 a + 704157\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(-1455a-13128\right){x}+77780a+704157$ |
| 4.1-a2 |
4.1-a |
$2$ |
$5$ |
\(\Q(\sqrt{365}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{30} \cdot 5^{12} \) |
$2.41435$ |
$(2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$3, 5$ |
3Nn, 5B.1.3 |
$25$ |
\( 1 \) |
$1$ |
$2.192250193$ |
2.868690489 |
\( \frac{139717566269}{32768} \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( -51330 a - 464628\) , \( -20176720 a - 182649468\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(-51330a-464628\right){x}-20176720a-182649468$ |
| 4.1-b1 |
4.1-b |
$2$ |
$5$ |
\(\Q(\sqrt{365}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{6} \) |
$2.41435$ |
$(2)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$3, 5$ |
3Nn, 5B.1.1 |
$9$ |
\( 1 \) |
$1$ |
$54.80625484$ |
1.032728576 |
\( \frac{3307949}{8} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -55 a - 344\) , \( 260 a + 2721\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-55a-344\right){x}+260a+2721$ |
| 4.1-b2 |
4.1-b |
$2$ |
$5$ |
\(\Q(\sqrt{365}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{30} \) |
$2.41435$ |
$(2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$3, 5$ |
3Nn, 5B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$2.192250193$ |
1.032728576 |
\( \frac{139717566269}{32768} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -2050 a - 18404\) , \( -174544 a - 1579692\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-2050a-18404\right){x}-174544a-1579692$ |
| 7.1-a1 |
7.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{365}) \) |
$2$ |
$[2, 0]$ |
7.1 |
\( 7 \) |
\( - 7^{2} \) |
$2.77690$ |
$(7,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$36$ |
\( 2 \) |
$1$ |
$2.358953226$ |
2.222518591 |
\( -\frac{1461038656717105}{49} a + \frac{14687071500142647}{49} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( 161 a + 1617\) , \( -9385 a - 84451\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(161a+1617\right){x}-9385a-84451$ |
| 7.1-a2 |
7.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{365}) \) |
$2$ |
$[2, 0]$ |
7.1 |
\( 7 \) |
\( 7^{2} \) |
$2.77690$ |
$(7,a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$9$ |
\( 2 \) |
$1$ |
$37.74325162$ |
2.222518591 |
\( \frac{3441}{49} a + \frac{309011}{49} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( -34 a - 148\) , \( 28 a + 762\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-34a-148\right){x}+28a+762$ |
| 7.1-a3 |
7.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{365}) \) |
$2$ |
$[2, 0]$ |
7.1 |
\( 7 \) |
\( 7^{4} \) |
$2.77690$ |
$(7,a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$36$ |
\( 2 \) |
$1$ |
$9.435812905$ |
2.222518591 |
\( -\frac{2998461405}{2401} a + \frac{30164003228}{2401} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( -129 a - 1008\) , \( -2923 a - 25952\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-129a-1008\right){x}-2923a-25952$ |
| 7.1-a4 |
7.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{365}) \) |
$2$ |
$[2, 0]$ |
7.1 |
\( 7 \) |
\( - 7^{8} \) |
$2.77690$ |
$(7,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$36$ |
\( 2 \) |
$1$ |
$2.358953226$ |
2.222518591 |
\( \frac{21289153705921}{5764801} a + \frac{192695676669353}{5764801} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( -1939 a - 17393\) , \( -155705 a - 1409009\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-1939a-17393\right){x}-155705a-1409009$ |
| 7.1-b1 |
7.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{365}) \) |
$2$ |
$[2, 0]$ |
7.1 |
\( 7 \) |
\( - 5^{12} \cdot 7^{2} \) |
$2.77690$ |
$(7,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$39.57492554$ |
$2.358953226$ |
4.886444877 |
\( -\frac{1461038656717105}{49} a + \frac{14687071500142647}{49} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 40667 a - 408770\) , \( 13909351 a - 139823639\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(40667a-408770\right){x}+13909351a-139823639$ |
| 7.1-b2 |
7.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{365}) \) |
$2$ |
$[2, 0]$ |
7.1 |
\( 7 \) |
\( 5^{12} \cdot 7^{2} \) |
$2.77690$ |
$(7,a)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$9.893731385$ |
$37.74325162$ |
4.886444877 |
\( \frac{3441}{49} a + \frac{309011}{49} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 167 a - 1645\) , \( 3476 a - 35014\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(167a-1645\right){x}+3476a-35014$ |
| 7.1-b3 |
7.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{365}) \) |
$2$ |
$[2, 0]$ |
7.1 |
\( 7 \) |
\( 5^{12} \cdot 7^{4} \) |
$2.77690$ |
$(7,a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$19.78746277$ |
$9.435812905$ |
4.886444877 |
\( -\frac{2998461405}{2401} a + \frac{30164003228}{2401} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 2542 a - 25520\) , \( 222601 a - 2237764\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(2542a-25520\right){x}+222601a-2237764$ |
| 7.1-b4 |
7.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{365}) \) |
$2$ |
$[2, 0]$ |
7.1 |
\( 7 \) |
\( - 5^{12} \cdot 7^{8} \) |
$2.77690$ |
$(7,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$9.893731385$ |
$2.358953226$ |
4.886444877 |
\( \frac{21289153705921}{5764801} a + \frac{192695676669353}{5764801} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 2417 a - 24270\) , \( 244351 a - 2456389\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(2417a-24270\right){x}+244351a-2456389$ |
| 7.2-a1 |
7.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{365}) \) |
$2$ |
$[2, 0]$ |
7.2 |
\( 7 \) |
\( - 7^{8} \) |
$2.77690$ |
$(7,a+6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$36$ |
\( 2 \) |
$1$ |
$2.358953226$ |
2.222518591 |
\( -\frac{21289153705921}{5764801} a + \frac{30569261482182}{823543} \) |
\( \bigl[1\) , \( -a\) , \( a\) , \( -97 a - 845\) , \( -1589 a - 14376\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-97a-845\right){x}-1589a-14376$ |
| 7.2-a2 |
7.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{365}) \) |
$2$ |
$[2, 0]$ |
7.2 |
\( 7 \) |
\( 7^{2} \) |
$2.77690$ |
$(7,a+6)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$9$ |
\( 2 \) |
$1$ |
$37.74325162$ |
2.222518591 |
\( -\frac{3441}{49} a + \frac{44636}{7} \) |
\( \bigl[1\) , \( -a\) , \( a\) , \( -7 a - 30\) , \( -6 a - 45\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-7a-30\right){x}-6a-45$ |
| 7.2-a3 |
7.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{365}) \) |
$2$ |
$[2, 0]$ |
7.2 |
\( 7 \) |
\( 7^{4} \) |
$2.77690$ |
$(7,a+6)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$36$ |
\( 2 \) |
$1$ |
$9.435812905$ |
2.222518591 |
\( \frac{2998461405}{2401} a + \frac{3880791689}{343} \) |
\( \bigl[1\) , \( -a\) , \( a\) , \( -102 a - 890\) , \( -1396 a - 12628\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-102a-890\right){x}-1396a-12628$ |
| 7.2-a4 |
7.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{365}) \) |
$2$ |
$[2, 0]$ |
7.2 |
\( 7 \) |
\( - 7^{2} \) |
$2.77690$ |
$(7,a+6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$36$ |
\( 2 \) |
$1$ |
$2.358953226$ |
2.222518591 |
\( \frac{1461038656717105}{49} a + \frac{1889433263346506}{7} \) |
\( \bigl[1\) , \( -a\) , \( a\) , \( -1627 a - 14695\) , \( -105063 a - 951072\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-1627a-14695\right){x}-105063a-951072$ |
| 7.2-b1 |
7.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{365}) \) |
$2$ |
$[2, 0]$ |
7.2 |
\( 7 \) |
\( - 5^{12} \cdot 7^{8} \) |
$2.77690$ |
$(7,a+6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$9.893731385$ |
$2.358953226$ |
4.886444877 |
\( -\frac{21289153705921}{5764801} a + \frac{30569261482182}{823543} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( -2416 a - 21853\) , \( -246768 a - 2233891\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-2416a-21853\right){x}-246768a-2233891$ |
| 7.2-b2 |
7.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{365}) \) |
$2$ |
$[2, 0]$ |
7.2 |
\( 7 \) |
\( 5^{12} \cdot 7^{2} \) |
$2.77690$ |
$(7,a+6)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$9.893731385$ |
$37.74325162$ |
4.886444877 |
\( -\frac{3441}{49} a + \frac{44636}{7} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( -166 a - 1478\) , \( -3643 a - 33016\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-166a-1478\right){x}-3643a-33016$ |
| 7.2-b3 |
7.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{365}) \) |
$2$ |
$[2, 0]$ |
7.2 |
\( 7 \) |
\( 5^{12} \cdot 7^{4} \) |
$2.77690$ |
$(7,a+6)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$19.78746277$ |
$9.435812905$ |
4.886444877 |
\( \frac{2998461405}{2401} a + \frac{3880791689}{343} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( -2541 a - 22978\) , \( -225143 a - 2038141\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-2541a-22978\right){x}-225143a-2038141$ |
| 7.2-b4 |
7.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{365}) \) |
$2$ |
$[2, 0]$ |
7.2 |
\( 7 \) |
\( - 5^{12} \cdot 7^{2} \) |
$2.77690$ |
$(7,a+6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$39.57492554$ |
$2.358953226$ |
4.886444877 |
\( \frac{1461038656717105}{49} a + \frac{1889433263346506}{7} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( -40666 a - 368103\) , \( -13950018 a - 126282391\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-40666a-368103\right){x}-13950018a-126282391$ |
*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.
