| Label |
Cremona label |
Class |
Cremona class |
Class size |
Class degree |
Conductor |
Discriminant |
Rank |
Torsion |
$\textrm{End}^0(E_{\overline\Q})$ |
CM |
Sato-Tate |
Semistable |
Potentially good |
Nonmax $\ell$ |
$\ell$-adic images |
mod-$\ell$ images |
Adelic level |
Adelic index |
Adelic genus |
Regulator |
$Ш_{\textrm{an}}$ |
Ш primes |
Integral points |
Modular degree |
Faltings height |
j-invariant |
$abc$ quality |
Szpiro ratio |
Weierstrass coefficients |
Weierstrass equation |
mod-$m$ images |
MW-generators |
| 2415.h4 |
2415e1 |
2415.h |
2415e |
$4$ |
$4$ |
\( 3 \cdot 5 \cdot 7 \cdot 23 \) |
\( 3 \cdot 5 \cdot 7^{4} \cdot 23 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
4.6.0.1 |
2B |
$19320$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$352$ |
$-0.174813$ |
$1439069689/828345$ |
$0.89965$ |
$2.70716$ |
$[1, 0, 1, -24, 1]$ |
\(y^2+xy+y=x^3-24x+1\) |
2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.2, 56.12.0-4.c.1.5, 168.24.0.?, $\ldots$ |
$[]$ |
| 7245.h4 |
7245t1 |
7245.h |
7245t |
$4$ |
$4$ |
\( 3^{2} \cdot 5 \cdot 7 \cdot 23 \) |
\( 3^{7} \cdot 5 \cdot 7^{4} \cdot 23 \) |
$0$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.12.0.7 |
2B |
$19320$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$3$ |
$2816$ |
$0.374493$ |
$1439069689/828345$ |
$0.89965$ |
$3.11417$ |
$[1, -1, 1, -212, -34]$ |
\(y^2+xy+y=x^3-x^2-212x-34\) |
2.3.0.a.1, 4.12.0-4.c.1.1, 168.24.0.?, 690.6.0.?, 1380.24.0.?, $\ldots$ |
$[]$ |
| 12075.f4 |
12075d1 |
12075.f |
12075d |
$4$ |
$4$ |
\( 3 \cdot 5^{2} \cdot 7 \cdot 23 \) |
\( 3 \cdot 5^{7} \cdot 7^{4} \cdot 23 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$19320$ |
$48$ |
$0$ |
$1.582938520$ |
$1$ |
|
$7$ |
$8448$ |
$0.629906$ |
$1439069689/828345$ |
$0.89965$ |
$3.27101$ |
$[1, 1, 1, -588, 156]$ |
\(y^2+xy+y=x^3+x^2-588x+156\) |
2.3.0.a.1, 4.6.0.c.1, 60.12.0-4.c.1.2, 92.12.0.?, 168.12.0.?, $\ldots$ |
$[(0, 12)]$ |
| 16905.w4 |
16905p1 |
16905.w |
16905p |
$4$ |
$4$ |
\( 3 \cdot 5 \cdot 7^{2} \cdot 23 \) |
\( 3 \cdot 5 \cdot 7^{10} \cdot 23 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.6 |
2B |
$19320$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$16896$ |
$0.798142$ |
$1439069689/828345$ |
$0.89965$ |
$3.36533$ |
$[1, 1, 0, -1152, -1581]$ |
\(y^2+xy=x^3+x^2-1152x-1581\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 84.12.0.?, 168.24.0.?, $\ldots$ |
$[]$ |
| 36225.bp4 |
36225bi1 |
36225.bp |
36225bi |
$4$ |
$4$ |
\( 3^{2} \cdot 5^{2} \cdot 7 \cdot 23 \) |
\( 3^{7} \cdot 5^{7} \cdot 7^{4} \cdot 23 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$19320$ |
$48$ |
$0$ |
$2.699919133$ |
$1$ |
|
$1$ |
$67584$ |
$1.179213$ |
$1439069689/828345$ |
$0.89965$ |
$3.55661$ |
$[1, -1, 0, -5292, -9509]$ |
\(y^2+xy=x^3-x^2-5292x-9509\) |
2.3.0.a.1, 4.6.0.c.1, 20.12.0-4.c.1.2, 168.12.0.?, 276.12.0.?, $\ldots$ |
$[(-109/2, 2809/2)]$ |
| 38640.o4 |
38640bf1 |
38640.o |
38640bf |
$4$ |
$4$ |
\( 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 23 \) |
\( 2^{12} \cdot 3 \cdot 5 \cdot 7^{4} \cdot 23 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$19320$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$22528$ |
$0.518334$ |
$1439069689/828345$ |
$0.89965$ |
$2.78403$ |
$[0, -1, 0, -376, -80]$ |
\(y^2=x^3-x^2-376x-80\) |
2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.1, 56.12.0-4.c.1.5, 168.24.0.?, $\ldots$ |
$[]$ |
| 50715.q4 |
50715s1 |
50715.q |
50715s |
$4$ |
$4$ |
\( 3^{2} \cdot 5 \cdot 7^{2} \cdot 23 \) |
\( 3^{7} \cdot 5 \cdot 7^{10} \cdot 23 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$19320$ |
$48$ |
$0$ |
$3.631035268$ |
$1$ |
|
$3$ |
$135168$ |
$1.347448$ |
$1439069689/828345$ |
$0.89965$ |
$3.63250$ |
$[1, -1, 1, -10373, 32316]$ |
\(y^2+xy+y=x^3-x^2-10373x+32316\) |
2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.3, 28.12.0-4.c.1.2, 168.24.0.?, $\ldots$ |
$[(-22, 510)]$ |
| 55545.v4 |
55545t1 |
55545.v |
55545t |
$4$ |
$4$ |
\( 3 \cdot 5 \cdot 7 \cdot 23^{2} \) |
\( 3 \cdot 5 \cdot 7^{4} \cdot 23^{7} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$19320$ |
$48$ |
$0$ |
$1$ |
$9$ |
$3$ |
$1$ |
$185856$ |
$1.392935$ |
$1439069689/828345$ |
$0.89965$ |
$3.65221$ |
$[1, 0, 1, -12443, -40087]$ |
\(y^2+xy+y=x^3-12443x-40087\) |
2.3.0.a.1, 4.6.0.c.1, 20.12.0-4.c.1.2, 168.12.0.?, 276.12.0.?, $\ldots$ |
$[]$ |
| 84525.r4 |
84525ca1 |
84525.r |
84525ca |
$4$ |
$4$ |
\( 3 \cdot 5^{2} \cdot 7^{2} \cdot 23 \) |
\( 3 \cdot 5^{7} \cdot 7^{10} \cdot 23 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$19320$ |
$48$ |
$0$ |
$3.129400859$ |
$1$ |
|
$3$ |
$405504$ |
$1.602861$ |
$1439069689/828345$ |
$0.89965$ |
$3.73910$ |
$[1, 0, 0, -28813, -140008]$ |
\(y^2+xy=x^3-28813x-140008\) |
2.3.0.a.1, 4.6.0.c.1, 40.12.0-4.c.1.5, 168.12.0.?, 420.12.0.?, $\ldots$ |
$[(-8, 304)]$ |
| 115920.cq4 |
115920eo1 |
115920.cq |
115920eo |
$4$ |
$4$ |
\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 23 \) |
\( 2^{12} \cdot 3^{7} \cdot 5 \cdot 7^{4} \cdot 23 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.12.0.8 |
2B |
$19320$ |
$48$ |
$0$ |
$2.205149760$ |
$1$ |
|
$5$ |
$180224$ |
$1.067640$ |
$1439069689/828345$ |
$0.89965$ |
$3.08702$ |
$[0, 0, 0, -3387, 5546]$ |
\(y^2=x^3-3387x+5546\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 168.24.0.?, 690.6.0.?, 1380.24.0.?, $\ldots$ |
$[(85, 576)]$ |
| 154560.ec4 |
154560gp1 |
154560.ec |
154560gp |
$4$ |
$4$ |
\( 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 23 \) |
\( 2^{18} \cdot 3 \cdot 5 \cdot 7^{4} \cdot 23 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$19320$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$180224$ |
$0.864907$ |
$1439069689/828345$ |
$0.89965$ |
$2.80909$ |
$[0, -1, 0, -1505, 2145]$ |
\(y^2=x^3-x^2-1505x+2145\) |
2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.2, 56.12.0-4.c.1.4, 168.24.0.?, $\ldots$ |
$[]$ |
| 154560.gh4 |
154560m1 |
154560.gh |
154560m |
$4$ |
$4$ |
\( 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 23 \) |
\( 2^{18} \cdot 3 \cdot 5 \cdot 7^{4} \cdot 23 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$19320$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$180224$ |
$0.864907$ |
$1439069689/828345$ |
$0.89965$ |
$2.80909$ |
$[0, 1, 0, -1505, -2145]$ |
\(y^2=x^3+x^2-1505x-2145\) |
2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.1, 56.12.0-4.c.1.4, 168.24.0.?, $\ldots$ |
$[]$ |
| 166635.m4 |
166635o1 |
166635.m |
166635o |
$4$ |
$4$ |
\( 3^{2} \cdot 5 \cdot 7 \cdot 23^{2} \) |
\( 3^{7} \cdot 5 \cdot 7^{4} \cdot 23^{7} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$19320$ |
$48$ |
$0$ |
$1.515874273$ |
$1$ |
|
$3$ |
$1486848$ |
$1.942240$ |
$1439069689/828345$ |
$0.89965$ |
$3.86673$ |
$[1, -1, 1, -111983, 1082342]$ |
\(y^2+xy+y=x^3-x^2-111983x+1082342\) |
2.3.0.a.1, 4.6.0.c.1, 60.12.0-4.c.1.2, 92.12.0.?, 168.12.0.?, $\ldots$ |
$[(765, 18661)]$ |
| 193200.hh4 |
193200br1 |
193200.hh |
193200br |
$4$ |
$4$ |
\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 23 \) |
\( 2^{12} \cdot 3 \cdot 5^{7} \cdot 7^{4} \cdot 23 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$19320$ |
$48$ |
$0$ |
$2.525249338$ |
$1$ |
|
$3$ |
$540672$ |
$1.323053$ |
$1439069689/828345$ |
$0.89965$ |
$3.20928$ |
$[0, 1, 0, -9408, -28812]$ |
\(y^2=x^3+x^2-9408x-28812\) |
2.3.0.a.1, 4.6.0.c.1, 60.12.0-4.c.1.1, 92.12.0.?, 168.12.0.?, $\ldots$ |
$[(-28, 462)]$ |
| 253575.fd4 |
253575fd1 |
253575.fd |
253575fd |
$4$ |
$4$ |
\( 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 23 \) |
\( 3^{7} \cdot 5^{7} \cdot 7^{10} \cdot 23 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$19320$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$3244032$ |
$2.152168$ |
$1439069689/828345$ |
$0.89965$ |
$3.93871$ |
$[1, -1, 0, -259317, 3780216]$ |
\(y^2+xy=x^3-x^2-259317x+3780216\) |
2.3.0.a.1, 4.6.0.c.1, 120.12.0.?, 140.12.0.?, 168.12.0.?, $\ldots$ |
$[]$ |
| 270480.jl4 |
270480jl1 |
270480.jl |
270480jl |
$4$ |
$4$ |
\( 2^{4} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 23 \) |
\( 2^{12} \cdot 3 \cdot 5 \cdot 7^{10} \cdot 23 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.6 |
2B |
$19320$ |
$48$ |
$0$ |
$5.993472485$ |
$1$ |
|
$1$ |
$1081344$ |
$1.491289$ |
$1439069689/828345$ |
$0.89965$ |
$3.28435$ |
$[0, 1, 0, -18440, 64308]$ |
\(y^2=x^3+x^2-18440x+64308\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 84.12.0.?, 168.24.0.?, $\ldots$ |
$[(-842/3, 26720/3)]$ |
| 277725.t4 |
277725t1 |
277725.t |
277725t |
$4$ |
$4$ |
\( 3 \cdot 5^{2} \cdot 7 \cdot 23^{2} \) |
\( 3 \cdot 5^{7} \cdot 7^{4} \cdot 23^{7} \) |
$1$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.12.0.7 |
2B |
$19320$ |
$48$ |
$0$ |
$5.991395273$ |
$1$ |
|
$3$ |
$4460544$ |
$2.197655$ |
$1439069689/828345$ |
$0.89965$ |
$3.95367$ |
$[1, 1, 1, -311063, -5010844]$ |
\(y^2+xy+y=x^3+x^2-311063x-5010844\) |
2.3.0.a.1, 4.12.0-4.c.1.1, 168.24.0.?, 690.6.0.?, 1380.24.0.?, $\ldots$ |
$[(-1945/2, 46891/2)]$ |
| 292215.j4 |
292215j1 |
292215.j |
292215j |
$4$ |
$4$ |
\( 3 \cdot 5 \cdot 7 \cdot 11^{2} \cdot 23 \) |
\( 3 \cdot 5 \cdot 7^{4} \cdot 11^{6} \cdot 23 \) |
$2$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$212520$ |
$48$ |
$0$ |
$7.199617202$ |
$1$ |
|
$5$ |
$450560$ |
$1.024134$ |
$1439069689/828345$ |
$0.89965$ |
$2.81875$ |
$[1, 0, 0, -2846, -4509]$ |
\(y^2+xy=x^3-2846x-4509\) |
2.3.0.a.1, 4.6.0.c.1, 132.12.0.?, 168.12.0.?, 616.12.0.?, $\ldots$ |
$[(-45, 204), (495, 10704)]$ |
| 388815.cy4 |
388815cy1 |
388815.cy |
388815cy |
$4$ |
$4$ |
\( 3 \cdot 5 \cdot 7^{2} \cdot 23^{2} \) |
\( 3 \cdot 5 \cdot 7^{10} \cdot 23^{7} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$19320$ |
$48$ |
$0$ |
$18.00661374$ |
$1$ |
|
$1$ |
$8921088$ |
$2.365891$ |
$1439069689/828345$ |
$0.89965$ |
$4.00717$ |
$[1, 1, 0, -609683, 13140072]$ |
\(y^2+xy=x^3+x^2-609683x+13140072\) |
2.3.0.a.1, 4.6.0.c.1, 120.12.0.?, 140.12.0.?, 168.12.0.?, $\ldots$ |
$[(-659400728/1247, 27534156942468/1247)]$ |
| 408135.r4 |
408135r1 |
408135.r |
408135r |
$4$ |
$4$ |
\( 3 \cdot 5 \cdot 7 \cdot 13^{2} \cdot 23 \) |
\( 3 \cdot 5 \cdot 7^{4} \cdot 13^{6} \cdot 23 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$251160$ |
$48$ |
$0$ |
$1$ |
$4$ |
$2$ |
$1$ |
$811008$ |
$1.107662$ |
$1439069689/828345$ |
$0.89965$ |
$2.82344$ |
$[1, 0, 0, -3975, 6720]$ |
\(y^2+xy=x^3-3975x+6720\) |
2.3.0.a.1, 4.6.0.c.1, 156.12.0.?, 168.12.0.?, 690.6.0.?, $\ldots$ |
$[]$ |
| 463680.db4 |
463680db1 |
463680.db |
463680db |
$4$ |
$4$ |
\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 23 \) |
\( 2^{18} \cdot 3^{7} \cdot 5 \cdot 7^{4} \cdot 23 \) |
$2$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.7 |
2B |
$19320$ |
$48$ |
$0$ |
$3.833191704$ |
$1$ |
|
$11$ |
$1441792$ |
$1.414213$ |
$1439069689/828345$ |
$0.89965$ |
$3.07778$ |
$[0, 0, 0, -13548, 44368]$ |
\(y^2=x^3-13548x+44368\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.3, 168.24.0.?, 690.6.0.?, $\ldots$ |
$[(-22, 576), (-112, 396)]$ |
| 463680.ec4 |
463680ec1 |
463680.ec |
463680ec |
$4$ |
$4$ |
\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 23 \) |
\( 2^{18} \cdot 3^{7} \cdot 5 \cdot 7^{4} \cdot 23 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.8 |
2B |
$19320$ |
$48$ |
$0$ |
$1.522257472$ |
$1$ |
|
$5$ |
$1441792$ |
$1.414213$ |
$1439069689/828345$ |
$0.89965$ |
$3.07778$ |
$[0, 0, 0, -13548, -44368]$ |
\(y^2=x^3-13548x-44368\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.4, 168.24.0.?, 690.6.0.?, $\ldots$ |
$[(-8, 252)]$ |
