| 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 |
| 54.b2 |
54b3 |
54.b |
54b |
$3$ |
$9$ |
\( 2 \cdot 3^{3} \) |
\( - 2^{9} \cdot 3^{5} \) |
$0$ |
$\Z/9\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
9.72.0.5 |
3B.1.1 |
$72$ |
$144$ |
$3$ |
$1$ |
$1$ |
|
$8$ |
$6$ |
$-0.315205$ |
$-1167051/512$ |
$1.04966$ |
$5.02065$ |
$[1, -1, 1, -14, 29]$ |
\(y^2+xy+y=x^3-x^2-14x+29\) |
3.8.0-3.a.1.2, 9.72.0-9.d.1.2, 24.16.0-24.d.1.8, 72.144.3.? |
$[]$ |
| 714.i3 |
714i1 |
714.i |
714i |
$3$ |
$9$ |
\( 2 \cdot 3 \cdot 7 \cdot 17 \) |
\( - 2^{9} \cdot 3^{9} \cdot 7^{3} \cdot 17 \) |
$0$ |
$\Z/9\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$3$ |
9.72.0.5 |
3B.1.1 |
$8568$ |
$144$ |
$3$ |
$1$ |
$1$ |
|
$8$ |
$1080$ |
$0.745499$ |
$139233463487/58763045376$ |
$1.03208$ |
$4.90804$ |
$[1, 0, 0, 108, 11664]$ |
\(y^2+xy=x^3+108x+11664\) |
3.8.0-3.a.1.2, 9.72.0-9.d.1.2, 2856.16.0.?, 8568.144.3.? |
$[]$ |
| 1482.j3 |
1482l1 |
1482.j |
1482l |
$3$ |
$9$ |
\( 2 \cdot 3 \cdot 13 \cdot 19 \) |
\( - 2^{18} \cdot 3^{9} \cdot 13^{3} \cdot 19 \) |
$1$ |
$\Z/9\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$3$ |
9.72.0.5 |
3B.1.1 |
$8892$ |
$144$ |
$3$ |
$1.735730763$ |
$1$ |
|
$24$ |
$7776$ |
$1.437672$ |
$240065464752030527/215384711233536$ |
$1.00262$ |
$5.48129$ |
$[1, 0, 0, 12948, 421776]$ |
\(y^2+xy=x^3+12948x+421776\) |
3.8.0-3.a.1.2, 9.72.0-9.d.1.2, 2964.16.0.?, 8892.144.3.? |
$[(-30, 96)]$ |
| 1554.l2 |
1554n1 |
1554.l |
1554n |
$3$ |
$9$ |
\( 2 \cdot 3 \cdot 7 \cdot 37 \) |
\( - 2^{9} \cdot 3^{9} \cdot 7^{3} \cdot 37 \) |
$1$ |
$\Z/9\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$3$ |
9.72.0.5 |
3B.1.1 |
$18648$ |
$144$ |
$3$ |
$1.255479514$ |
$1$ |
|
$24$ |
$3888$ |
$0.947635$ |
$-11980221891814513/127896039936$ |
$0.96940$ |
$5.04047$ |
$[1, 0, 0, -4767, 127449]$ |
\(y^2+xy=x^3-4767x+127449\) |
3.8.0-3.a.1.2, 9.72.0-9.d.1.2, 6216.16.0.?, 18648.144.3.? |
$[(48, 75)]$ |
| 1890.x3 |
1890r3 |
1890.x |
1890r |
$3$ |
$9$ |
\( 2 \cdot 3^{3} \cdot 5 \cdot 7 \) |
\( - 2^{18} \cdot 3^{5} \cdot 5^{9} \cdot 7^{3} \) |
$0$ |
$\Z/9\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
9.72.0.5 |
3B.1.1 |
$1260$ |
$144$ |
$3$ |
$1$ |
$1$ |
|
$8$ |
$19440$ |
$1.876335$ |
$114115456478544693/175616000000000$ |
$1.04652$ |
$6.00125$ |
$[1, -1, 1, 63058, -7866691]$ |
\(y^2+xy+y=x^3-x^2+63058x-7866691\) |
3.8.0-3.a.1.2, 9.72.0-9.d.1.2, 420.16.0.?, 1260.144.3.? |
$[]$ |
| 6942.l2 |
6942n1 |
6942.l |
6942n |
$3$ |
$9$ |
\( 2 \cdot 3 \cdot 13 \cdot 89 \) |
\( - 2^{18} \cdot 3^{9} \cdot 13^{3} \cdot 89 \) |
$0$ |
$\Z/9\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$3$ |
9.72.0.5 |
3B.1.1 |
$20826$ |
$144$ |
$3$ |
$1$ |
$1$ |
|
$8$ |
$65664$ |
$1.799290$ |
$-1026784744653907139473/1008907331567616$ |
$0.98411$ |
$5.46982$ |
$[1, 0, 0, -210177, 37101321]$ |
\(y^2+xy=x^3-210177x+37101321\) |
3.8.0-3.a.1.2, 9.72.0-9.d.1.2, 6942.16.0.?, 20826.144.3.? |
$[]$ |
| 15810.u1 |
15810u1 |
15810.u |
15810u |
$3$ |
$9$ |
\( 2 \cdot 3 \cdot 5 \cdot 17 \cdot 31 \) |
\( - 2^{9} \cdot 3^{9} \cdot 5^{9} \cdot 17^{2} \cdot 31^{3} \) |
$1$ |
$\Z/9\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$3$ |
9.72.0.5 |
3B.1.1 |
$11160$ |
$144$ |
$3$ |
$1.001590490$ |
$1$ |
|
$26$ |
$1329696$ |
$2.972321$ |
$-4888687926204690735691893601/169462737117000000000$ |
$1.01525$ |
$6.59435$ |
$[1, 0, 0, -35358150, 80924422500]$ |
\(y^2+xy=x^3-35358150x+80924422500\) |
3.8.0-3.a.1.2, 9.72.0-9.d.1.2, 3720.16.0.?, 11160.144.3.? |
$[(3420, 330)]$ |
| 17670.z3 |
17670bb1 |
17670.z |
17670bb |
$3$ |
$9$ |
\( 2 \cdot 3 \cdot 5 \cdot 19 \cdot 31 \) |
\( 2^{9} \cdot 3^{9} \cdot 5^{9} \cdot 19 \cdot 31^{3} \) |
$0$ |
$\Z/9\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$3$ |
9.72.0.5 |
3B.1.1 |
$212040$ |
$144$ |
$3$ |
$1$ |
$1$ |
|
$8$ |
$427680$ |
$2.429310$ |
$350792849898814825511281/11141148807000000000$ |
$0.98697$ |
$5.54362$ |
$[1, 0, 0, -1469295, 666308025]$ |
\(y^2+xy=x^3-1469295x+666308025\) |
3.8.0-3.a.1.2, 9.72.0-9.d.1.2, 70680.16.0.?, 212040.144.3.? |
$[]$ |
| 35910.by1 |
35910bt3 |
35910.by |
35910bt |
$3$ |
$9$ |
\( 2 \cdot 3^{3} \cdot 5 \cdot 7 \cdot 19 \) |
\( - 2^{18} \cdot 3^{5} \cdot 5^{9} \cdot 7^{3} \cdot 19 \) |
$1$ |
$\Z/9\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
9.72.0.5 |
3B.1.1 |
$11970$ |
$144$ |
$3$ |
$1.798177555$ |
$1$ |
|
$22$ |
$1259712$ |
$2.447514$ |
$-21351492553819653671547/3336704000000000$ |
$1.00189$ |
$5.42568$ |
$[1, -1, 1, -3606647, 2637610319]$ |
\(y^2+xy+y=x^3-x^2-3606647x+2637610319\) |
3.8.0-3.a.1.2, 9.72.0-9.d.1.2, 3990.16.0.?, 11970.144.3.? |
$[(1077, 736)]$ |
| 60990.bh2 |
60990bj1 |
60990.bh |
60990bj |
$3$ |
$9$ |
\( 2 \cdot 3 \cdot 5 \cdot 19 \cdot 107 \) |
\( - 2^{9} \cdot 3^{9} \cdot 5^{9} \cdot 19^{3} \cdot 107 \) |
$1$ |
$\Z/9\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$3$ |
9.72.0.5 |
3B.1.1 |
$731880$ |
$144$ |
$3$ |
$2.495055653$ |
$1$ |
|
$18$ |
$1469664$ |
$2.358532$ |
$-1367453954870275397761/14445609579000000000$ |
$0.97308$ |
$4.68531$ |
$[1, 0, 0, -231240, 187785792]$ |
\(y^2+xy=x^3-231240x+187785792\) |
3.8.0-3.a.1.2, 9.72.0-9.d.1.2, 243960.16.0.?, 731880.144.3.? |
$[(-696, 3768)]$ |
| 83370.x2 |
83370x1 |
83370.x |
83370x |
$3$ |
$9$ |
\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 397 \) |
\( - 2^{27} \cdot 3^{9} \cdot 5^{9} \cdot 7^{6} \cdot 397 \) |
$0$ |
$\Z/9\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$3$ |
9.72.0.5 |
3B.1.1 |
$142920$ |
$144$ |
$3$ |
$1$ |
$1$ |
|
$8$ |
$39424320$ |
$3.742001$ |
$-3626272648660625410108067281/240996070457081856000000000$ |
$1.06987$ |
$6.01976$ |
$[1, 0, 0, -32007045, 750143318337]$ |
\(y^2+xy=x^3-32007045x+750143318337\) |
3.8.0-3.a.1.2, 9.72.0-9.d.1.2, 47640.16.0.?, 142920.144.3.? |
$[]$ |
| 92910.bd2 |
92910bi1 |
92910.bd |
92910bi |
$3$ |
$9$ |
\( 2 \cdot 3 \cdot 5 \cdot 19 \cdot 163 \) |
\( - 2^{9} \cdot 3^{9} \cdot 5^{9} \cdot 19^{3} \cdot 163 \) |
$0$ |
$\Z/9\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$3$ |
9.72.0.5 |
3B.1.1 |
$1114920$ |
$144$ |
$3$ |
$1$ |
$1$ |
|
$8$ |
$3394224$ |
$2.472027$ |
$-433836620224795849583521/22005928611000000000$ |
$0.95907$ |
$4.76520$ |
$[1, 0, 0, -1577130, 794918052]$ |
\(y^2+xy=x^3-1577130x+794918052\) |
3.8.0-3.a.1.2, 9.72.0-9.d.1.2, 371640.16.0.?, 1114920.144.3.? |
$[]$ |
| 118698.f3 |
118698i1 |
118698.f |
118698i |
$3$ |
$9$ |
\( 2 \cdot 3 \cdot 73 \cdot 271 \) |
\( 2^{27} \cdot 3^{18} \cdot 73^{3} \cdot 271 \) |
$1$ |
$\Z/9\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$3$ |
9.72.0.5 |
3B.1.1 |
$1424376$ |
$144$ |
$3$ |
$5.522076526$ |
$1$ |
|
$14$ |
$69004224$ |
$3.830963$ |
$139690200244171980376257072833953/5481890282879036260614144$ |
$1.00889$ |
$6.33472$ |
$[1, 0, 0, -1080971082, 13678914712356]$ |
\(y^2+xy=x^3-1080971082x+13678914712356\) |
3.8.0-3.a.1.2, 9.72.0-9.d.1.2, 158264.2.0.?, 474792.16.0.?, 1424376.144.3.? |
$[(53556, 10432614)]$ |
| 122094.be2 |
122094bl3 |
122094.be |
122094bl |
$3$ |
$9$ |
\( 2 \cdot 3^{3} \cdot 7 \cdot 17 \cdot 19 \) |
\( 2^{27} \cdot 3^{5} \cdot 7^{9} \cdot 17 \cdot 19^{3} \) |
$0$ |
$\Z/9\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
9.72.0.5 |
3B.1.1 |
$162792$ |
$144$ |
$3$ |
$1$ |
$1$ |
|
$8$ |
$31492800$ |
$3.449272$ |
$3272351648557113352874597691/631541606162039308288$ |
$1.01402$ |
$5.87817$ |
$[1, -1, 1, -193010459, 1031970436427]$ |
\(y^2+xy+y=x^3-x^2-193010459x+1031970436427\) |
3.8.0-3.a.1.2, 9.72.0-9.d.1.2, 54264.16.0.?, 162792.144.3.? |
$[]$ |
| 128226.s3 |
128226ba1 |
128226.s |
128226ba |
$3$ |
$9$ |
\( 2 \cdot 3 \cdot 7 \cdot 43 \cdot 71 \) |
\( 2^{9} \cdot 3^{9} \cdot 7^{9} \cdot 43^{3} \cdot 71 \) |
$1$ |
$\Z/9\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$3$ |
9.72.0.5 |
3B.1.1 |
$1538712$ |
$144$ |
$3$ |
$2.128858521$ |
$1$ |
|
$18$ |
$16796160$ |
$2.999702$ |
$1544204814149745316374461713/2295658741816117891584$ |
$0.97926$ |
$5.32279$ |
$[1, 0, 0, -24080217, 45421448121]$ |
\(y^2+xy=x^3-24080217x+45421448121\) |
3.8.0-3.a.1.2, 9.72.0-9.d.1.2, 512904.16.0.?, 1538712.144.3.? |
$[(2730, 4179)]$ |
| 129162.bf3 |
129162bh1 |
129162.bf |
129162bh |
$3$ |
$9$ |
\( 2 \cdot 3 \cdot 11 \cdot 19 \cdot 103 \) |
\( 2^{9} \cdot 3^{18} \cdot 11^{9} \cdot 19 \cdot 103^{3} \) |
$0$ |
$\Z/9\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$3$ |
9.72.0.5 |
3B.1.1 |
$1549944$ |
$144$ |
$3$ |
$1$ |
$1$ |
|
$8$ |
$100745856$ |
$4.063385$ |
$19687440505944790974585155384593/9710732423439397326945222144$ |
$1.01689$ |
$6.12275$ |
$[1, 0, 0, -562542297, 1973424349881]$ |
\(y^2+xy=x^3-562542297x+1973424349881\) |
3.8.0-3.a.1.2, 9.72.0-9.d.1.2, 172216.2.0.?, 516648.16.0.?, 1549944.144.3.? |
$[]$ |
| 143430.u2 |
143430b1 |
143430.u |
143430b |
$3$ |
$9$ |
\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 683 \) |
\( - 2^{27} \cdot 3^{9} \cdot 5^{9} \cdot 7^{6} \cdot 683 \) |
$1$ |
$\Z/9\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$3$ |
9.72.0.5 |
3B.1.1 |
$245880$ |
$144$ |
$3$ |
$1.851792099$ |
$1$ |
|
$22$ |
$87340032$ |
$3.886715$ |
$-14313500104002032435046925025521/414610368065961984000000000$ |
$1.00150$ |
$6.04598$ |
$[1, 0, 0, -505833255, 4487049903177]$ |
\(y^2+xy=x^3-505833255x+4487049903177\) |
3.8.0-3.a.1.2, 9.72.0-9.d.1.2, 81960.16.0.?, 245880.144.3.? |
$[(12918, 322821)]$ |
| 357378.l3 |
357378l1 |
357378.l |
357378l |
$3$ |
$9$ |
\( 2 \cdot 3 \cdot 7 \cdot 67 \cdot 127 \) |
\( - 2^{9} \cdot 3^{18} \cdot 7^{9} \cdot 67^{3} \cdot 127 \) |
$0$ |
$\Z/9\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$3$ |
9.72.0.5 |
3B.1.1 |
$4288536$ |
$144$ |
$3$ |
$1$ |
$1$ |
|
$8$ |
$217323648$ |
$3.771526$ |
$527737231583370421518916605167/305747584820092901684491776$ |
$1.03034$ |
$5.35237$ |
$[1, 0, 0, 168357063, -28208561031]$ |
\(y^2+xy=x^3+168357063x-28208561031\) |
3.8.0-3.a.1.2, 9.72.0-9.d.1.2, 476504.2.0.?, 1429512.16.0.?, 4288536.144.3.? |
$[]$ |
| 402522.g1 |
402522g1 |
402522.g |
402522g |
$3$ |
$9$ |
\( 2 \cdot 3 \cdot 73 \cdot 919 \) |
\( - 2^{27} \cdot 3^{18} \cdot 73^{3} \cdot 919 \) |
$1$ |
$\Z/9\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$3$ |
9.72.0.5 |
3B.1.1 |
$4830264$ |
$144$ |
$3$ |
$13.16387443$ |
$1$ |
|
$8$ |
$446497920$ |
$4.131203$ |
$-15726464326139854896588126629981953/18589878855962488278614016$ |
$1.00278$ |
$6.10132$ |
$[1, 0, 0, -5219582832, 145144621322496]$ |
\(y^2+xy=x^3-5219582832x+145144621322496\) |
3.8.0-3.a.1.2, 9.72.0-9.d.1.2, 536696.2.0.?, 1610088.16.0.?, 4830264.144.3.? |
$[(34911656/29, 1238873320/29)]$ |
| 417690.cy3 |
417690cy2 |
417690.cy |
417690cy |
$3$ |
$9$ |
\( 2 \cdot 3^{3} \cdot 5 \cdot 7 \cdot 13 \cdot 17 \) |
\( - 2^{9} \cdot 3^{5} \cdot 5^{9} \cdot 7^{9} \cdot 13^{3} \cdot 17 \) |
$1$ |
$\Z/9\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
9.72.0.5 |
3B.1.1 |
$556920$ |
$144$ |
$3$ |
$2.144954042$ |
$1$ |
|
$22$ |
$85660416$ |
$3.204266$ |
$397090089854833871209893/1507166867843000000000$ |
$0.98483$ |
$4.75541$ |
$[1, -1, 1, 9555583, 26802839441]$ |
\(y^2+xy+y=x^3-x^2+9555583x+26802839441\) |
3.8.0-3.a.1.2, 9.72.0-9.d.1.2, 185640.16.0.?, 556920.144.3.? |
$[(4681, 414894)]$ |
