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 |
Regulator |
$Ш_{\textrm{an}}$ |
Ш primes |
Integral points |
Modular degree |
Faltings height |
j-invariant |
Weierstrass coefficients |
Weierstrass equation |
2310.k4 |
2310j1 |
2310.k |
2310j |
$4$ |
$4$ |
\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11 \) |
\( - 2^{12} \cdot 3^{4} \cdot 5 \cdot 7^{4} \cdot 11 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
4.6.0.1 |
2B |
$0.666885710$ |
$1$ |
|
$7$ |
$3072$ |
$0.748379$ |
$-95575628340361/43812679680$ |
$[1, 0, 1, -953, 15068]$ |
\(y^2+xy+y=x^3-953x+15068\) |
6930.w4 |
6930x1 |
6930.w |
6930x |
$4$ |
$4$ |
\( 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \) |
\( - 2^{12} \cdot 3^{10} \cdot 5 \cdot 7^{4} \cdot 11 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$1$ |
$1$ |
|
$1$ |
$24576$ |
$1.297686$ |
$-95575628340361/43812679680$ |
$[1, -1, 1, -8573, -406843]$ |
\(y^2+xy+y=x^3-x^2-8573x-406843\) |
11550.bt4 |
11550bq1 |
11550.bt |
11550bq |
$4$ |
$4$ |
\( 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 \) |
\( - 2^{12} \cdot 3^{4} \cdot 5^{7} \cdot 7^{4} \cdot 11 \) |
$1$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.12.0.7 |
2B |
$0.520317837$ |
$1$ |
|
$19$ |
$73728$ |
$1.553097$ |
$-95575628340361/43812679680$ |
$[1, 1, 1, -23813, 1883531]$ |
\(y^2+xy+y=x^3+x^2-23813x+1883531\) |
16170.c4 |
16170d1 |
16170.c |
16170d |
$4$ |
$4$ |
\( 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 11 \) |
\( - 2^{12} \cdot 3^{4} \cdot 5 \cdot 7^{10} \cdot 11 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.12 |
2B |
$1$ |
$1$ |
|
$1$ |
$147456$ |
$1.721334$ |
$-95575628340361/43812679680$ |
$[1, 1, 0, -46673, -5215083]$ |
\(y^2+xy=x^3+x^2-46673x-5215083\) |
18480.bs4 |
18480cj1 |
18480.bs |
18480cj |
$4$ |
$4$ |
\( 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 11 \) |
\( - 2^{24} \cdot 3^{4} \cdot 5 \cdot 7^{4} \cdot 11 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$3.100105865$ |
$1$ |
|
$3$ |
$73728$ |
$1.441526$ |
$-95575628340361/43812679680$ |
$[0, -1, 0, -15240, -964368]$ |
\(y^2=x^3-x^2-15240x-964368\) |
25410.cw4 |
25410cx1 |
25410.cw |
25410cx |
$4$ |
$4$ |
\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11^{2} \) |
\( - 2^{12} \cdot 3^{4} \cdot 5 \cdot 7^{4} \cdot 11^{7} \) |
$0$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.12.0.7 |
2B |
$1$ |
$1$ |
|
$3$ |
$368640$ |
$1.947327$ |
$-95575628340361/43812679680$ |
$[1, 0, 0, -115255, -20171095]$ |
\(y^2+xy=x^3-115255x-20171095\) |
34650.bw4 |
34650bj1 |
34650.bw |
34650bj |
$4$ |
$4$ |
\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11 \) |
\( - 2^{12} \cdot 3^{10} \cdot 5^{7} \cdot 7^{4} \cdot 11 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$1$ |
$1$ |
|
$1$ |
$589824$ |
$2.102406$ |
$-95575628340361/43812679680$ |
$[1, -1, 0, -214317, -51069659]$ |
\(y^2+xy=x^3-x^2-214317x-51069659\) |
48510.dw4 |
48510ef1 |
48510.dw |
48510ef |
$4$ |
$4$ |
\( 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 11 \) |
\( - 2^{12} \cdot 3^{10} \cdot 5 \cdot 7^{10} \cdot 11 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$1$ |
$1$ |
|
$1$ |
$1179648$ |
$2.270641$ |
$-95575628340361/43812679680$ |
$[1, -1, 1, -420062, 140387181]$ |
\(y^2+xy+y=x^3-x^2-420062x+140387181\) |
55440.bv4 |
55440di1 |
55440.bv |
55440di |
$4$ |
$4$ |
\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \) |
\( - 2^{24} \cdot 3^{10} \cdot 5 \cdot 7^{4} \cdot 11 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$1$ |
$1$ |
|
$1$ |
$589824$ |
$1.990831$ |
$-95575628340361/43812679680$ |
$[0, 0, 0, -137163, 26175098]$ |
\(y^2=x^3-137163x+26175098\) |
73920.u4 |
73920g1 |
73920.u |
73920g |
$4$ |
$4$ |
\( 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 11 \) |
\( - 2^{30} \cdot 3^{4} \cdot 5 \cdot 7^{4} \cdot 11 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$1$ |
$1$ |
|
$1$ |
$589824$ |
$1.788099$ |
$-95575628340361/43812679680$ |
$[0, -1, 0, -60961, 7775905]$ |
\(y^2=x^3-x^2-60961x+7775905\) |
73920.fj4 |
73920gr1 |
73920.fj |
73920gr |
$4$ |
$4$ |
\( 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 11 \) |
\( - 2^{30} \cdot 3^{4} \cdot 5 \cdot 7^{4} \cdot 11 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$1$ |
$1$ |
|
$1$ |
$589824$ |
$1.788099$ |
$-95575628340361/43812679680$ |
$[0, 1, 0, -60961, -7775905]$ |
\(y^2=x^3+x^2-60961x-7775905\) |
76230.s4 |
76230bg1 |
76230.s |
76230bg |
$4$ |
$4$ |
\( 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11^{2} \) |
\( - 2^{12} \cdot 3^{10} \cdot 5 \cdot 7^{4} \cdot 11^{7} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$1$ |
$1$ |
|
$1$ |
$2949120$ |
$2.496632$ |
$-95575628340361/43812679680$ |
$[1, -1, 0, -1037295, 544619565]$ |
\(y^2+xy=x^3-x^2-1037295x+544619565\) |
80850.gf4 |
80850fu1 |
80850.gf |
80850fu |
$4$ |
$4$ |
\( 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 11 \) |
\( - 2^{12} \cdot 3^{4} \cdot 5^{7} \cdot 7^{10} \cdot 11 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$1$ |
$1$ |
|
$1$ |
$3538944$ |
$2.526054$ |
$-95575628340361/43812679680$ |
$[1, 0, 0, -1166838, -649551708]$ |
\(y^2+xy=x^3-1166838x-649551708\) |
92400.fs4 |
92400gn1 |
92400.fs |
92400gn |
$4$ |
$4$ |
\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 \) |
\( - 2^{24} \cdot 3^{4} \cdot 5^{7} \cdot 7^{4} \cdot 11 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.12.0.8 |
2B |
$1$ |
$1$ |
|
$1$ |
$1769472$ |
$2.246246$ |
$-95575628340361/43812679680$ |
$[0, 1, 0, -381008, -121308012]$ |
\(y^2=x^3+x^2-381008x-121308012\) |
127050.q4 |
127050d1 |
127050.q |
127050d |
$4$ |
$4$ |
\( 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11^{2} \) |
\( - 2^{12} \cdot 3^{4} \cdot 5^{7} \cdot 7^{4} \cdot 11^{7} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$1$ |
$1$ |
|
$1$ |
$8847360$ |
$2.752045$ |
$-95575628340361/43812679680$ |
$[1, 1, 0, -2881375, -2521386875]$ |
\(y^2+xy=x^3+x^2-2881375x-2521386875\) |
129360.ey4 |
129360gn1 |
129360.ey |
129360gn |
$4$ |
$4$ |
\( 2^{4} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 11 \) |
\( - 2^{24} \cdot 3^{4} \cdot 5 \cdot 7^{10} \cdot 11 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.12 |
2B |
$2.379257921$ |
$1$ |
|
$5$ |
$3538944$ |
$2.414482$ |
$-95575628340361/43812679680$ |
$[0, 1, 0, -746776, 332271764]$ |
\(y^2=x^3+x^2-746776x+332271764\) |
177870.fg4 |
177870dz1 |
177870.fg |
177870dz |
$4$ |
$4$ |
\( 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 11^{2} \) |
\( - 2^{12} \cdot 3^{4} \cdot 5 \cdot 7^{10} \cdot 11^{7} \) |
$2$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$1.393480839$ |
$1$ |
|
$25$ |
$17694720$ |
$2.920280$ |
$-95575628340361/43812679680$ |
$[1, 1, 1, -5647496, 6913038089]$ |
\(y^2+xy+y=x^3+x^2-5647496x+6913038089\) |
203280.cm4 |
203280cu1 |
203280.cm |
203280cu |
$4$ |
$4$ |
\( 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 11^{2} \) |
\( - 2^{24} \cdot 3^{4} \cdot 5 \cdot 7^{4} \cdot 11^{7} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.12.0.8 |
2B |
$1$ |
$1$ |
|
$1$ |
$8847360$ |
$2.640472$ |
$-95575628340361/43812679680$ |
$[0, -1, 0, -1844080, 1290950080]$ |
\(y^2=x^3-x^2-1844080x+1290950080\) |
221760.gz4 |
221760jw1 |
221760.gz |
221760jw |
$4$ |
$4$ |
\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \) |
\( - 2^{30} \cdot 3^{10} \cdot 5 \cdot 7^{4} \cdot 11 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$24.77628163$ |
$1$ |
|
$1$ |
$4718592$ |
$2.337406$ |
$-95575628340361/43812679680$ |
$[0, 0, 0, -548652, -209400784]$ |
\(y^2=x^3-548652x-209400784\) |
221760.mw4 |
221760d1 |
221760.mw |
221760d |
$4$ |
$4$ |
\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \) |
\( - 2^{30} \cdot 3^{10} \cdot 5 \cdot 7^{4} \cdot 11 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$1$ |
$1$ |
|
$1$ |
$4718592$ |
$2.337406$ |
$-95575628340361/43812679680$ |
$[0, 0, 0, -548652, 209400784]$ |
\(y^2=x^3-548652x+209400784\) |
242550.gr4 |
242550gr1 |
242550.gr |
242550gr |
$4$ |
$4$ |
\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 11 \) |
\( - 2^{12} \cdot 3^{10} \cdot 5^{7} \cdot 7^{10} \cdot 11 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$1$ |
$1$ |
|
$1$ |
$28311552$ |
$3.075359$ |
$-95575628340361/43812679680$ |
$[1, -1, 0, -10501542, 17537896116]$ |
\(y^2+xy=x^3-x^2-10501542x+17537896116\) |
277200.x4 |
277200x1 |
277200.x |
277200x |
$4$ |
$4$ |
\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11 \) |
\( - 2^{24} \cdot 3^{10} \cdot 5^{7} \cdot 7^{4} \cdot 11 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$7.354080745$ |
$1$ |
|
$1$ |
$14155776$ |
$2.795551$ |
$-95575628340361/43812679680$ |
$[0, 0, 0, -3429075, 3271887250]$ |
\(y^2=x^3-3429075x+3271887250\) |
369600.ci4 |
369600ci1 |
369600.ci |
369600ci |
$4$ |
$4$ |
\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 \) |
\( - 2^{30} \cdot 3^{4} \cdot 5^{7} \cdot 7^{4} \cdot 11 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.7 |
2B |
$1$ |
$1$ |
|
$1$ |
$14155776$ |
$2.592819$ |
$-95575628340361/43812679680$ |
$[0, -1, 0, -1524033, -968940063]$ |
\(y^2=x^3-x^2-1524033x-968940063\) |
369600.wu4 |
369600wu1 |
369600.wu |
369600wu |
$4$ |
$4$ |
\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 \) |
\( - 2^{30} \cdot 3^{4} \cdot 5^{7} \cdot 7^{4} \cdot 11 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.8 |
2B |
$1$ |
$1$ |
|
$1$ |
$14155776$ |
$2.592819$ |
$-95575628340361/43812679680$ |
$[0, 1, 0, -1524033, 968940063]$ |
\(y^2=x^3+x^2-1524033x+968940063\) |
381150.lr4 |
381150lr1 |
381150.lr |
381150lr |
$4$ |
$4$ |
\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11^{2} \) |
\( - 2^{12} \cdot 3^{10} \cdot 5^{7} \cdot 7^{4} \cdot 11^{7} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$1$ |
$1$ |
|
$1$ |
$70778880$ |
$3.301350$ |
$-95575628340361/43812679680$ |
$[1, -1, 1, -25932380, 68051513247]$ |
\(y^2+xy+y=x^3-x^2-25932380x+68051513247\) |
388080.im4 |
388080im1 |
388080.im |
388080im |
$4$ |
$4$ |
\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 11 \) |
\( - 2^{24} \cdot 3^{10} \cdot 5 \cdot 7^{10} \cdot 11 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$16.55716924$ |
$1$ |
|
$1$ |
$28311552$ |
$2.963787$ |
$-95575628340361/43812679680$ |
$[0, 0, 0, -6720987, -8978058614]$ |
\(y^2=x^3-6720987x-8978058614\) |
390390.ei4 |
390390ei1 |
390390.ei |
390390ei |
$4$ |
$4$ |
\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11 \cdot 13^{2} \) |
\( - 2^{12} \cdot 3^{4} \cdot 5 \cdot 7^{4} \cdot 11 \cdot 13^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$0.289848291$ |
$1$ |
|
$11$ |
$7077888$ |
$2.030853$ |
$-95575628340361/43812679680$ |
$[1, 0, 0, -160976, 33265920]$ |
\(y^2+xy=x^3-160976x+33265920\) |