Learn more

Refine search


Results (1-50 of 310 matches)

Next   Download to        
Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
9.1-a1 9.1-a 3.3.257.1 \( 3^{2} \) $0$ $\Z/2\Z$ $1$ $31.43077920$ 0.980299069 \( \frac{17690975205668}{9} a^{2} + \frac{20899317547511}{9} a - \frac{7973191675235}{3} \) \( \bigl[a^{2} - 3\) , \( -a^{2} - a + 3\) , \( a\) , \( -116 a^{2} + 341 a - 191\) , \( 1561 a^{2} - 4537 a + 2428\bigr] \) ${y}^2+\left(a^{2}-3\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}-a+3\right){x}^{2}+\left(-116a^{2}+341a-191\right){x}+1561a^{2}-4537a+2428$
9.1-a2 9.1-a 3.3.257.1 \( 3^{2} \) $0$ $\Z/2\Z$ $1$ $7.857694801$ 0.980299069 \( -\frac{637339485144964}{6561} a^{2} + \frac{182573580343201}{6561} a + \frac{893210373928667}{2187} \) \( \bigl[a^{2} - 3\) , \( -a^{2} - a + 3\) , \( a\) , \( 24 a^{2} + 21 a - 161\) , \( 195 a^{2} - 45 a - 846\bigr] \) ${y}^2+\left(a^{2}-3\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}-a+3\right){x}^{2}+\left(24a^{2}+21a-161\right){x}+195a^{2}-45a-846$
9.1-a3 9.1-a 3.3.257.1 \( 3^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $62.86155840$ 0.980299069 \( \frac{35323985}{81} a^{2} + \frac{17367094}{27} a - 64775 \) \( \bigl[a^{2} - 3\) , \( -a^{2} - a + 3\) , \( a\) , \( -6 a^{2} + 21 a - 16\) , \( 26 a^{2} - 65 a + 15\bigr] \) ${y}^2+\left(a^{2}-3\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}-a+3\right){x}^{2}+\left(-6a^{2}+21a-16\right){x}+26a^{2}-65a+15$
9.1-a4 9.1-a 3.3.257.1 \( 3^{2} \) $0$ $\Z/4\Z$ $1$ $125.7231168$ 0.980299069 \( \frac{4519}{9} a^{2} + \frac{4861}{9} a - \frac{2698}{3} \) \( \bigl[a^{2} - 3\) , \( -a^{2} - a + 3\) , \( a\) , \( -a^{2} + a + 4\) , \( -2 a + 2\bigr] \) ${y}^2+\left(a^{2}-3\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}-a+3\right){x}^{2}+\left(-a^{2}+a+4\right){x}-2a+2$
9.1-b1 9.1-b 3.3.257.1 \( 3^{2} \) $1$ $\Z/2\Z$ $1.119566432$ $8.307343432$ 0.870235370 \( \frac{17690975205668}{9} a^{2} + \frac{20899317547511}{9} a - \frac{7973191675235}{3} \) \( \bigl[a^{2} - 2\) , \( -a^{2} + 2\) , \( a^{2} + a - 3\) , \( -998 a^{2} + 2900 a - 1562\) , \( -39467 a^{2} + 114933 a - 61916\bigr] \) ${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}+\left(-998a^{2}+2900a-1562\right){x}-39467a^{2}+114933a-61916$
9.1-b2 9.1-b 3.3.257.1 \( 3^{2} \) $1$ $\Z/2\Z$ $0.279891608$ $33.22937372$ 0.870235370 \( -\frac{637339485144964}{6561} a^{2} + \frac{182573580343201}{6561} a + \frac{893210373928667}{2187} \) \( \bigl[a^{2} - 2\) , \( -a^{2} + 2\) , \( a^{2} + a - 3\) , \( -88 a^{2} + 260 a - 152\) , \( 13 a^{2} - 45 a + 32\bigr] \) ${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}+\left(-88a^{2}+260a-152\right){x}+13a^{2}-45a+32$
9.1-b3 9.1-b 3.3.257.1 \( 3^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $0.559783216$ $66.45874745$ 0.870235370 \( \frac{35323985}{81} a^{2} + \frac{17367094}{27} a - 64775 \) \( \bigl[a^{2} - 2\) , \( -a^{2} + 2\) , \( a^{2} + a - 3\) , \( -63 a^{2} + 180 a - 97\) , \( -601 a^{2} + 1748 a - 942\bigr] \) ${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}+\left(-63a^{2}+180a-97\right){x}-601a^{2}+1748a-942$
9.1-b4 9.1-b 3.3.257.1 \( 3^{2} \) $1$ $\Z/4\Z$ $0.279891608$ $132.9174949$ 0.870235370 \( \frac{4519}{9} a^{2} + \frac{4861}{9} a - \frac{2698}{3} \) \( \bigl[a^{2} - 2\) , \( -a^{2} + 2\) , \( a^{2} + a - 3\) , \( -3 a^{2} + 5 a - 2\) , \( -18 a^{2} + 50 a - 27\bigr] \) ${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}+\left(-3a^{2}+5a-2\right){x}-18a^{2}+50a-27$
9.2-a1 9.2-a 3.3.257.1 \( 3^{2} \) $0$ $\Z/2\Z$ $1$ $15.26036525$ 0.951915430 \( -\frac{169564940890516}{282429536481} a^{2} - \frac{93767995435637}{282429536481} a + \frac{1032142453154629}{282429536481} \) \( \bigl[a^{2} + a - 3\) , \( -a^{2} + a + 3\) , \( a^{2} - 2\) , \( 2 a^{2} + 2 a - 6\) , \( -8 a^{2} - 11 a + 9\bigr] \) ${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(2a^{2}+2a-6\right){x}-8a^{2}-11a+9$
9.2-a2 9.2-a 3.3.257.1 \( 3^{2} \) $0$ $\Z/2\Z$ $1$ $30.52073051$ 0.951915430 \( \frac{1812669625}{531441} a^{2} + \frac{2069390414}{531441} a - \frac{1917539791}{531441} \) \( \bigl[a^{2} + a - 3\) , \( -a^{2} + a + 3\) , \( a^{2} - 2\) , \( -3 a^{2} - 3 a + 9\) , \( -7 a^{2} - 6 a + 12\bigr] \) ${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-3a^{2}-3a+9\right){x}-7a^{2}-6a+12$
9.2-a3 9.2-a 3.3.257.1 \( 3^{2} \) $0$ $\Z/2\Z$ $1$ $15.26036525$ 0.951915430 \( \frac{952377494237}{6561} a^{2} - \frac{2793434061809}{6561} a + \frac{1537874453914}{6561} \) \( \bigl[1\) , \( -a^{2} - a + 2\) , \( a\) , \( 29 a^{2} - 9 a - 123\) , \( 148 a^{2} - 17 a - 575\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a^{2}-a+2\right){x}^{2}+\left(29a^{2}-9a-123\right){x}+148a^{2}-17a-575$
9.2-a4 9.2-a 3.3.257.1 \( 3^{2} \) $0$ $\Z/2\Z$ $1$ $30.52073051$ 0.951915430 \( \frac{1737352}{81} a^{2} + \frac{3240461}{81} a - \frac{3315481}{81} \) \( \bigl[1\) , \( -a^{2} - a + 2\) , \( a\) , \( -a^{2} - 4 a - 3\) , \( 15 a^{2} + 14 a - 29\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a^{2}-a+2\right){x}^{2}+\left(-a^{2}-4a-3\right){x}+15a^{2}+14a-29$
9.2-b1 9.2-b 3.3.257.1 \( 3^{2} \) $0$ $\Z/2\Z$ $1$ $13.93653059$ 0.869336893 \( -\frac{169564940890516}{282429536481} a^{2} - \frac{93767995435637}{282429536481} a + \frac{1032142453154629}{282429536481} \) \( \bigl[a^{2} - 3\) , \( -a^{2} - a + 3\) , \( a^{2} - 3\) , \( -2 a^{2} + 14 a - 9\) , \( -18 a^{2} - 32 a + 31\bigr] \) ${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{2}-a+3\right){x}^{2}+\left(-2a^{2}+14a-9\right){x}-18a^{2}-32a+31$
9.2-b2 9.2-b 3.3.257.1 \( 3^{2} \) $0$ $\Z/2\Z$ $1$ $27.87306118$ 0.869336893 \( \frac{1812669625}{531441} a^{2} + \frac{2069390414}{531441} a - \frac{1917539791}{531441} \) \( \bigl[a^{2} - 3\) , \( -a^{2} - a + 3\) , \( a^{2} - 3\) , \( -2 a^{2} - 6 a + 6\) , \( -a^{2} - 5 a + 4\bigr] \) ${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{2}-a+3\right){x}^{2}+\left(-2a^{2}-6a+6\right){x}-a^{2}-5a+4$
9.2-b3 9.2-b 3.3.257.1 \( 3^{2} \) $0$ $\Z/6\Z$ $1$ $125.4287753$ 0.869336893 \( \frac{952377494237}{6561} a^{2} - \frac{2793434061809}{6561} a + \frac{1537874453914}{6561} \) \( \bigl[a^{2} + a - 2\) , \( a^{2} + a - 4\) , \( 0\) , \( 4 a^{2} + 4 a - 12\) , \( 21 a^{2} + 28 a - 12\bigr] \) ${y}^2+\left(a^{2}+a-2\right){x}{y}={x}^{3}+\left(a^{2}+a-4\right){x}^{2}+\left(4a^{2}+4a-12\right){x}+21a^{2}+28a-12$
9.2-b4 9.2-b 3.3.257.1 \( 3^{2} \) $0$ $\Z/6\Z$ $1$ $250.8575506$ 0.869336893 \( \frac{1737352}{81} a^{2} + \frac{3240461}{81} a - \frac{3315481}{81} \) \( \bigl[a^{2} + a - 2\) , \( a^{2} + a - 4\) , \( 0\) , \( -a^{2} - a + 3\) , \( 0\bigr] \) ${y}^2+\left(a^{2}+a-2\right){x}{y}={x}^{3}+\left(a^{2}+a-4\right){x}^{2}+\left(-a^{2}-a+3\right){x}$
15.1-a1 15.1-a 3.3.257.1 \( 3 \cdot 5 \) $0$ $\Z/2\Z$ $1$ $1.884794823$ 0.940562166 \( \frac{4561952344347894508816}{50625} a^{2} + \frac{5468372973632837498513}{50625} a - \frac{6224545788789433223542}{50625} \) \( \bigl[a\) , \( a - 1\) , \( 0\) , \( -80 a^{2} - 340 a - 369\) , \( -2244 a^{2} - 5118 a - 1584\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-80a^{2}-340a-369\right){x}-2244a^{2}-5118a-1584$
15.1-a2 15.1-a 3.3.257.1 \( 3 \cdot 5 \) $0$ $\Z/4\Z$ $1$ $60.31343436$ 0.940562166 \( \frac{25393788989964280607}{225} a^{2} - \frac{73952533248919150724}{225} a + \frac{39839035941583441516}{225} \) \( \bigl[a\) , \( a - 1\) , \( 0\) , \( 5 a^{2} + 20 a - 64\) , \( -2 a^{2} - 91 a + 193\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(5a^{2}+20a-64\right){x}-2a^{2}-91a+193$
15.1-a3 15.1-a 3.3.257.1 \( 3 \cdot 5 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $15.07835859$ 0.940562166 \( \frac{311251219371829121}{2562890625} a^{2} + \frac{373240221797370628}{2562890625} a - \frac{424319657035623452}{2562890625} \) \( \bigl[a\) , \( a - 1\) , \( 0\) , \( -5 a^{2} - 20 a - 24\) , \( -44 a^{2} - 93 a - 9\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-5a^{2}-20a-24\right){x}-44a^{2}-93a-9$
15.1-a4 15.1-a 3.3.257.1 \( 3 \cdot 5 \) $0$ $\Z/2\Z\oplus\Z/4\Z$ $1$ $120.6268687$ 0.940562166 \( \frac{5176756484309}{50625} a^{2} - \frac{15075007347263}{50625} a + \frac{8121003692917}{50625} \) \( \bigl[a\) , \( a - 1\) , \( 0\) , \( -4\) , \( -a^{2} - 4 a + 4\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}-4{x}-a^{2}-4a+4$
15.1-a5 15.1-a 3.3.257.1 \( 3 \cdot 5 \) $0$ $\Z/2\Z$ $1$ $1.884794823$ 0.940562166 \( -\frac{28443849277171190300944}{6568408355712890625} a^{2} - \frac{34194402733320830270417}{6568408355712890625} a + \frac{38637799905139432891078}{6568408355712890625} \) \( \bigl[a\) , \( a - 1\) , \( 0\) , \( -10 a^{2} - 20 a + 1\) , \( -16 a^{2} - 104 a - 126\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-10a^{2}-20a+1\right){x}-16a^{2}-104a-126$
15.1-a6 15.1-a 3.3.257.1 \( 3 \cdot 5 \) $0$ $\Z/8\Z$ $1$ $241.2537374$ 0.940562166 \( -\frac{660182}{225} a^{2} + \frac{2137499}{225} a - \frac{807616}{225} \) \( \bigl[a\) , \( a - 1\) , \( 0\) , \( 1\) , \( 0\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+{x}$
15.1-b1 15.1-b 3.3.257.1 \( 3 \cdot 5 \) $0$ $\Z/2\Z$ $1$ $4.387233228$ 1.094672359 \( \frac{25393788989964280607}{225} a^{2} - \frac{73952533248919150724}{225} a + \frac{39839035941583441516}{225} \) \( \bigl[1\) , \( a^{2} - a - 3\) , \( 1\) , \( -66 a^{2} + 195 a - 107\) , \( -762 a^{2} + 2197 a - 1180\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(-66a^{2}+195a-107\right){x}-762a^{2}+2197a-1180$
15.1-b2 15.1-b 3.3.257.1 \( 3 \cdot 5 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $35.09786582$ 1.094672359 \( \frac{5176756484309}{50625} a^{2} - \frac{15075007347263}{50625} a + \frac{8121003692917}{50625} \) \( \bigl[1\) , \( a^{2} - a - 3\) , \( 1\) , \( -6 a^{2} + 10 a - 2\) , \( -16 a^{2} + 41 a - 22\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(-6a^{2}+10a-2\right){x}-16a^{2}+41a-22$
15.1-b3 15.1-b 3.3.257.1 \( 3 \cdot 5 \) $0$ $\Z/4\Z$ $1$ $70.19573165$ 1.094672359 \( -\frac{660182}{225} a^{2} + \frac{2137499}{225} a - \frac{807616}{225} \) \( \bigl[1\) , \( a^{2} - a - 3\) , \( 1\) , \( -a^{2} + 3\) , \( a - 2\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(-a^{2}+3\right){x}+a-2$
15.1-b4 15.1-b 3.3.257.1 \( 3 \cdot 5 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $17.54893291$ 1.094672359 \( \frac{311251219371829121}{2562890625} a^{2} + \frac{373240221797370628}{2562890625} a - \frac{424319657035623452}{2562890625} \) \( \bigl[1\) , \( a^{2} - a - 3\) , \( 1\) , \( -26 a^{2} - 15 a + 23\) , \( -114 a^{2} - 75 a + 116\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(-26a^{2}-15a+23\right){x}-114a^{2}-75a+116$
15.1-b5 15.1-b 3.3.257.1 \( 3 \cdot 5 \) $0$ $\Z/2\Z$ $1$ $2.193616614$ 1.094672359 \( -\frac{28443849277171190300944}{6568408355712890625} a^{2} - \frac{34194402733320830270417}{6568408355712890625} a + \frac{38637799905139432891078}{6568408355712890625} \) \( \bigl[1\) , \( a^{2} - a - 3\) , \( 1\) , \( -21 a^{2} - 30 a + 33\) , \( -136 a^{2} - 19 a + 88\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(-21a^{2}-30a+33\right){x}-136a^{2}-19a+88$
15.1-b6 15.1-b 3.3.257.1 \( 3 \cdot 5 \) $0$ $\Z/2\Z$ $1$ $8.774466456$ 1.094672359 \( \frac{4561952344347894508816}{50625} a^{2} + \frac{5468372973632837498513}{50625} a - \frac{6224545788789433223542}{50625} \) \( \bigl[1\) , \( a^{2} - a - 3\) , \( 1\) , \( -351 a^{2} - 400 a + 413\) , \( -6364 a^{2} - 7615 a + 8876\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(-351a^{2}-400a+413\right){x}-6364a^{2}-7615a+8876$
19.1-a1 19.1-a 3.3.257.1 \( 19 \) $0$ $\Z/2\Z$ $1$ $7.793500282$ 1.458435572 \( \frac{33777701165536011237}{2213314919066161} a^{2} - \frac{277355301401585077884}{2213314919066161} a + \frac{184960608190583522339}{2213314919066161} \) \( \bigl[a^{2} + a - 2\) , \( -a + 1\) , \( a^{2} - 2\) , \( 22 a^{2} - a - 116\) , \( 36 a^{2} - 32 a - 143\bigr] \) ${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(22a^{2}-a-116\right){x}+36a^{2}-32a-143$
19.1-a2 19.1-a 3.3.257.1 \( 19 \) $0$ $\Z/2\Z$ $1$ $23.38050084$ 1.458435572 \( -\frac{28175458029840}{130321} a^{2} + \frac{8070882399369}{130321} a + \frac{118461749726429}{130321} \) \( \bigl[a^{2} + a - 2\) , \( -a + 1\) , \( a^{2} - 2\) , \( 22 a^{2} - 6 a - 91\) , \( 79 a^{2} - 21 a - 332\bigr] \) ${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(22a^{2}-6a-91\right){x}+79a^{2}-21a-332$
19.1-a3 19.1-a 3.3.257.1 \( 19 \) $0$ $\Z/2\Z$ $1$ $46.76100169$ 1.458435572 \( \frac{2816089}{361} a^{2} - \frac{532982}{361} a - \frac{11269471}{361} \) \( \bigl[a^{2} + a - 2\) , \( -a + 1\) , \( a^{2} - 2\) , \( 2 a^{2} - a - 6\) , \( 2 a^{2} - 7\bigr] \) ${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(2a^{2}-a-6\right){x}+2a^{2}-7$
19.1-a4 19.1-a 3.3.257.1 \( 19 \) $0$ $\Z/2\Z$ $1$ $15.58700056$ 1.458435572 \( \frac{108976900762638027}{47045881} a^{2} + \frac{130629686944915561}{47045881} a - \frac{148693269376177306}{47045881} \) \( \bigl[a^{2} + a - 2\) , \( -a + 1\) , \( a^{2} - 2\) , \( -8 a^{2} - a + 29\) , \( -3 a^{2} - 9 a - 5\bigr] \) ${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-8a^{2}-a+29\right){x}-3a^{2}-9a-5$
19.1-b1 19.1-b 3.3.257.1 \( 19 \) $0$ $\Z/2\Z$ $1$ $4.157201887$ 0.777957386 \( \frac{33777701165536011237}{2213314919066161} a^{2} - \frac{277355301401585077884}{2213314919066161} a + \frac{184960608190583522339}{2213314919066161} \) \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -30 a^{2} + 79 a - 51\) , \( -206 a^{2} + 565 a - 298\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-30a^{2}+79a-51\right){x}-206a^{2}+565a-298$
19.1-b2 19.1-b 3.3.257.1 \( 19 \) $0$ $\Z/6\Z$ $1$ $112.2444509$ 0.777957386 \( -\frac{28175458029840}{130321} a^{2} + \frac{8070882399369}{130321} a + \frac{118461749726429}{130321} \) \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 4 a - 11\) , \( a^{2} - 7 a + 9\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(4a-11\right){x}+a^{2}-7a+9$
19.1-b3 19.1-b 3.3.257.1 \( 19 \) $0$ $\Z/6\Z$ $1$ $224.4889018$ 0.777957386 \( \frac{2816089}{361} a^{2} - \frac{532982}{361} a - \frac{11269471}{361} \) \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -a - 1\) , \( -a\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}-a$
19.1-b4 19.1-b 3.3.257.1 \( 19 \) $0$ $\Z/2\Z$ $1$ $8.314403774$ 0.777957386 \( \frac{108976900762638027}{47045881} a^{2} + \frac{130629686944915561}{47045881} a - \frac{148693269376177306}{47045881} \) \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -5 a^{2} - a + 4\) , \( -14 a^{2} + 6 a + 3\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-5a^{2}-a+4\right){x}-14a^{2}+6a+3$
21.1-a1 21.1-a 3.3.257.1 \( 3 \cdot 7 \) $0$ $\Z/4\Z$ $1$ $8.362730790$ 1.043305628 \( -\frac{7508368686128970279577}{299096375126409} a^{2} + \frac{1616589880731750120535}{299096375126409} a + \frac{32458428323711052321331}{299096375126409} \) \( \bigl[a^{2} - 3\) , \( a^{2} - a - 4\) , \( a^{2} - 3\) , \( -160 a^{2} + 399 a - 230\) , \( 2052 a^{2} - 6371 a + 3573\bigr] \) ${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(-160a^{2}+399a-230\right){x}+2052a^{2}-6371a+3573$
21.1-a2 21.1-a 3.3.257.1 \( 3 \cdot 7 \) $0$ $\Z/2\Z$ $1$ $4.181365395$ 1.043305628 \( \frac{95456569237420574}{2109289329} a^{2} - \frac{317812138936041299}{2109289329} a + \frac{237309629218867696}{2109289329} \) \( \bigl[a^{2} - 3\) , \( a^{2} - a - 4\) , \( a^{2} - 3\) , \( -60 a^{2} + 174 a - 100\) , \( -630 a^{2} + 1828 a - 986\bigr] \) ${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(-60a^{2}+174a-100\right){x}-630a^{2}+1828a-986$
21.1-a3 21.1-a 3.3.257.1 \( 3 \cdot 7 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $33.45092316$ 1.043305628 \( \frac{2469125117705}{15752961} a^{2} + \frac{2848919682052}{15752961} a - \frac{3194204179760}{15752961} \) \( \bigl[a^{2} - 3\) , \( a^{2} - a - 4\) , \( a^{2} - 3\) , \( -5 a^{2} + 9 a - 5\) , \( -12 a^{2} + 31 a - 18\bigr] \) ${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(-5a^{2}+9a-5\right){x}-12a^{2}+31a-18$
21.1-a4 21.1-a 3.3.257.1 \( 3 \cdot 7 \) $0$ $\Z/4\Z$ $1$ $66.90184632$ 1.043305628 \( \frac{897469}{3969} a^{2} + \frac{1607729}{3969} a - \frac{153931}{3969} \) \( \bigl[a^{2} - 3\) , \( a^{2} - a - 4\) , \( a^{2} - 3\) , \( -a\) , \( a - 3\bigr] \) ${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}-a{x}+a-3$
21.1-a5 21.1-a 3.3.257.1 \( 3 \cdot 7 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $16.72546158$ 1.043305628 \( \frac{69292788128748168482}{466948881} a^{2} + \frac{83060659682984324659}{466948881} a - \frac{94546406199955131680}{466948881} \) \( \bigl[a^{2} - 3\) , \( a^{2} - a - 4\) , \( a^{2} - 3\) , \( -30 a^{2} + 4 a + 10\) , \( -62 a^{2} - 166 a + 150\bigr] \) ${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(-30a^{2}+4a+10\right){x}-62a^{2}-166a+150$
21.1-a6 21.1-a 3.3.257.1 \( 3 \cdot 7 \) $0$ $\Z/2\Z$ $1$ $2.090682697$ 1.043305628 \( \frac{2905242808362156164576920441}{21609} a^{2} + \frac{3482489114671540668959169161}{21609} a - \frac{3964052911380531038654086531}{21609} \) \( \bigl[a^{2} - 3\) , \( a^{2} - a - 4\) , \( a^{2} - 3\) , \( -300 a^{2} - 471 a + 490\) , \( -5356 a^{2} - 7249 a + 7899\bigr] \) ${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(-300a^{2}-471a+490\right){x}-5356a^{2}-7249a+7899$
21.1-b1 21.1-b 3.3.257.1 \( 3 \cdot 7 \) $0$ $\Z/2\Z$ $1$ $1.143972128$ 1.141744332 \( -\frac{7508368686128970279577}{299096375126409} a^{2} + \frac{1616589880731750120535}{299096375126409} a + \frac{32458428323711052321331}{299096375126409} \) \( \bigl[a^{2} + a - 3\) , \( 1\) , \( a^{2} + a - 3\) , \( 50 a^{2} + 10 a - 350\) , \( 432 a^{2} + 24 a - 2598\bigr] \) ${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+{x}^{2}+\left(50a^{2}+10a-350\right){x}+432a^{2}+24a-2598$
21.1-b2 21.1-b 3.3.257.1 \( 3 \cdot 7 \) $0$ $\Z/8\Z$ $1$ $36.60710812$ 1.141744332 \( \frac{95456569237420574}{2109289329} a^{2} - \frac{317812138936041299}{2109289329} a + \frac{237309629218867696}{2109289329} \) \( \bigl[a^{2} + a - 3\) , \( 1\) , \( a^{2} + a - 3\) , \( 10 a^{2} + 15 a - 85\) , \( -27 a^{2} - 50 a + 227\bigr] \) ${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+{x}^{2}+\left(10a^{2}+15a-85\right){x}-27a^{2}-50a+227$
21.1-b3 21.1-b 3.3.257.1 \( 3 \cdot 7 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $9.151777031$ 1.141744332 \( \frac{69292788128748168482}{466948881} a^{2} + \frac{83060659682984324659}{466948881} a - \frac{94546406199955131680}{466948881} \) \( \bigl[a^{2} + a - 3\) , \( 1\) , \( a^{2} + a - 3\) , \( -10 a^{2} - 15 a - 5\) , \( -65 a^{2} - 88 a + 51\bigr] \) ${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+{x}^{2}+\left(-10a^{2}-15a-5\right){x}-65a^{2}-88a+51$
21.1-b4 21.1-b 3.3.257.1 \( 3 \cdot 7 \) $0$ $\Z/2\Z\oplus\Z/4\Z$ $1$ $73.21421624$ 1.141744332 \( \frac{2469125117705}{15752961} a^{2} + \frac{2848919682052}{15752961} a - \frac{3194204179760}{15752961} \) \( \bigl[a^{2} + a - 3\) , \( 1\) , \( a^{2} + a - 3\) , \( -5\) , \( -2 a^{2} - 3 a + 3\bigr] \) ${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+{x}^{2}-5{x}-2a^{2}-3a+3$
21.1-b5 21.1-b 3.3.257.1 \( 3 \cdot 7 \) $0$ $\Z/8\Z$ $1$ $146.4284324$ 1.141744332 \( \frac{897469}{3969} a^{2} + \frac{1607729}{3969} a - \frac{153931}{3969} \) \( \bigl[a^{2} + a - 3\) , \( 1\) , \( a^{2} + a - 3\) , \( 0\) , \( 0\bigr] \) ${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+{x}^{2}$
21.1-b6 21.1-b 3.3.257.1 \( 3 \cdot 7 \) $0$ $\Z/2\Z$ $1$ $1.143972128$ 1.141744332 \( \frac{2905242808362156164576920441}{21609} a^{2} + \frac{3482489114671540668959169161}{21609} a - \frac{3964052911380531038654086531}{21609} \) \( \bigl[a^{2} + a - 3\) , \( 1\) , \( a^{2} + a - 3\) , \( -230 a^{2} - 280 a + 340\) , \( -3614 a^{2} - 4360 a + 4812\bigr] \) ${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+{x}^{2}+\left(-230a^{2}-280a+340\right){x}-3614a^{2}-4360a+4812$
24.1-a1 24.1-a 3.3.257.1 \( 2^{3} \cdot 3 \) $0$ $\Z/2\Z$ $1$ $2.555000411$ 1.434388921 \( -\frac{154293134081829766900361}{162} a^{2} + \frac{176796519237114293338739}{648} a + \frac{2594841168555327735277343}{648} \) \( \bigl[1\) , \( a^{2} + a - 3\) , \( a^{2} - 3\) , \( 981 a^{2} - 259 a - 4177\) , \( 23174 a^{2} - 6568 a - 97609\bigr] \) ${y}^2+{x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}+a-3\right){x}^{2}+\left(981a^{2}-259a-4177\right){x}+23174a^{2}-6568a-97609$
24.1-a2 24.1-a 3.3.257.1 \( 2^{3} \cdot 3 \) $0$ $\Z/2\Z$ $1$ $2.555000411$ 1.434388921 \( \frac{9015229605265}{576} a^{2} - \frac{1281213726707}{288} a - \frac{37865221303999}{576} \) \( \bigl[1\) , \( a^{2} + a - 3\) , \( a^{2} - 3\) , \( 61 a^{2} - 19 a - 257\) , \( 334 a^{2} - 96 a - 1425\bigr] \) ${y}^2+{x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}+a-3\right){x}^{2}+\left(61a^{2}-19a-257\right){x}+334a^{2}-96a-1425$
Next   Download to        

  *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.