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Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
67.1-a1 67.1-a \(\Q(\sqrt{-67}) \) \( 67 \) $0$ $\mathsf{trivial}$ $1$ $3.859482961$ 1.886043555 \( -\frac{207474688}{67} \) \( \bigl[0\) , \( 1\) , \( 1\) , \( -12\) , \( -21\bigr] \) ${y}^2+{y}={x}^3+{x}^2-12{x}-21$
121.1-a1 121.1-a \(\Q(\sqrt{-67}) \) \( 11^{2} \) $0$ $\mathsf{trivial}$ $1$ $0.370308724$ 0.814327400 \( -\frac{52893159101157376}{11} \) \( \bigl[0\) , \( -1\) , \( 1\) , \( -7820\) , \( -263580\bigr] \) ${y}^2+{y}={x}^3-{x}^2-7820{x}-263580$
121.1-a2 121.1-a \(\Q(\sqrt{-67}) \) \( 11^{2} \) $0$ $\Z/5\Z$ $1$ $1.851543623$ 0.814327400 \( -\frac{122023936}{161051} \) \( \bigl[0\) , \( -1\) , \( 1\) , \( -10\) , \( -20\bigr] \) ${y}^2+{y}={x}^3-{x}^2-10{x}-20$
121.1-a3 121.1-a \(\Q(\sqrt{-67}) \) \( 11^{2} \) $0$ $\Z/5\Z$ $1$ $9.257718117$ 0.814327400 \( -\frac{4096}{11} \) \( \bigl[0\) , \( -1\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{y}={x}^3-{x}^2$
153.1-a1 153.1-a \(\Q(\sqrt{-67}) \) \( 3^{2} \cdot 17 \) $1$ $\mathsf{trivial}$ $0.178252297$ $2.171532488$ 3.783154287 \( \frac{232667875}{6765201} a + \frac{294541375}{20295603} \) \( \bigl[a\) , \( a + 1\) , \( a\) , \( -3 a - 1\) , \( -5 a + 16\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^3+\left(a+1\right){x}^2+\left(-3a-1\right){x}-5a+16$
153.2-a1 153.2-a \(\Q(\sqrt{-67}) \) \( 3^{2} \cdot 17 \) $1$ $\mathsf{trivial}$ $0.178252297$ $2.171532488$ 3.783154287 \( -\frac{232667875}{6765201} a + \frac{58385000}{1193859} \) \( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( -5 a - 14\) , \( 20\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^3+\left(a-1\right){x}^2+\left(-5a-14\right){x}+20$
196.1-a1 196.1-a \(\Q(\sqrt{-67}) \) \( 2^{2} \cdot 7^{2} \) $0 \le r \le 1$ $\Z/2\Z$ $1$ $0.875417135$ 4.861651226 \( -\frac{548347731625}{1835008} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -171\) , \( -874\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-171{x}-874$
196.1-a2 196.1-a \(\Q(\sqrt{-67}) \) \( 2^{2} \cdot 7^{2} \) $0 \le r \le 1$ $\Z/6\Z$ $1$ $7.878754216$ 4.861651226 \( -\frac{15625}{28} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( 0\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-{x}$
196.1-a3 196.1-a \(\Q(\sqrt{-67}) \) \( 2^{2} \cdot 7^{2} \) $0 \le r \le 1$ $\Z/6\Z$ $1$ $2.626251405$ 4.861651226 \( \frac{9938375}{21952} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( 4\) , \( -6\bigr] \) ${y}^2+{x}{y}+{y}={x}^3+4{x}-6$
196.1-a4 196.1-a \(\Q(\sqrt{-67}) \) \( 2^{2} \cdot 7^{2} \) $0 \le r \le 1$ $\Z/6\Z$ $1$ $1.313125702$ 4.861651226 \( \frac{4956477625}{941192} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -36\) , \( -70\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-36{x}-70$
196.1-a5 196.1-a \(\Q(\sqrt{-67}) \) \( 2^{2} \cdot 7^{2} \) $0 \le r \le 1$ $\Z/6\Z$ $1$ $3.939377108$ 4.861651226 \( \frac{128787625}{98} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -11\) , \( 12\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-11{x}+12$
196.1-a6 196.1-a \(\Q(\sqrt{-67}) \) \( 2^{2} \cdot 7^{2} \) $0 \le r \le 1$ $\Z/2\Z$ $1$ $0.437708567$ 4.861651226 \( \frac{2251439055699625}{25088} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -2731\) , \( -55146\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-2731{x}-55146$
225.1-a1 225.1-a \(\Q(\sqrt{-67}) \) \( 3^{2} \cdot 5^{2} \) $1$ $\Z/2\Z$ $3.066020343$ $0.558925428$ 3.349742948 \( -\frac{147281603041}{215233605} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -110\) , \( -880\bigr] \) ${y}^2+{x}{y}+{y}={x}^3+{x}^2-110{x}-880$
225.1-a2 225.1-a \(\Q(\sqrt{-67}) \) \( 3^{2} \cdot 5^{2} \) $1$ $\Z/4\Z$ $12.26408137$ $8.942806850$ 3.349742948 \( -\frac{1}{15} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{x}{y}+{y}={x}^3+{x}^2$
225.1-a3 225.1-a \(\Q(\sqrt{-67}) \) \( 3^{2} \cdot 5^{2} \) $1$ $\Z/8\Z$ $24.52816274$ $1.117850856$ 3.349742948 \( \frac{4733169839}{3515625} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( 35\) , \( -28\bigr] \) ${y}^2+{x}{y}+{y}={x}^3+{x}^2+35{x}-28$
225.1-a4 225.1-a \(\Q(\sqrt{-67}) \) \( 3^{2} \cdot 5^{2} \) $1$ $\Z/2\Z\oplus\Z/4\Z$ $12.26408137$ $2.235701712$ 3.349742948 \( \frac{111284641}{50625} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -10\) , \( -10\bigr] \) ${y}^2+{x}{y}+{y}={x}^3+{x}^2-10{x}-10$
225.1-a5 225.1-a \(\Q(\sqrt{-67}) \) \( 3^{2} \cdot 5^{2} \) $1$ $\Z/2\Z\oplus\Z/4\Z$ $24.52816274$ $4.471403425$ 3.349742948 \( \frac{13997521}{225} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -5\) , \( 2\bigr] \) ${y}^2+{x}{y}+{y}={x}^3+{x}^2-5{x}+2$
225.1-a6 225.1-a \(\Q(\sqrt{-67}) \) \( 3^{2} \cdot 5^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $6.132040686$ $1.117850856$ 3.349742948 \( \frac{272223782641}{164025} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -135\) , \( -660\bigr] \) ${y}^2+{x}{y}+{y}={x}^3+{x}^2-135{x}-660$
225.1-a7 225.1-a \(\Q(\sqrt{-67}) \) \( 3^{2} \cdot 5^{2} \) $1$ $\Z/4\Z$ $49.05632549$ $2.235701712$ 3.349742948 \( \frac{56667352321}{15} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -80\) , \( 242\bigr] \) ${y}^2+{x}{y}+{y}={x}^3+{x}^2-80{x}+242$
225.1-a8 225.1-a \(\Q(\sqrt{-67}) \) \( 3^{2} \cdot 5^{2} \) $1$ $\Z/2\Z$ $12.26408137$ $0.558925428$ 3.349742948 \( \frac{1114544804970241}{405} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -2160\) , \( -39540\bigr] \) ${y}^2+{x}{y}+{y}={x}^3+{x}^2-2160{x}-39540$
261.1-a1 261.1-a \(\Q(\sqrt{-67}) \) \( 3^{2} \cdot 29 \) $0$ $\mathsf{trivial}$ $1$ $8.758249111$ 2.139980855 \( -\frac{863}{87} a + \frac{8884}{29} \) \( \bigl[a\) , \( a\) , \( a + 1\) , \( -4 a + 6\) , \( 12\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^3+a{x}^2+\left(-4a+6\right){x}+12$
261.2-a1 261.2-a \(\Q(\sqrt{-67}) \) \( 3^{2} \cdot 29 \) $0$ $\mathsf{trivial}$ $1$ $8.758249111$ 2.139980855 \( \frac{863}{87} a + \frac{25789}{87} \) \( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -4 a - 6\) , \( -3 a + 17\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(a+1\right){x}^2+\left(-4a-6\right){x}-3a+17$
284.1-a1 284.1-a \(\Q(\sqrt{-67}) \) \( 2^{2} \cdot 71 \) $0$ $\mathsf{trivial}$ $1$ $1.614969731$ 3.156799276 \( -\frac{5091264344375}{715822} a - \frac{39429602184747}{1431644} \) \( \bigl[a\) , \( a + 1\) , \( 0\) , \( 18 a + 36\) , \( 8 a - 552\bigr] \) ${y}^2+a{x}{y}={x}^3+\left(a+1\right){x}^2+\left(18a+36\right){x}+8a-552$
284.1-a2 284.1-a \(\Q(\sqrt{-67}) \) \( 2^{2} \cdot 71 \) $0$ $\Z/3\Z$ $1$ $4.844909195$ 3.156799276 \( -\frac{157087}{2272} a + \frac{3906953}{4544} \) \( \bigl[a\) , \( a + 1\) , \( 0\) , \( -2 a - 4\) , \( 4\bigr] \) ${y}^2+a{x}{y}={x}^3+\left(a+1\right){x}^2+\left(-2a-4\right){x}+4$
284.2-a1 284.2-a \(\Q(\sqrt{-67}) \) \( 2^{2} \cdot 71 \) $0$ $\mathsf{trivial}$ $1$ $1.614969731$ 3.156799276 \( \frac{5091264344375}{715822} a - \frac{49612130873497}{1431644} \) \( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( -26 a + 61\) , \( 53 a - 244\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^3+\left(a-1\right){x}^2+\left(-26a+61\right){x}+53a-244$
284.2-a2 284.2-a \(\Q(\sqrt{-67}) \) \( 2^{2} \cdot 71 \) $0$ $\Z/3\Z$ $1$ $4.844909195$ 3.156799276 \( \frac{157087}{2272} a + \frac{3592779}{4544} \) \( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( -6 a + 1\) , \( a + 24\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^3+\left(a-1\right){x}^2+\left(-6a+1\right){x}+a+24$
289.2-a1 289.2-a \(\Q(\sqrt{-67}) \) \( 17^{2} \) $1$ $\Z/4\Z$ $2.255518444$ $2.123938699$ 2.341051409 \( -\frac{35937}{83521} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( -1\) , \( -14\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-{x}^2-{x}-14$
289.2-a2 289.2-a \(\Q(\sqrt{-67}) \) \( 17^{2} \) $1$ $\Z/4\Z$ $9.022073779$ $8.495754796$ 2.341051409 \( \frac{35937}{17} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( -1\) , \( 0\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-{x}^2-{x}$
289.2-a3 289.2-a \(\Q(\sqrt{-67}) \) \( 17^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $4.511036889$ $4.247877398$ 2.341051409 \( \frac{20346417}{289} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( -6\) , \( -4\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-{x}^2-6{x}-4$
289.2-a4 289.2-a \(\Q(\sqrt{-67}) \) \( 17^{2} \) $1$ $\Z/2\Z$ $9.022073779$ $2.123938699$ 2.341051409 \( \frac{82483294977}{17} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( -91\) , \( -310\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-{x}^2-91{x}-310$
289.2-b1 289.2-b \(\Q(\sqrt{-67}) \) \( 17^{2} \) $0 \le r \le 1$ $\Z/4\Z$ $1$ $6.344730303$ 5.440745087 \( -\frac{148207}{289} a - \frac{1202001}{289} \) \( \bigl[a\) , \( -1\) , \( a\) , \( -a + 17\) , \( 0\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^3-{x}^2+\left(-a+17\right){x}$
289.2-b2 289.2-b \(\Q(\sqrt{-67}) \) \( 17^{2} \) $0 \le r \le 1$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $3.172365151$ 5.440745087 \( \frac{38622639}{83521} a - \frac{261111040}{83521} \) \( \bigl[a\) , \( -1\) , \( a\) , \( -a + 12\) , \( -a + 14\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^3-{x}^2+\left(-a+12\right){x}-a+14$
289.2-b3 289.2-b \(\Q(\sqrt{-67}) \) \( 17^{2} \) $0 \le r \le 1$ $\Z/2\Z$ $1$ $1.586182575$ 5.440745087 \( -\frac{1630752658559}{6975757441} a - \frac{13563750492577}{6975757441} \) \( \bigl[a\) , \( -1\) , \( a\) , \( -6 a + 17\) , \( -a + 31\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^3-{x}^2+\left(-6a+17\right){x}-a+31$
289.2-b4 289.2-b \(\Q(\sqrt{-67}) \) \( 17^{2} \) $0 \le r \le 1$ $\Z/4\Z$ $1$ $1.586182575$ 5.440745087 \( -\frac{281039152449}{83521} a + \frac{53838709537}{4913} \) \( \bigl[a\) , \( -1\) , \( a\) , \( 4 a - 73\) , \( -45 a + 473\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^3-{x}^2+\left(4a-73\right){x}-45a+473$
289.2-c1 289.2-c \(\Q(\sqrt{-67}) \) \( 17^{2} \) $1$ $\Z/4\Z$ $14.03823826$ $6.344730303$ 5.440745087 \( \frac{148207}{289} a - 4672 \) \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -a + 16\) , \( -a\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(-a-1\right){x}^2+\left(-a+16\right){x}-a$
289.2-c2 289.2-c \(\Q(\sqrt{-67}) \) \( 17^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $7.019119134$ $3.172365151$ 5.440745087 \( -\frac{38622639}{83521} a - \frac{13087553}{4913} \) \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -a + 11\) , \( 13\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(-a-1\right){x}^2+\left(-a+11\right){x}+13$
289.2-c3 289.2-c \(\Q(\sqrt{-67}) \) \( 17^{2} \) $1$ $\Z/2\Z$ $3.509559567$ $1.586182575$ 5.440745087 \( \frac{1630752658559}{6975757441} a - \frac{893794303008}{410338673} \) \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 4 a + 11\) , \( 30\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(-a-1\right){x}^2+\left(4a+11\right){x}+30$
289.2-c4 289.2-c \(\Q(\sqrt{-67}) \) \( 17^{2} \) $1$ $\Z/4\Z$ $14.03823826$ $1.586182575$ 5.440745087 \( \frac{281039152449}{83521} a + \frac{634218909680}{83521} \) \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -6 a - 69\) , \( 44 a + 428\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(-a-1\right){x}^2+\left(-6a-69\right){x}+44a+428$
323.1-a1 323.1-a \(\Q(\sqrt{-67}) \) \( 17 \cdot 19 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $12.20177321$ $1.261704143$ 5.642405987 \( \frac{1748866680606381}{8713662409} a - \frac{9094554943235725}{8713662409} \) \( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( -16 a + 79\) , \( 27 a + 217\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^3+\left(-a-1\right){x}^2+\left(-16a+79\right){x}+27a+217$
323.1-a2 323.1-a \(\Q(\sqrt{-67}) \) \( 17 \cdot 19 \) $1$ $\Z/2\Z$ $6.100886608$ $0.630852071$ 5.642405987 \( -\frac{2419318767383236671}{11069822507365459} a + \frac{4286199549368669726}{11069822507365459} \) \( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( -11 a + 84\) , \( -5 a + 394\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^3+\left(-a-1\right){x}^2+\left(-11a+84\right){x}-5a+394$
323.1-a3 323.1-a \(\Q(\sqrt{-67}) \) \( 17 \cdot 19 \) $1$ $\Z/4\Z$ $6.100886608$ $2.523408287$ 5.642405987 \( \frac{136407521111}{640267073} a + \frac{689979389248}{640267073} \) \( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( -a - 1\) , \( 0\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^3+\left(-a-1\right){x}^2+\left(-a-1\right){x}$
323.1-a4 323.1-a \(\Q(\sqrt{-67}) \) \( 17 \cdot 19 \) $1$ $\Z/2\Z$ $24.40354643$ $0.630852071$ 5.642405987 \( -\frac{35375796455931953}{93347} a + \frac{37907536261605426}{93347} \) \( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( -261 a + 1354\) , \( 2647 a + 18968\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^3+\left(-a-1\right){x}^2+\left(-261a+1354\right){x}+2647a+18968$
323.4-a1 323.4-a \(\Q(\sqrt{-67}) \) \( 17 \cdot 19 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $12.20177321$ $1.261704143$ 5.642405987 \( -\frac{1748866680606381}{8713662409} a - \frac{432099309566432}{512568377} \) \( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( 17 a + 63\) , \( -12 a + 308\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^3+\left(a+1\right){x}^2+\left(17a+63\right){x}-12a+308$
323.4-a2 323.4-a \(\Q(\sqrt{-67}) \) \( 17 \cdot 19 \) $1$ $\Z/2\Z$ $6.100886608$ $0.630852071$ 5.642405987 \( \frac{2419318767383236671}{11069822507365459} a + \frac{109816516587378415}{651166029845027} \) \( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( 12 a + 73\) , \( 15 a + 463\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^3+\left(a+1\right){x}^2+\left(12a+73\right){x}+15a+463$
323.4-a3 323.4-a \(\Q(\sqrt{-67}) \) \( 17 \cdot 19 \) $1$ $\Z/4\Z$ $6.100886608$ $2.523408287$ 5.642405987 \( -\frac{136407521111}{640267073} a + \frac{48610994727}{37662769} \) \( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( 2 a - 2\) , \( -1\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^3+\left(a+1\right){x}^2+\left(2a-2\right){x}-1$
323.4-a4 323.4-a \(\Q(\sqrt{-67}) \) \( 17 \cdot 19 \) $1$ $\Z/2\Z$ $24.40354643$ $0.630852071$ 5.642405987 \( \frac{35375796455931953}{93347} a + \frac{148925870921969}{5491} \) \( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( 262 a + 1093\) , \( -2387 a + 22709\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^3+\left(a+1\right){x}^2+\left(262a+1093\right){x}-2387a+22709$
361.2-a1 361.2-a \(\Q(\sqrt{-67}) \) \( 19^{2} \) $1$ $\mathsf{trivial}$ $5.618953292$ $0.935309008$ 2.568225355 \( -\frac{50357871050752}{19} \) \( \bigl[0\) , \( 1\) , \( 1\) , \( -769\) , \( -8470\bigr] \) ${y}^2+{y}={x}^3+{x}^2-769{x}-8470$
361.2-a2 361.2-a \(\Q(\sqrt{-67}) \) \( 19^{2} \) $1$ $\Z/3\Z$ $1.872984430$ $2.805927025$ 2.568225355 \( -\frac{89915392}{6859} \) \( \bigl[0\) , \( 1\) , \( 1\) , \( -9\) , \( -15\bigr] \) ${y}^2+{y}={x}^3+{x}^2-9{x}-15$
361.2-a3 361.2-a \(\Q(\sqrt{-67}) \) \( 19^{2} \) $1$ $\Z/3\Z$ $5.618953292$ $8.417781075$ 2.568225355 \( \frac{32768}{19} \) \( \bigl[0\) , \( 1\) , \( 1\) , \( 1\) , \( 0\bigr] \) ${y}^2+{y}={x}^3+{x}^2+{x}$
400.1-a1 400.1-a \(\Q(\sqrt{-67}) \) \( 2^{4} \cdot 5^{2} \) $0$ $\Z/2\Z$ $1$ $1.070515942$ 1.177059041 \( -\frac{20720464}{15625} \) \( \bigl[0\) , \( 1\) , \( 0\) , \( -36\) , \( -140\bigr] \) ${y}^2={x}^3+{x}^2-36{x}-140$
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  *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.