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Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
43.1-a1 43.1-a \(\Q(\sqrt{-43}) \) \( 43 \) $1$ $\mathsf{trivial}$ $0.062816507$ $7.454821417$ 2.285213487 \( -\frac{4096}{43} \) \( \bigl[0\) , \( 1\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{y}={x}^3+{x}^2$
121.2-a1 121.2-a \(\Q(\sqrt{-43}) \) \( 11^{2} \) $1$ $\mathsf{trivial}$ $13.35189329$ $0.370308724$ 3.016008498 \( -\frac{52893159101157376}{11} \) \( \bigl[0\) , \( -1\) , \( 1\) , \( -7820\) , \( -263580\bigr] \) ${y}^2+{y}={x}^3-{x}^2-7820{x}-263580$
121.2-a2 121.2-a \(\Q(\sqrt{-43}) \) \( 11^{2} \) $1$ $\Z/5\Z$ $2.670378659$ $1.851543623$ 3.016008498 \( -\frac{122023936}{161051} \) \( \bigl[0\) , \( -1\) , \( 1\) , \( -10\) , \( -20\bigr] \) ${y}^2+{y}={x}^3-{x}^2-10{x}-20$
121.2-a3 121.2-a \(\Q(\sqrt{-43}) \) \( 11^{2} \) $1$ $\Z/5\Z$ $13.35189329$ $9.257718117$ 3.016008498 \( -\frac{4096}{11} \) \( \bigl[0\) , \( -1\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{y}={x}^3-{x}^2$
124.1-a1 124.1-a \(\Q(\sqrt{-43}) \) \( 2^{2} \cdot 31 \) $1$ $\mathsf{trivial}$ $0.402305613$ $0.766622012$ 3.386379653 \( \frac{74220480103668775}{52879244321342} a - \frac{604398001378036417}{105758488642684} \) \( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -16 a + 104\) , \( -84 a - 258\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^3+\left(-16a+104\right){x}-84a-258$
124.1-a2 124.1-a \(\Q(\sqrt{-43}) \) \( 2^{2} \cdot 31 \) $1$ $\Z/3\Z$ $3.620750519$ $6.899598111$ 3.386379653 \( \frac{1172807}{124} a + \frac{363245}{124} \) \( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -a - 1\) , \( 0\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^3+\left(-a-1\right){x}$
124.1-a3 124.1-a \(\Q(\sqrt{-43}) \) \( 2^{2} \cdot 31 \) $1$ $\Z/3\Z$ $1.206916839$ $2.299866037$ 3.386379653 \( -\frac{21870514825}{953312} a + \frac{38581946683}{1906624} \) \( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 4 a + 4\) , \( -4 a - 50\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^3+\left(4a+4\right){x}-4a-50$
124.2-a1 124.2-a \(\Q(\sqrt{-43}) \) \( 2^{2} \cdot 31 \) $1$ $\mathsf{trivial}$ $0.402305613$ $0.766622012$ 3.386379653 \( -\frac{74220480103668775}{52879244321342} a - \frac{455957041170698867}{105758488642684} \) \( \bigl[a\) , \( -a + 1\) , \( 1\) , \( 15 a + 89\) , \( 84 a - 342\bigr] \) ${y}^2+a{x}{y}+{y}={x}^3+\left(-a+1\right){x}^2+\left(15a+89\right){x}+84a-342$
124.2-a2 124.2-a \(\Q(\sqrt{-43}) \) \( 2^{2} \cdot 31 \) $1$ $\Z/3\Z$ $1.206916839$ $2.299866037$ 3.386379653 \( \frac{21870514825}{953312} a - \frac{5159082967}{1906624} \) \( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -5 a + 9\) , \( 4 a - 54\bigr] \) ${y}^2+a{x}{y}+{y}={x}^3+\left(-a+1\right){x}^2+\left(-5a+9\right){x}+4a-54$
124.2-a3 124.2-a \(\Q(\sqrt{-43}) \) \( 2^{2} \cdot 31 \) $1$ $\Z/3\Z$ $3.620750519$ $6.899598111$ 3.386379653 \( -\frac{1172807}{124} a + \frac{384013}{31} \) \( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -1\) , \( 0\bigr] \) ${y}^2+a{x}{y}+{y}={x}^3+\left(-a+1\right){x}^2-{x}$
193.1-a1 193.1-a \(\Q(\sqrt{-43}) \) \( 193 \) $1$ $\mathsf{trivial}$ $0.902745848$ $7.218276118$ 3.974886700 \( \frac{2543616}{193} a + \frac{3915776}{193} \) \( \bigl[0\) , \( -a\) , \( a + 1\) , \( -2\) , \( -a + 1\bigr] \) ${y}^2+\left(a+1\right){y}={x}^3-a{x}^2-2{x}-a+1$
193.2-a1 193.2-a \(\Q(\sqrt{-43}) \) \( 193 \) $1$ $\mathsf{trivial}$ $0.902745848$ $7.218276118$ 3.974886700 \( -\frac{2543616}{193} a + \frac{6459392}{193} \) \( \bigl[0\) , \( a - 1\) , \( a\) , \( -2\) , \( 1\bigr] \) ${y}^2+a{y}={x}^3+\left(a-1\right){x}^2-2{x}+1$
196.1-a1 196.1-a \(\Q(\sqrt{-43}) \) \( 2^{2} \cdot 7^{2} \) $1$ $\Z/2\Z$ $1.527623763$ $0.875417135$ 3.670876096 \( -\frac{548347731625}{1835008} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -171\) , \( -874\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-171{x}-874$
196.1-a2 196.1-a \(\Q(\sqrt{-43}) \) \( 2^{2} \cdot 7^{2} \) $1$ $\Z/6\Z$ $13.74861386$ $7.878754216$ 3.670876096 \( -\frac{15625}{28} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( 0\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-{x}$
196.1-a3 196.1-a \(\Q(\sqrt{-43}) \) \( 2^{2} \cdot 7^{2} \) $1$ $\Z/6\Z$ $4.582871289$ $2.626251405$ 3.670876096 \( \frac{9938375}{21952} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( 4\) , \( -6\bigr] \) ${y}^2+{x}{y}+{y}={x}^3+4{x}-6$
196.1-a4 196.1-a \(\Q(\sqrt{-43}) \) \( 2^{2} \cdot 7^{2} \) $1$ $\Z/6\Z$ $9.165742579$ $1.313125702$ 3.670876096 \( \frac{4956477625}{941192} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -36\) , \( -70\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-36{x}-70$
196.1-a5 196.1-a \(\Q(\sqrt{-43}) \) \( 2^{2} \cdot 7^{2} \) $1$ $\Z/6\Z$ $27.49722773$ $3.939377108$ 3.670876096 \( \frac{128787625}{98} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -11\) , \( 12\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-11{x}+12$
196.1-a6 196.1-a \(\Q(\sqrt{-43}) \) \( 2^{2} \cdot 7^{2} \) $1$ $\Z/2\Z$ $3.055247526$ $0.437708567$ 3.670876096 \( \frac{2251439055699625}{25088} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -2731\) , \( -55146\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-2731{x}-55146$
225.1-a1 225.1-a \(\Q(\sqrt{-43}) \) \( 3^{2} \cdot 5^{2} \) $1$ $\Z/2\Z$ $1.620411224$ $0.558925428$ 2.209860534 \( -\frac{147281603041}{215233605} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -110\) , \( -880\bigr] \) ${y}^2+{x}{y}+{y}={x}^3+{x}^2-110{x}-880$
225.1-a2 225.1-a \(\Q(\sqrt{-43}) \) \( 3^{2} \cdot 5^{2} \) $1$ $\Z/4\Z$ $6.481644899$ $8.942806850$ 2.209860534 \( -\frac{1}{15} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{x}{y}+{y}={x}^3+{x}^2$
225.1-a3 225.1-a \(\Q(\sqrt{-43}) \) \( 3^{2} \cdot 5^{2} \) $1$ $\Z/8\Z$ $12.96328979$ $1.117850856$ 2.209860534 \( \frac{4733169839}{3515625} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( 35\) , \( -28\bigr] \) ${y}^2+{x}{y}+{y}={x}^3+{x}^2+35{x}-28$
225.1-a4 225.1-a \(\Q(\sqrt{-43}) \) \( 3^{2} \cdot 5^{2} \) $1$ $\Z/2\Z\oplus\Z/4\Z$ $6.481644899$ $2.235701712$ 2.209860534 \( \frac{111284641}{50625} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -10\) , \( -10\bigr] \) ${y}^2+{x}{y}+{y}={x}^3+{x}^2-10{x}-10$
225.1-a5 225.1-a \(\Q(\sqrt{-43}) \) \( 3^{2} \cdot 5^{2} \) $1$ $\Z/2\Z\oplus\Z/4\Z$ $12.96328979$ $4.471403425$ 2.209860534 \( \frac{13997521}{225} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -5\) , \( 2\bigr] \) ${y}^2+{x}{y}+{y}={x}^3+{x}^2-5{x}+2$
225.1-a6 225.1-a \(\Q(\sqrt{-43}) \) \( 3^{2} \cdot 5^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $3.240822449$ $1.117850856$ 2.209860534 \( \frac{272223782641}{164025} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -135\) , \( -660\bigr] \) ${y}^2+{x}{y}+{y}={x}^3+{x}^2-135{x}-660$
225.1-a7 225.1-a \(\Q(\sqrt{-43}) \) \( 3^{2} \cdot 5^{2} \) $1$ $\Z/4\Z$ $25.92657959$ $2.235701712$ 2.209860534 \( \frac{56667352321}{15} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -80\) , \( 242\bigr] \) ${y}^2+{x}{y}+{y}={x}^3+{x}^2-80{x}+242$
225.1-a8 225.1-a \(\Q(\sqrt{-43}) \) \( 3^{2} \cdot 5^{2} \) $1$ $\Z/2\Z$ $6.481644899$ $0.558925428$ 2.209860534 \( \frac{1114544804970241}{405} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -2160\) , \( -39540\bigr] \) ${y}^2+{x}{y}+{y}={x}^3+{x}^2-2160{x}-39540$
256.1-a1 256.1-a \(\Q(\sqrt{-43}) \) \( 2^{8} \) $1$ $\mathsf{trivial}$ $0.515788028$ $5.386195457$ 3.389293089 \( -1024 \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a - 2\) , \( 1\bigr] \) ${y}^2={x}^3+\left(-a-1\right){x}^2+\left(a-2\right){x}+1$
256.1-b1 256.1-b \(\Q(\sqrt{-43}) \) \( 2^{8} \) $1$ $\mathsf{trivial}$ $0.515788028$ $5.386195457$ 3.389293089 \( -1024 \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( a - 2\) , \( -1\bigr] \) ${y}^2={x}^3+\left(a+1\right){x}^2+\left(a-2\right){x}-1$
289.2-a1 289.2-a \(\Q(\sqrt{-43}) \) \( 17^{2} \) $1$ $\Z/4\Z$ $1.624745338$ $2.123938699$ 2.105004561 \( -\frac{35937}{83521} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( -1\) , \( -14\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-{x}^2-{x}-14$
289.2-a2 289.2-a \(\Q(\sqrt{-43}) \) \( 17^{2} \) $1$ $\Z/4\Z$ $6.498981354$ $8.495754796$ 2.105004561 \( \frac{35937}{17} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( -1\) , \( 0\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-{x}^2-{x}$
289.2-a3 289.2-a \(\Q(\sqrt{-43}) \) \( 17^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $3.249490677$ $4.247877398$ 2.105004561 \( \frac{20346417}{289} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( -6\) , \( -4\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-{x}^2-6{x}-4$
289.2-a4 289.2-a \(\Q(\sqrt{-43}) \) \( 17^{2} \) $1$ $\Z/2\Z$ $6.498981354$ $2.123938699$ 2.105004561 \( \frac{82483294977}{17} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( -91\) , \( -310\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-{x}^2-91{x}-310$
289.2-b1 289.2-b \(\Q(\sqrt{-43}) \) \( 17^{2} \) $0$ $\Z/3\Z$ $1$ $5.376904279$ 2.186587241 \( -\frac{691835}{4913} a + \frac{2612401}{4913} \) \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -3 a - 6\) , \( 8\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^3+\left(a-1\right){x}^2+\left(-3a-6\right){x}+8$
289.2-b2 289.2-b \(\Q(\sqrt{-43}) \) \( 17^{2} \) $0$ $\mathsf{trivial}$ $1$ $1.792301426$ 2.186587241 \( \frac{417268775795}{4913} a + \frac{1080597007046}{4913} \) \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -8 a + 94\) , \( 175 a - 41\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^3+\left(a-1\right){x}^2+\left(-8a+94\right){x}+175a-41$
289.2-c1 289.2-c \(\Q(\sqrt{-43}) \) \( 17^{2} \) $0$ $\Z/3\Z$ $1$ $5.376904279$ 2.186587241 \( \frac{691835}{4913} a + \frac{1920566}{4913} \) \( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( -2 a + 2\) , \( -a + 5\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^3+\left(a+1\right){x}^2+\left(-2a+2\right){x}-a+5$
289.2-c2 289.2-c \(\Q(\sqrt{-43}) \) \( 17^{2} \) $0$ $\mathsf{trivial}$ $1$ $1.792301426$ 2.186587241 \( -\frac{417268775795}{4913} a + \frac{1497865782841}{4913} \) \( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( 3 a + 97\) , \( -76 a + 76\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^3+\left(a+1\right){x}^2+\left(3a+97\right){x}-76a+76$
361.1-a1 361.1-a \(\Q(\sqrt{-43}) \) \( 19^{2} \) $0$ $\mathsf{trivial}$ $1$ $0.935309008$ 0.285266573 \( -\frac{50357871050752}{19} \) \( \bigl[0\) , \( 1\) , \( 1\) , \( -769\) , \( -8470\bigr] \) ${y}^2+{y}={x}^3+{x}^2-769{x}-8470$
361.1-a2 361.1-a \(\Q(\sqrt{-43}) \) \( 19^{2} \) $0$ $\Z/3\Z$ $1$ $2.805927025$ 0.285266573 \( -\frac{89915392}{6859} \) \( \bigl[0\) , \( 1\) , \( 1\) , \( -9\) , \( -15\bigr] \) ${y}^2+{y}={x}^3+{x}^2-9{x}-15$
361.1-a3 361.1-a \(\Q(\sqrt{-43}) \) \( 19^{2} \) $0$ $\Z/3\Z$ $1$ $8.417781075$ 0.285266573 \( \frac{32768}{19} \) \( \bigl[0\) , \( 1\) , \( 1\) , \( 1\) , \( 0\bigr] \) ${y}^2+{y}={x}^3+{x}^2+{x}$
387.1-a1 387.1-a \(\Q(\sqrt{-43}) \) \( 3^{2} \cdot 43 \) $2$ $\mathsf{trivial}$ $0.161423666$ $2.545244737$ 4.009982725 \( -\frac{799178752}{3483} \) \( \bigl[0\) , \( -1\) , \( 1\) , \( -19\) , \( 39\bigr] \) ${y}^2+{y}={x}^3-{x}^2-19{x}+39$
387.1-b1 387.1-b \(\Q(\sqrt{-43}) \) \( 3^{2} \cdot 43 \) $0$ $\Z/2\Z$ $1$ $0.648136583$ 0.296519706 \( \frac{129784785047}{92307627} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( 105\) , \( -191\bigr] \) ${y}^2+{x}{y}+{y}={x}^3+105{x}-191$
387.1-b2 387.1-b \(\Q(\sqrt{-43}) \) \( 3^{2} \cdot 43 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $1.296273166$ 0.296519706 \( \frac{2845178713}{1347921} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -30\) , \( -29\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-30{x}-29$
387.1-b3 387.1-b \(\Q(\sqrt{-43}) \) \( 3^{2} \cdot 43 \) $0$ $\Z/4\Z$ $1$ $0.648136583$ 0.296519706 \( \frac{1616855892553}{22851963} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -245\) , \( 1433\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-245{x}+1433$
387.1-b4 387.1-b \(\Q(\sqrt{-43}) \) \( 3^{2} \cdot 43 \) $0$ $\Z/4\Z$ $1$ $2.592546333$ 0.296519706 \( \frac{1630532233}{1161} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -25\) , \( -49\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-25{x}-49$
396.1-a1 396.1-a \(\Q(\sqrt{-43}) \) \( 2^{2} \cdot 3^{2} \cdot 11 \) $0$ $\Z/2\Z$ $1$ $6.217985297$ 1.896467736 \( \frac{3169}{1452} a - \frac{1579}{726} \) \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -3 a + 7\) , \( 3\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3-{x}^2+\left(-3a+7\right){x}+3$
396.1-a2 396.1-a \(\Q(\sqrt{-43}) \) \( 2^{2} \cdot 3^{2} \cdot 11 \) $0$ $\Z/2\Z$ $1$ $3.108992648$ 1.896467736 \( \frac{844497593}{87846} a + \frac{9288678439}{263538} \) \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -3 a + 17\) , \( 6 a - 11\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3-{x}^2+\left(-3a+17\right){x}+6a-11$
396.2-a1 396.2-a \(\Q(\sqrt{-43}) \) \( 2^{2} \cdot 3^{2} \cdot 11 \) $0$ $\Z/2\Z$ $1$ $6.217985297$ 1.896467736 \( -\frac{3169}{1452} a + \frac{1}{132} \) \( \bigl[a\) , \( -a\) , \( a\) , \( a + 6\) , \( -a + 4\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^3-a{x}^2+\left(a+6\right){x}-a+4$
396.2-a2 396.2-a \(\Q(\sqrt{-43}) \) \( 2^{2} \cdot 3^{2} \cdot 11 \) $0$ $\Z/2\Z$ $1$ $3.108992648$ 1.896467736 \( -\frac{844497593}{87846} a + \frac{537371419}{11979} \) \( \bigl[a\) , \( -a\) , \( a\) , \( a + 16\) , \( -7 a - 4\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^3-a{x}^2+\left(a+16\right){x}-7a-4$
400.1-a1 400.1-a \(\Q(\sqrt{-43}) \) \( 2^{4} \cdot 5^{2} \) $0$ $\Z/2\Z$ $1$ $1.070515942$ 1.469269357 \( -\frac{20720464}{15625} \) \( \bigl[0\) , \( 1\) , \( 0\) , \( -36\) , \( -140\bigr] \) ${y}^2={x}^3+{x}^2-36{x}-140$
400.1-a2 400.1-a \(\Q(\sqrt{-43}) \) \( 2^{4} \cdot 5^{2} \) $0$ $\Z/6\Z$ $1$ $3.211547828$ 1.469269357 \( \frac{21296}{25} \) \( \bigl[0\) , \( 1\) , \( 0\) , \( 4\) , \( 4\bigr] \) ${y}^2={x}^3+{x}^2+4{x}+4$
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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.