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Results (40 matches)

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Label Class Base field Conductor norm Rank Torsion CM Sato-Tate Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
784.1-a1 784.1-a \(\Q(\sqrt{2}) \) \( 2^{4} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $3.513854052$ 1.242335014 \( -\frac{548347731625}{1835008} \) \( \bigl[a\) , \( -1\) , \( 0\) , \( -682\) , \( 6990\bigr] \) ${y}^2+a{x}{y}={x}^{3}-{x}^{2}-682{x}+6990$
784.1-a2 784.1-a \(\Q(\sqrt{2}) \) \( 2^{4} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $3.513854052$ 1.242335014 \( -\frac{15625}{28} \) \( \bigl[a\) , \( -1\) , \( 0\) , \( -2\) , \( -2\bigr] \) ${y}^2+a{x}{y}={x}^{3}-{x}^{2}-2{x}-2$
784.1-a3 784.1-a \(\Q(\sqrt{2}) \) \( 2^{4} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $3.513854052$ 1.242335014 \( \frac{9938375}{21952} \) \( \bigl[a\) , \( -1\) , \( 0\) , \( 18\) , \( 46\bigr] \) ${y}^2+a{x}{y}={x}^{3}-{x}^{2}+18{x}+46$
784.1-a4 784.1-a \(\Q(\sqrt{2}) \) \( 2^{4} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.756927026$ 1.242335014 \( -\frac{2928743223192875}{4802} a + \frac{2070934198465000}{2401} \) \( \bigl[a\) , \( -1\) , \( 0\) , \( 220 a - 362\) , \( 2320 a - 3330\bigr] \) ${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(220a-362\right){x}+2320a-3330$
784.1-a5 784.1-a \(\Q(\sqrt{2}) \) \( 2^{4} \cdot 7^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $3.513854052$ 1.242335014 \( \frac{4956477625}{941192} \) \( \bigl[a\) , \( -1\) , \( 0\) , \( -142\) , \( 558\bigr] \) ${y}^2+a{x}{y}={x}^{3}-{x}^{2}-142{x}+558$
784.1-a6 784.1-a \(\Q(\sqrt{2}) \) \( 2^{4} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.756927026$ 1.242335014 \( -\frac{392127492092318125}{55365148804} a + \frac{138814532776321000}{13841287201} \) \( \bigl[a\) , \( -1\) , \( 0\) , \( 520 a - 1422\) , \( -16000 a + 16302\bigr] \) ${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(520a-1422\right){x}-16000a+16302$
784.1-a7 784.1-a \(\Q(\sqrt{2}) \) \( 2^{4} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.756927026$ 1.242335014 \( -\frac{218768831290078842857759125}{76832} a + \frac{9668307757341907702465000}{2401} \) \( \bigl[a\) , \( -1\) , \( 0\) , \( 57920 a - 92842\) , \( -9795840 a + 14293838\bigr] \) ${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(57920a-92842\right){x}-9795840a+14293838$
784.1-a8 784.1-a \(\Q(\sqrt{2}) \) \( 2^{4} \cdot 7^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $3.513854052$ 1.242335014 \( \frac{128787625}{98} \) \( \bigl[a\) , \( -1\) , \( 0\) , \( -42\) , \( -98\bigr] \) ${y}^2+a{x}{y}={x}^{3}-{x}^{2}-42{x}-98$
784.1-a9 784.1-a \(\Q(\sqrt{2}) \) \( 2^{4} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.756927026$ 1.242335014 \( \frac{392127492092318125}{55365148804} a + \frac{138814532776321000}{13841287201} \) \( \bigl[a\) , \( -1\) , \( 0\) , \( -520 a - 1422\) , \( 16000 a + 16302\bigr] \) ${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-520a-1422\right){x}+16000a+16302$
784.1-a10 784.1-a \(\Q(\sqrt{2}) \) \( 2^{4} \cdot 7^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $3.513854052$ 1.242335014 \( \frac{2251439055699625}{25088} \) \( \bigl[a\) , \( -1\) , \( 0\) , \( -10922\) , \( 441166\bigr] \) ${y}^2+a{x}{y}={x}^{3}-{x}^{2}-10922{x}+441166$
784.1-a11 784.1-a \(\Q(\sqrt{2}) \) \( 2^{4} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.756927026$ 1.242335014 \( \frac{2928743223192875}{4802} a + \frac{2070934198465000}{2401} \) \( \bigl[a\) , \( -1\) , \( 0\) , \( -220 a - 362\) , \( -2320 a - 3330\bigr] \) ${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-220a-362\right){x}-2320a-3330$
784.1-a12 784.1-a \(\Q(\sqrt{2}) \) \( 2^{4} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.756927026$ 1.242335014 \( \frac{218768831290078842857759125}{76832} a + \frac{9668307757341907702465000}{2401} \) \( \bigl[a\) , \( -1\) , \( 0\) , \( -57920 a - 92842\) , \( 9795840 a + 14293838\bigr] \) ${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-57920a-92842\right){x}+9795840a+14293838$
784.1-b1 784.1-b \(\Q(\sqrt{2}) \) \( 2^{4} \cdot 7^{2} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $8.330553587$ 1.472647733 \( -\frac{69495892205440052}{49} a + \frac{98282033286152638}{49} \) \( \bigl[a\) , \( a - 1\) , \( 0\) , \( 115 a - 122\) , \( -322 a + 1587\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(115a-122\right){x}-322a+1587$
784.1-b2 784.1-b \(\Q(\sqrt{2}) \) \( 2^{4} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $4.165276793$ 1.472647733 \( -\frac{13282665232}{5764801} a + \frac{23566456972}{5764801} \) \( \bigl[a\) , \( a - 1\) , \( 0\) , \( 15 a + 18\) , \( -30 a - 43\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(15a+18\right){x}-30a-43$
784.1-b3 784.1-b \(\Q(\sqrt{2}) \) \( 2^{4} \cdot 7^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $16.66110717$ 1.472647733 \( -\frac{4566144}{2401} a + \frac{14497232}{2401} \) \( \bigl[a\) , \( a - 1\) , \( 0\) , \( -5 a - 7\) , \( -7 a - 9\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-5a-7\right){x}-7a-9$
784.1-b4 784.1-b \(\Q(\sqrt{2}) \) \( 2^{4} \cdot 7^{2} \) 0 $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $16.66110717$ 1.472647733 \( -\frac{53744933616}{2401} a + \frac{76065896132}{2401} \) \( \bigl[a\) , \( a - 1\) , \( 0\) , \( -25 a - 52\) , \( 84 a + 159\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-25a-52\right){x}+84a+159$
784.1-b5 784.1-b \(\Q(\sqrt{2}) \) \( 2^{4} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $8.330553587$ 1.472647733 \( \frac{110288896}{49} a + \frac{155981824}{49} \) \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -6 a + 7\) , \( -23 a + 32\bigr] \) ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-6a+7\right){x}-23a+32$
784.1-b6 784.1-b \(\Q(\sqrt{2}) \) \( 2^{4} \cdot 7^{2} \) 0 $\Z/8\Z$ $\mathrm{SU}(2)$ $1$ $8.330553587$ 1.472647733 \( \frac{1159856388322676}{5764801} a + \frac{1640242904389426}{5764801} \) \( \bigl[a\) , \( a\) , \( 0\) , \( 194 a - 314\) , \( -2200 a + 3186\bigr] \) ${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(194a-314\right){x}-2200a+3186$
784.1-c1 784.1-c \(\Q(\sqrt{2}) \) \( 2^{4} \cdot 7^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.239919898$ $22.75712104$ 1.930361270 \( -\frac{4}{7} \) \( \bigl[a\) , \( 0\) , \( a\) , \( -1\) , \( 0\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-{x}$
784.1-c2 784.1-c \(\Q(\sqrt{2}) \) \( 2^{4} \cdot 7^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.239919898$ $11.37856052$ 1.930361270 \( -\frac{4347206325605}{2401} a + \frac{6147883179496}{2401} \) \( \bigl[a\) , \( 0\) , \( a\) , \( 50 a - 91\) , \( -274 a + 370\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(50a-91\right){x}-274a+370$
784.1-c3 784.1-c \(\Q(\sqrt{2}) \) \( 2^{4} \cdot 7^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.119959949$ $22.75712104$ 1.930361270 \( \frac{3543122}{49} \) \( \bigl[a\) , \( 0\) , \( a\) , \( -11\) , \( 10\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-11{x}+10$
784.1-c4 784.1-c \(\Q(\sqrt{2}) \) \( 2^{4} \cdot 7^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.239919898$ $11.37856052$ 1.930361270 \( \frac{4347206325605}{2401} a + \frac{6147883179496}{2401} \) \( \bigl[a\) , \( 0\) , \( a\) , \( -50 a - 91\) , \( 274 a + 370\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-50a-91\right){x}+274a+370$
784.1-d1 784.1-d \(\Q(\sqrt{2}) \) \( 2^{4} \cdot 7^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.069108576$ $10.54517411$ 1.992969164 \( \frac{432}{7} \) \( \bigl[a\) , \( 1\) , \( 0\) , \( 1\) , \( 0\bigr] \) ${y}^2+a{x}{y}={x}^{3}+{x}^{2}+{x}$
784.1-d2 784.1-d \(\Q(\sqrt{2}) \) \( 2^{4} \cdot 7^{2} \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $0.133638572$ $5.272587057$ 1.992969164 \( -\frac{29774895462729}{5764801} a + \frac{42111203990760}{5764801} \) \( \bigl[a\) , \( 1\) , \( 0\) , \( 90 a - 94\) , \( -368 a + 642\bigr] \) ${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(90a-94\right){x}-368a+642$
784.1-d3 784.1-d \(\Q(\sqrt{2}) \) \( 2^{4} \cdot 7^{2} \) $1$ $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $0.267277144$ $10.54517411$ 1.992969164 \( \frac{11090466}{2401} \) \( \bigl[a\) , \( 1\) , \( 0\) , \( -14\) , \( 10\bigr] \) ${y}^2+a{x}{y}={x}^{3}+{x}^{2}-14{x}+10$
784.1-d4 784.1-d \(\Q(\sqrt{2}) \) \( 2^{4} \cdot 7^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.534554288$ $10.54517411$ 1.992969164 \( \frac{740772}{49} \) \( \bigl[a\) , \( 1\) , \( 0\) , \( -4\) , \( -6\bigr] \) ${y}^2+a{x}{y}={x}^{3}+{x}^{2}-4{x}-6$
784.1-d5 784.1-d \(\Q(\sqrt{2}) \) \( 2^{4} \cdot 7^{2} \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $0.133638572$ $5.272587057$ 1.992969164 \( \frac{29774895462729}{5764801} a + \frac{42111203990760}{5764801} \) \( \bigl[a\) , \( 1\) , \( 0\) , \( -90 a - 94\) , \( 368 a + 642\bigr] \) ${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-90a-94\right){x}+368a+642$
784.1-d6 784.1-d \(\Q(\sqrt{2}) \) \( 2^{4} \cdot 7^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.069108576$ $2.636293528$ 1.992969164 \( \frac{1443468546}{7} \) \( \bigl[a\) , \( 1\) , \( 0\) , \( -74\) , \( -286\bigr] \) ${y}^2+a{x}{y}={x}^{3}+{x}^{2}-74{x}-286$
784.1-e1 784.1-e \(\Q(\sqrt{2}) \) \( 2^{4} \cdot 7^{2} \) 0 $\Z/8\Z$ $\mathrm{SU}(2)$ $1$ $8.330553587$ 1.472647733 \( -\frac{1159856388322676}{5764801} a + \frac{1640242904389426}{5764801} \) \( \bigl[a\) , \( -a\) , \( 0\) , \( -194 a - 314\) , \( 2200 a + 3186\bigr] \) ${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(-194a-314\right){x}+2200a+3186$
784.1-e2 784.1-e \(\Q(\sqrt{2}) \) \( 2^{4} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $8.330553587$ 1.472647733 \( -\frac{110288896}{49} a + \frac{155981824}{49} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 6 a + 7\) , \( 23 a + 32\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(6a+7\right){x}+23a+32$
784.1-e3 784.1-e \(\Q(\sqrt{2}) \) \( 2^{4} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $4.165276793$ 1.472647733 \( \frac{13282665232}{5764801} a + \frac{23566456972}{5764801} \) \( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -15 a + 18\) , \( 30 a - 43\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-15a+18\right){x}+30a-43$
784.1-e4 784.1-e \(\Q(\sqrt{2}) \) \( 2^{4} \cdot 7^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $16.66110717$ 1.472647733 \( \frac{4566144}{2401} a + \frac{14497232}{2401} \) \( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 5 a - 7\) , \( 7 a - 9\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(5a-7\right){x}+7a-9$
784.1-e5 784.1-e \(\Q(\sqrt{2}) \) \( 2^{4} \cdot 7^{2} \) 0 $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $16.66110717$ 1.472647733 \( \frac{53744933616}{2401} a + \frac{76065896132}{2401} \) \( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 25 a - 52\) , \( -84 a + 159\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(25a-52\right){x}-84a+159$
784.1-e6 784.1-e \(\Q(\sqrt{2}) \) \( 2^{4} \cdot 7^{2} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $8.330553587$ 1.472647733 \( \frac{69495892205440052}{49} a + \frac{98282033286152638}{49} \) \( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -115 a - 122\) , \( 322 a + 1587\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-115a-122\right){x}+322a+1587$
784.1-f1 784.1-f \(\Q(\sqrt{2}) \) \( 2^{4} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $7.680735453$ 1.357775030 \( -\frac{551719468601289472}{49} a + \frac{780249146376863552}{49} \) \( \bigl[0\) , \( -a\) , \( 0\) , \( 1562 a - 3681\) , \( -52607 a + 96844\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(1562a-3681\right){x}-52607a+96844$
784.1-f2 784.1-f \(\Q(\sqrt{2}) \) \( 2^{4} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $7.680735453$ 1.357775030 \( -\frac{13219923200}{117649} a + \frac{18683377472}{117649} \) \( \bigl[0\) , \( -a\) , \( 0\) , \( 22 a - 41\) , \( -51 a + 132\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(22a-41\right){x}-51a+132$
784.1-f3 784.1-f \(\Q(\sqrt{2}) \) \( 2^{4} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $7.680735453$ 1.357775030 \( -\frac{210688}{49} a + \frac{302912}{49} \) \( \bigl[0\) , \( -a\) , \( 0\) , \( 2 a - 1\) , \( a - 4\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(2a-1\right){x}+a-4$
784.1-f4 784.1-f \(\Q(\sqrt{2}) \) \( 2^{4} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $7.680735453$ 1.357775030 \( \frac{210688}{49} a + \frac{302912}{49} \) \( \bigl[0\) , \( a\) , \( 0\) , \( -2 a - 1\) , \( -a - 4\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(-2a-1\right){x}-a-4$
784.1-f5 784.1-f \(\Q(\sqrt{2}) \) \( 2^{4} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $7.680735453$ 1.357775030 \( \frac{13219923200}{117649} a + \frac{18683377472}{117649} \) \( \bigl[0\) , \( a\) , \( 0\) , \( -22 a - 41\) , \( 51 a + 132\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(-22a-41\right){x}+51a+132$
784.1-f6 784.1-f \(\Q(\sqrt{2}) \) \( 2^{4} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $7.680735453$ 1.357775030 \( \frac{551719468601289472}{49} a + \frac{780249146376863552}{49} \) \( \bigl[0\) , \( a\) , \( 0\) , \( -1562 a - 3681\) , \( 52607 a + 96844\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(-1562a-3681\right){x}+52607a+96844$
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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.