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Results (24 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
441.1-a1 441.1-a \(\Q(\sqrt{7}) \) \( 3^{2} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.651668904$ 1.970461553 \( -\frac{4354703137}{17294403} \) \( \bigl[a\) , \( -a - 1\) , \( 1\) , \( 11430 a - 30242\) , \( -3021358 a + 7993761\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(11430a-30242\right){x}-3021358a+7993761$
441.1-a2 441.1-a \(\Q(\sqrt{7}) \) \( 3^{2} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.651668904$ 1.970461553 \( -\frac{1153486390269896663}{301327047} a + \frac{435976874792639720}{43046721} \) \( \bigl[1\) , \( -a - 1\) , \( a\) , \( -4956 a - 13127\) , \( 2950874 a + 7807239\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-4956a-13127\right){x}+2950874a+7807239$
441.1-a3 441.1-a \(\Q(\sqrt{7}) \) \( 3^{2} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $5.213351238$ 1.970461553 \( \frac{103823}{63} \) \( \bigl[a\) , \( -a - 1\) , \( 1\) , \( -330 a + 873\) , \( -1537 a + 4066\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-330a+873\right){x}-1537a+4066$
441.1-a4 441.1-a \(\Q(\sqrt{7}) \) \( 3^{2} \cdot 7^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $5.213351238$ 1.970461553 \( \frac{7189057}{3969} \) \( \bigl[1\) , \( -a - 1\) , \( a\) , \( -1351 a - 3572\) , \( -7900 a - 20903\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-1351a-3572\right){x}-7900a-20903$
441.1-a5 441.1-a \(\Q(\sqrt{7}) \) \( 3^{2} \cdot 7^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.606675619$ 1.970461553 \( \frac{6570725617}{45927} \) \( \bigl[1\) , \( -a - 1\) , \( a\) , \( -13111 a - 34687\) , \( 1336023 a + 3534782\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-13111a-34687\right){x}+1336023a+3534782$
441.1-a6 441.1-a \(\Q(\sqrt{7}) \) \( 3^{2} \cdot 7^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.606675619$ 1.970461553 \( \frac{13027640977}{21609} \) \( \bigl[a\) , \( -a - 1\) , \( 1\) , \( 16470 a - 43577\) , \( -1850335 a + 4895526\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(16470a-43577\right){x}-1850335a+4895526$
441.1-a7 441.1-a \(\Q(\sqrt{7}) \) \( 3^{2} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.303337809$ 1.970461553 \( \frac{1153486390269896663}{301327047} a + \frac{435976874792639720}{43046721} \) \( \bigl[a\) , \( -a - 1\) , \( 1\) , \( 4955 a - 13127\) , \( 2950874 a - 7807241\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(4955a-13127\right){x}+2950874a-7807241$
441.1-a8 441.1-a \(\Q(\sqrt{7}) \) \( 3^{2} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.303337809$ 1.970461553 \( \frac{53297461115137}{147} \) \( \bigl[a\) , \( -a - 1\) , \( 1\) , \( 263430 a - 696992\) , \( -119416672 a + 315946791\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(263430a-696992\right){x}-119416672a+315946791$
441.1-b1 441.1-b \(\Q(\sqrt{7}) \) \( 3^{2} \cdot 7^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.315189189$ 0.774347053 \( -\frac{1713910976512}{1594323} \) \( \bigl[0\) , \( -a\) , \( 1\) , \( 306544 a - 811062\) , \( -150125458 a + 397194600\bigr] \) ${y}^2+{y}={x}^{3}-a{x}^{2}+\left(306544a-811062\right){x}-150125458a+397194600$
441.1-b2 441.1-b \(\Q(\sqrt{7}) \) \( 3^{2} \cdot 7^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $4.097459464$ 0.774347053 \( -\frac{28672}{3} \) \( \bigl[0\) , \( -a\) , \( a\) , \( -784 a - 2072\) , \( 21812 a + 57708\bigr] \) ${y}^2+a{y}={x}^{3}-a{x}^{2}+\left(-784a-2072\right){x}+21812a+57708$
441.1-c1 441.1-c \(\Q(\sqrt{7}) \) \( 3^{2} \cdot 7^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.188631360$ 6.024507996 \( -\frac{1713910976512}{1594323} \) \( \bigl[0\) , \( 1\) , \( a\) , \( -912\) , \( -10921\bigr] \) ${y}^2+a{y}={x}^{3}+{x}^{2}-912{x}-10921$
441.1-c2 441.1-c \(\Q(\sqrt{7}) \) \( 3^{2} \cdot 7^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $31.87869985$ 6.024507996 \( -\frac{28672}{3} \) \( \bigl[0\) , \( 1\) , \( a\) , \( -2\) , \( -1\bigr] \) ${y}^2+a{y}={x}^{3}+{x}^{2}-2{x}-1$
441.1-d1 441.1-d \(\Q(\sqrt{7}) \) \( 3^{2} \cdot 7^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.315189189$ 0.774347053 \( -\frac{1713910976512}{1594323} \) \( \bigl[0\) , \( a\) , \( 1\) , \( -306544 a - 811062\) , \( 150125458 a + 397194600\bigr] \) ${y}^2+{y}={x}^{3}+a{x}^{2}+\left(-306544a-811062\right){x}+150125458a+397194600$
441.1-d2 441.1-d \(\Q(\sqrt{7}) \) \( 3^{2} \cdot 7^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $4.097459464$ 0.774347053 \( -\frac{28672}{3} \) \( \bigl[0\) , \( a\) , \( 1\) , \( -784 a - 2072\) , \( -21812 a - 57710\bigr] \) ${y}^2+{y}={x}^{3}+a{x}^{2}+\left(-784a-2072\right){x}-21812a-57710$
441.1-e1 441.1-e \(\Q(\sqrt{7}) \) \( 3^{2} \cdot 7^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $3.686606385$ 2.090109359 \( -\frac{1713910976512}{1594323} \) \( \bigl[0\) , \( -1\) , \( 1\) , \( -912\) , \( 10919\bigr] \) ${y}^2+{y}={x}^{3}-{x}^{2}-912{x}+10919$
441.1-e2 441.1-e \(\Q(\sqrt{7}) \) \( 3^{2} \cdot 7^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $3.686606385$ 2.090109359 \( -\frac{28672}{3} \) \( \bigl[0\) , \( -1\) , \( 1\) , \( -2\) , \( -1\bigr] \) ${y}^2+{y}={x}^{3}-{x}^{2}-2{x}-1$
441.1-f1 441.1-f \(\Q(\sqrt{7}) \) \( 3^{2} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.651668904$ 1.970461553 \( -\frac{4354703137}{17294403} \) \( \bigl[a\) , \( a - 1\) , \( 1\) , \( -11431 a - 30242\) , \( 3021358 a + 7993761\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-11431a-30242\right){x}+3021358a+7993761$
441.1-f2 441.1-f \(\Q(\sqrt{7}) \) \( 3^{2} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.303337809$ 1.970461553 \( -\frac{1153486390269896663}{301327047} a + \frac{435976874792639720}{43046721} \) \( \bigl[a\) , \( a - 1\) , \( 1\) , \( -4956 a - 13127\) , \( -2950874 a - 7807241\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-4956a-13127\right){x}-2950874a-7807241$
441.1-f3 441.1-f \(\Q(\sqrt{7}) \) \( 3^{2} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $5.213351238$ 1.970461553 \( \frac{103823}{63} \) \( \bigl[1\) , \( a - 1\) , \( a\) , \( -330 a + 873\) , \( 1537 a - 4068\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-330a+873\right){x}+1537a-4068$
441.1-f4 441.1-f \(\Q(\sqrt{7}) \) \( 3^{2} \cdot 7^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $5.213351238$ 1.970461553 \( \frac{7189057}{3969} \) \( \bigl[1\) , \( a - 1\) , \( a\) , \( 1350 a - 3572\) , \( 7900 a - 20903\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(1350a-3572\right){x}+7900a-20903$
441.1-f5 441.1-f \(\Q(\sqrt{7}) \) \( 3^{2} \cdot 7^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.606675619$ 1.970461553 \( \frac{6570725617}{45927} \) \( \bigl[a\) , \( a - 1\) , \( 1\) , \( -13111 a - 34687\) , \( -1336023 a - 3534784\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-13111a-34687\right){x}-1336023a-3534784$
441.1-f6 441.1-f \(\Q(\sqrt{7}) \) \( 3^{2} \cdot 7^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.606675619$ 1.970461553 \( \frac{13027640977}{21609} \) \( \bigl[a\) , \( a - 1\) , \( 1\) , \( -16471 a - 43577\) , \( 1850335 a + 4895526\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-16471a-43577\right){x}+1850335a+4895526$
441.1-f7 441.1-f \(\Q(\sqrt{7}) \) \( 3^{2} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.651668904$ 1.970461553 \( \frac{1153486390269896663}{301327047} a + \frac{435976874792639720}{43046721} \) \( \bigl[1\) , \( a - 1\) , \( a\) , \( 4955 a - 13127\) , \( -2950874 a + 7807239\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(4955a-13127\right){x}-2950874a+7807239$
441.1-f8 441.1-f \(\Q(\sqrt{7}) \) \( 3^{2} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.303337809$ 1.970461553 \( \frac{53297461115137}{147} \) \( \bigl[a\) , \( a - 1\) , \( 1\) , \( -263431 a - 696992\) , \( 119416672 a + 315946791\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-263431a-696992\right){x}+119416672a+315946791$
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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.