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Results (11 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
242.3-a1 242.3-a \(\Q(\sqrt{-7}) \) \( 2 \cdot 11^{2} \) 0 $\Z/3\Z$ $\mathrm{SU}(2)$ $1$ $2.651529103$ 0.668122533 \( \frac{263}{2} a + \frac{643}{2} \) \( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( -a - 5\) , \( a + 3\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-a-5\right){x}+a+3$
1936.3-b1 1936.3-b \(\Q(\sqrt{-7}) \) \( 2^{4} \cdot 11^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.075498423$ $4.397063578$ 2.007574132 \( \frac{263}{2} a + \frac{643}{2} \) \( \bigl[0\) , \( -a\) , \( a\) , \( 1\) , \( -1\bigr] \) ${y}^2+a{y}={x}^{3}-a{x}^{2}+{x}-1$
3872.15-d1 3872.15-d \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 11^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $4.397063578$ 3.323867636 \( \frac{263}{2} a + \frac{643}{2} \) \( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -a - 1\) , \( -a - 1\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-a-1\right){x}-a-1$
7744.3-a1 7744.3-a \(\Q(\sqrt{-7}) \) \( 2^{6} \cdot 11^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.937457104$ 1.417301922 \( \frac{263}{2} a + \frac{643}{2} \) \( \bigl[0\) , \( a\) , \( a\) , \( -19 a - 14\) , \( 47 a - 131\bigr] \) ${y}^2+a{y}={x}^{3}+a{x}^{2}+\left(-19a-14\right){x}+47a-131$
7744.3-b1 7744.3-b \(\Q(\sqrt{-7}) \) \( 2^{6} \cdot 11^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.152203951$ $3.109193473$ 2.861835308 \( \frac{263}{2} a + \frac{643}{2} \) \( \bigl[0\) , \( a + 1\) , \( a\) , \( 3 a - 3\) , \( a - 6\bigr] \) ${y}^2+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(3a-3\right){x}+a-6$
11858.3-a1 11858.3-a \(\Q(\sqrt{-7}) \) \( 2 \cdot 7^{2} \cdot 11^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.251895883$ $3.323867636$ 2.531662201 \( \frac{263}{2} a + \frac{643}{2} \) \( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( -a - 1\) , \( -2 a + 5\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-a-1\right){x}-2a+5$
15488.21-a1 15488.21-a \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 11^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.254094213$ $6.218386947$ 2.388820344 \( \frac{263}{2} a + \frac{643}{2} \) \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -2 a + 1\) , \( -a\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-2a+1\right){x}-a$
15488.21-g1 15488.21-g \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 11^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.697253854$ $1.874914209$ 5.929315373 \( \frac{263}{2} a + \frac{643}{2} \) \( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 4 a + 4\) , \( 13 a + 7\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(4a+4\right){x}+13a+7$
19602.3-b1 19602.3-b \(\Q(\sqrt{-7}) \) \( 2 \cdot 3^{4} \cdot 11^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $2.073055864$ $0.883843034$ 5.540221346 \( \frac{263}{2} a + \frac{643}{2} \) \( \bigl[a + 1\) , \( 1\) , \( 1\) , \( 4 a - 41\) , \( -119 a - 33\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(4a-41\right){x}-119a-33$
29282.3-c1 29282.3-c \(\Q(\sqrt{-7}) \) \( 2 \cdot 11^{4} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $2.651529103$ 2.004367600 \( \frac{263}{2} a + \frac{643}{2} \) \( \bigl[a + 1\) , \( 0\) , \( a\) , \( -3 a + 5\) , \( -4 a + 5\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-3a+5\right){x}-4a+5$
30976.15-b1 30976.15-b \(\Q(\sqrt{-7}) \) \( 2^{8} \cdot 11^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.662882275$ 1.002183800 \( \frac{263}{2} a + \frac{643}{2} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 8 a - 72\) , \( -244 a - 20\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(8a-72\right){x}-244a-20$
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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.