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Results (10 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
4.1-a1 4.1-a \(\Q(\sqrt{13}) \) \( 2^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $1.142260539$ 0.316806072 \( -\frac{1250637664527933}{32} a - \frac{1629300280935823}{32} \) \( \bigl[1\) , \( 1\) , \( a\) , \( -29 a + 2\) , \( -52 a - 106\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-29a+2\right){x}-52a-106$
36.2-a1 36.2-a \(\Q(\sqrt{13}) \) \( 2^{2} \cdot 3^{2} \) 0 $\Z/3\Z$ $\mathrm{SU}(2)$ $1$ $6.839032582$ 1.053781309 \( -\frac{1250637664527933}{32} a - \frac{1629300280935823}{32} \) \( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -113 a - 80\) , \( 590 a + 599\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-113a-80\right){x}+590a+599$
36.3-a1 36.3-a \(\Q(\sqrt{13}) \) \( 2^{2} \cdot 3^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.759892509$ 1.053781309 \( -\frac{1250637664527933}{32} a - \frac{1629300280935823}{32} \) \( \bigl[a\) , \( a + 1\) , \( 0\) , \( -85 a + 94\) , \( -352 a + 209\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-85a+94\right){x}-352a+209$
256.1-c1 256.1-c \(\Q(\sqrt{13}) \) \( 2^{8} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $3.412266367$ 1.892784823 \( -\frac{1250637664527933}{32} a - \frac{1629300280935823}{32} \) \( \bigl[0\) , \( 1\) , \( 0\) , \( -456 a + 24\) , \( 2400 a + 6788\bigr] \) ${y}^2={x}^{3}+{x}^{2}+\left(-456a+24\right){x}+2400a+6788$
256.1-d1 256.1-d \(\Q(\sqrt{13}) \) \( 2^{8} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.281337676$ $2.961387977$ 1.848593902 \( -\frac{1250637664527933}{32} a - \frac{1629300280935823}{32} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -1894 a + 4271\) , \( 34785 a - 79853\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-1894a+4271\right){x}+34785a-79853$
256.1-f1 256.1-f \(\Q(\sqrt{13}) \) \( 2^{8} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $2.532039089$ $0.329043108$ 1.848593902 \( -\frac{1250637664527933}{32} a - \frac{1629300280935823}{32} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -1894 a + 4271\) , \( -34785 a + 79853\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-1894a+4271\right){x}-34785a+79853$
324.1-a1 324.1-a \(\Q(\sqrt{13}) \) \( 2^{2} \cdot 3^{4} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $4.549688489$ 1.261856548 \( -\frac{1250637664527933}{32} a - \frac{1629300280935823}{32} \) \( \bigl[1\) , \( -1\) , \( a + 1\) , \( -257 a + 13\) , \( 1140 a + 2856\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-257a+13\right){x}+1140a+2856$
676.1-d1 676.1-d \(\Q(\sqrt{13}) \) \( 2^{2} \cdot 13^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.092209650$ $3.785569646$ 1.936270087 \( -\frac{1250637664527933}{32} a - \frac{1629300280935823}{32} \) \( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -1540 a + 3469\) , \( -25760 a + 59481\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-1540a+3469\right){x}-25760a+59481$
1156.2-b1 1156.2-b \(\Q(\sqrt{13}) \) \( 2^{2} \cdot 17^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $3.310384624$ 0.918135500 \( -\frac{1250637664527933}{32} a - \frac{1629300280935823}{32} \) \( \bigl[a\) , \( a - 1\) , \( a\) , \( -555 a + 811\) , \( -2520 a + 9274\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-555a+811\right){x}-2520a+9274$
1156.3-b1 1156.3-b \(\Q(\sqrt{13}) \) \( 2^{2} \cdot 17^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $3.310384624$ 0.918135500 \( -\frac{1250637664527933}{32} a - \frac{1629300280935823}{32} \) \( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( -784 a - 740\) , \( 12288 a + 16948\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-784a-740\right){x}+12288a+16948$
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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.