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Results (16 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
5.1-a1 5.1-a \(\Q(\sqrt{105}) \) \( 5 \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $1.378497038$ $33.76254038$ 1.703246763 \( -\frac{1145960298}{25} a + \frac{6444279999}{25} \) \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 101 a + 507\) , \( 12625 a + 58420\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(101a+507\right){x}+12625a+58420$
5.1-a2 5.1-a \(\Q(\sqrt{105}) \) \( 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.344624259$ $8.440635095$ 1.703246763 \( \frac{55306341}{15625} \) \( \bigl[1\) , \( -1\) , \( a\) , \( -426911 a - 1973810\) , \( -245763021 a - 1136279283\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-426911a-1973810\right){x}-245763021a-1136279283$
5.1-a3 5.1-a \(\Q(\sqrt{105}) \) \( 5 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.689248519$ $33.76254038$ 1.703246763 \( \frac{2803221}{125} \) \( \bigl[1\) , \( -1\) , \( a\) , \( -157991 a - 730465\) , \( 74372212 a + 343858086\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-157991a-730465\right){x}+74372212a+343858086$
5.1-a4 5.1-a \(\Q(\sqrt{105}) \) \( 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.344624259$ $33.76254038$ 1.703246763 \( \frac{1145960298}{25} a + \frac{5298319701}{25} \) \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -2500155 a - 11559365\) , \( 4867995135 a + 22507055720\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2500155a-11559365\right){x}+4867995135a+22507055720$
5.1-b1 5.1-b \(\Q(\sqrt{105}) \) \( 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $6.686095992$ 0.652496156 \( -\frac{1145960298}{25} a + \frac{6444279999}{25} \) \( \bigl[1\) , \( -1\) , \( a + 1\) , \( -2\) , \( -a - 10\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}-2{x}-a-10$
5.1-b2 5.1-b \(\Q(\sqrt{105}) \) \( 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $13.37219198$ 0.652496156 \( \frac{55306341}{15625} \) \( \bigl[a\) , \( -a + 1\) , \( a\) , \( -12 a - 37\) , \( 12 a + 69\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-12a-37\right){x}+12a+69$
5.1-b3 5.1-b \(\Q(\sqrt{105}) \) \( 5 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $13.37219198$ 0.652496156 \( \frac{2803221}{125} \) \( \bigl[a\) , \( -a + 1\) , \( a\) , \( -7 a - 7\) , \( -14 a - 39\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-7a-7\right){x}-14a-39$
5.1-b4 5.1-b \(\Q(\sqrt{105}) \) \( 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $6.686095992$ 0.652496156 \( \frac{1145960298}{25} a + \frac{5298319701}{25} \) \( \bigl[1\) , \( -1\) , \( a + 1\) , \( -2624 a - 12130\) , \( -164909 a - 762456\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-2624a-12130\right){x}-164909a-762456$
5.1-c1 5.1-c \(\Q(\sqrt{105}) \) \( 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $6.686095992$ 0.652496156 \( -\frac{1145960298}{25} a + \frac{6444279999}{25} \) \( \bigl[1\) , \( -1\) , \( a\) , \( 2623 a - 14753\) , \( 164908 a - 927364\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(2623a-14753\right){x}+164908a-927364$
5.1-c2 5.1-c \(\Q(\sqrt{105}) \) \( 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $13.37219198$ 0.652496156 \( \frac{55306341}{15625} \) \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 7164 a - 40283\) , \( -508682 a + 2860562\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(7164a-40283\right){x}-508682a+2860562$
5.1-c3 5.1-c \(\Q(\sqrt{105}) \) \( 5 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $13.37219198$ 0.652496156 \( \frac{2803221}{125} \) \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 2649 a - 14893\) , \( 171401 a - 963868\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(2649a-14893\right){x}+171401a-963868$
5.1-c4 5.1-c \(\Q(\sqrt{105}) \) \( 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $6.686095992$ 0.652496156 \( \frac{1145960298}{25} a + \frac{5298319701}{25} \) \( \bigl[1\) , \( -1\) , \( a\) , \( -a - 1\) , \( -10\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-a-1\right){x}-10$
5.1-d1 5.1-d \(\Q(\sqrt{105}) \) \( 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.344624259$ $33.76254038$ 1.703246763 \( -\frac{1145960298}{25} a + \frac{6444279999}{25} \) \( \bigl[a\) , \( -a + 1\) , \( a\) , \( 40 a - 237\) , \( -204 a + 1141\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(40a-237\right){x}-204a+1141$
5.1-d2 5.1-d \(\Q(\sqrt{105}) \) \( 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.344624259$ $8.440635095$ 1.703246763 \( \frac{55306341}{15625} \) \( \bigl[1\) , \( -1\) , \( a + 1\) , \( -64 a - 294\) , \( -431 a - 1996\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-64a-294\right){x}-431a-1996$
5.1-d3 5.1-d \(\Q(\sqrt{105}) \) \( 5 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.689248519$ $33.76254038$ 1.703246763 \( \frac{2803221}{125} \) \( \bigl[1\) , \( -1\) , \( a + 1\) , \( -24 a - 109\) , \( 140 a + 644\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-24a-109\right){x}+140a+644$
5.1-d4 5.1-d \(\Q(\sqrt{105}) \) \( 5 \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $1.378497038$ $33.76254038$ 1.703246763 \( \frac{1145960298}{25} a + \frac{5298319701}{25} \) \( \bigl[a\) , \( -a + 1\) , \( a\) , \( -376 a - 1709\) , \( 8426 a + 39001\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-376a-1709\right){x}+8426a+39001$
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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.