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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
2601.1-a1 2601.1-a \(\Q(\sqrt{2}) \) \( 3^{2} \cdot 17^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $3.542758762$ $0.739701511$ 1.853032724 \( -\frac{23100424192}{14739} \) \( \bigl[0\) , \( 1\) , \( 1\) , \( -59\) , \( -196\bigr] \) ${y}^2+{y}={x}^{3}+{x}^{2}-59{x}-196$
2601.1-a2 2601.1-a \(\Q(\sqrt{2}) \) \( 3^{2} \cdot 17^{2} \) $1$ $\Z/3\Z$ $\mathrm{SU}(2)$ $1.180919587$ $6.657313600$ 1.853032724 \( \frac{32768}{459} \) \( \bigl[0\) , \( 1\) , \( 1\) , \( 1\) , \( -1\bigr] \) ${y}^2+{y}={x}^{3}+{x}^{2}+{x}-1$
2601.1-b1 2601.1-b \(\Q(\sqrt{2}) \) \( 3^{2} \cdot 17^{2} \) $2$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.033070029$ $18.34402248$ 1.715829564 \( -\frac{6644672}{2601} \) \( \bigl[a\) , \( -a\) , \( 1\) , \( 7 a - 11\) , \( -14 a + 20\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(7a-11\right){x}-14a+20$
2601.1-b2 2601.1-b \(\Q(\sqrt{2}) \) \( 3^{2} \cdot 17^{2} \) $2$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.132280117$ $36.68804497$ 1.715829564 \( \frac{535387328}{51} \) \( \bigl[a\) , \( a - 1\) , \( 1\) , \( 33 a - 50\) , \( -155 a + 220\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(33a-50\right){x}-155a+220$
2601.1-c1 2601.1-c \(\Q(\sqrt{2}) \) \( 3^{2} \cdot 17^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.158409345$ $4.270200071$ 1.434945077 \( -\frac{35905570493}{72412707} a + \frac{172936548119}{72412707} \) \( \bigl[a + 1\) , \( -a + 1\) , \( 1\) , \( 22 a - 27\) , \( 60 a - 84\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(22a-27\right){x}+60a-84$
2601.1-c2 2601.1-c \(\Q(\sqrt{2}) \) \( 3^{2} \cdot 17^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.079204672$ $17.08080028$ 1.434945077 \( -\frac{416202982}{44217} a + \frac{74095371}{4913} \) \( \bigl[a + 1\) , \( -a + 1\) , \( 1\) , \( 7 a - 12\) , \( -9 a + 12\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(7a-12\right){x}-9a+12$
2601.1-d1 2601.1-d \(\Q(\sqrt{2}) \) \( 3^{2} \cdot 17^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.158409345$ $4.270200071$ 1.434945077 \( \frac{35905570493}{72412707} a + \frac{172936548119}{72412707} \) \( \bigl[a + 1\) , \( 1\) , \( 1\) , \( -23 a - 27\) , \( -60 a - 84\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(-23a-27\right){x}-60a-84$
2601.1-d2 2601.1-d \(\Q(\sqrt{2}) \) \( 3^{2} \cdot 17^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.079204672$ $17.08080028$ 1.434945077 \( \frac{416202982}{44217} a + \frac{74095371}{4913} \) \( \bigl[a + 1\) , \( 1\) , \( 1\) , \( -8 a - 12\) , \( 9 a + 12\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(-8a-12\right){x}+9a+12$
2601.1-e1 2601.1-e \(\Q(\sqrt{2}) \) \( 3^{2} \cdot 17^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.295578960$ 0.811609724 \( -\frac{6630840767433356679751}{582622237229761} a + \frac{84274075539679424994809}{5243600135067849} \) \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -363 a - 1984\) , \( 9592 a + 35746\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-363a-1984\right){x}+9592a+35746$
2601.1-e2 2601.1-e \(\Q(\sqrt{2}) \) \( 3^{2} \cdot 17^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $4.591157920$ 0.811609724 \( \frac{18812414348}{3581577} a + \frac{563103442961}{32234193} \) \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -48 a - 94\) , \( 268 a + 340\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-48a-94\right){x}+268a+340$
2601.1-e3 2601.1-e \(\Q(\sqrt{2}) \) \( 3^{2} \cdot 17^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $4.591157920$ 0.811609724 \( \frac{44776214704960466}{217238121} a + \frac{569920783435014403}{1955143089} \) \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -858 a - 1309\) , \( 16954 a + 24316\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-858a-1309\right){x}+16954a+24316$
2601.1-e4 2601.1-e \(\Q(\sqrt{2}) \) \( 3^{2} \cdot 17^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.295578960$ 0.811609724 \( \frac{10036258969402086757063}{83521} a + \frac{127740721950153724072663}{751689} \) \( \bigl[1\) , \( -a\) , \( a\) , \( -2431 a + 2251\) , \( -114886 a + 178668\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-2431a+2251\right){x}-114886a+178668$
2601.1-f1 2601.1-f \(\Q(\sqrt{2}) \) \( 3^{2} \cdot 17^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.295578960$ 0.811609724 \( -\frac{10036258969402086757063}{83521} a + \frac{127740721950153724072663}{751689} \) \( \bigl[1\) , \( a\) , \( a\) , \( 2430 a + 2251\) , \( 114886 a + 178668\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(2430a+2251\right){x}+114886a+178668$
2601.1-f2 2601.1-f \(\Q(\sqrt{2}) \) \( 3^{2} \cdot 17^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $4.591157920$ 0.811609724 \( -\frac{44776214704960466}{217238121} a + \frac{569920783435014403}{1955143089} \) \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 856 a - 1309\) , \( -16955 a + 24316\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(856a-1309\right){x}-16955a+24316$
2601.1-f3 2601.1-f \(\Q(\sqrt{2}) \) \( 3^{2} \cdot 17^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $4.591157920$ 0.811609724 \( -\frac{18812414348}{3581577} a + \frac{563103442961}{32234193} \) \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 46 a - 94\) , \( -269 a + 340\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(46a-94\right){x}-269a+340$
2601.1-f4 2601.1-f \(\Q(\sqrt{2}) \) \( 3^{2} \cdot 17^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.295578960$ 0.811609724 \( \frac{6630840767433356679751}{582622237229761} a + \frac{84274075539679424994809}{5243600135067849} \) \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 361 a - 1984\) , \( -9593 a + 35746\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(361a-1984\right){x}-9593a+35746$
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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.