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Results (20 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
135.2-a1 135.2-a \(\Q(\sqrt{10}) \) \( 3^{3} \cdot 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $5.140502805$ 2.438354577 \( \frac{336226}{135} a - \frac{1062059}{135} \) \( \bigl[1\) , \( -a + 1\) , \( a\) , \( 8\) , \( -22 a - 69\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+8{x}-22a-69$
135.2-a2 135.2-a \(\Q(\sqrt{10}) \) \( 3^{3} \cdot 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $5.140502805$ 2.438354577 \( -\frac{156415766633}{3645} a + \frac{98945821613}{729} \) \( \bigl[1\) , \( -a + 1\) , \( a\) , \( -55 a - 167\) , \( -336 a - 1064\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-55a-167\right){x}-336a-1064$
135.2-b1 135.2-b \(\Q(\sqrt{10}) \) \( 3^{3} \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.459288555$ $16.24433986$ 2.359324574 \( \frac{1026304}{3645} a + \frac{949568}{729} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -4 a - 10\) , \( -10 a - 32\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-4a-10\right){x}-10a-32$
135.2-b2 135.2-b \(\Q(\sqrt{10}) \) \( 3^{3} \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.688932833$ $3.609853302$ 2.359324574 \( -\frac{66006784}{375} a + \frac{226222784}{375} \) \( \bigl[a\) , \( a\) , \( 1\) , \( -16 a - 62\) , \( -113 a - 373\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-16a-62\right){x}-113a-373$
135.2-b3 135.2-b \(\Q(\sqrt{10}) \) \( 3^{3} \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.229644277$ $32.48867972$ 2.359324574 \( \frac{1217792}{135} a + \frac{4608704}{135} \) \( \bigl[a\) , \( a\) , \( 1\) , \( -a - 2\) , \( 0\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-a-2\right){x}$
135.2-b4 135.2-b \(\Q(\sqrt{10}) \) \( 3^{3} \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.377865667$ $1.804926651$ 2.359324574 \( \frac{74932775168}{225} a + \frac{47391625792}{45} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -304 a - 970\) , \( -5610 a - 17760\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-304a-970\right){x}-5610a-17760$
135.2-c1 135.2-c \(\Q(\sqrt{10}) \) \( 3^{3} \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.193173311$ $13.37120092$ 1.633606813 \( -\frac{6184497677}{3645} a + \frac{19558082533}{3645} \) \( \bigl[1\) , \( a\) , \( 0\) , \( 4 a + 4\) , \( 5 a + 41\bigr] \) ${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(4a+4\right){x}+5a+41$
135.2-c2 135.2-c \(\Q(\sqrt{10}) \) \( 3^{3} \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.386346623$ $26.74240184$ 1.633606813 \( \frac{211922}{135} a + \frac{64105}{27} \) \( \bigl[1\) , \( a\) , \( 0\) , \( -a - 1\) , \( 0\bigr] \) ${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(-a-1\right){x}$
135.2-d1 135.2-d \(\Q(\sqrt{10}) \) \( 3^{3} \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.198884253$ $3.102293440$ 4.704572026 \( \frac{24897088}{18225} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -48 a + 174\) , \( 226 a - 676\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-48a+174\right){x}+226a-676$
135.2-d2 135.2-d \(\Q(\sqrt{10}) \) \( 3^{3} \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $2.397768506$ $6.204586881$ 4.704572026 \( \frac{36594368}{16875} \) \( \bigl[a\) , \( a\) , \( 1\) , \( 15 a - 43\) , \( 21 a - 67\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(15a-43\right){x}+21a-67$
135.2-e1 135.2-e \(\Q(\sqrt{10}) \) \( 3^{3} \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.088005746$ $3.102293440$ 2.072073465 \( \frac{24897088}{18225} \) \( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -15 a + 50\) , \( -7 a + 24\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-15a+50\right){x}-7a+24$
135.2-e2 135.2-e \(\Q(\sqrt{10}) \) \( 3^{3} \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.044002873$ $6.204586881$ 2.072073465 \( \frac{36594368}{16875} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 56 a - 190\) , \( 242 a - 728\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(56a-190\right){x}+242a-728$
135.2-f1 135.2-f \(\Q(\sqrt{10}) \) \( 3^{3} \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.174021352$ $13.37120092$ 4.414933890 \( -\frac{6184497677}{3645} a + \frac{19558082533}{3645} \) \( \bigl[a\) , \( -a + 1\) , \( a\) , \( 13 a + 5\) , \( 48 a + 178\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(13a+5\right){x}+48a+178$
135.2-f2 135.2-f \(\Q(\sqrt{10}) \) \( 3^{3} \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.348042704$ $26.74240184$ 4.414933890 \( \frac{211922}{135} a + \frac{64105}{27} \) \( \bigl[a\) , \( -a + 1\) , \( a\) , \( -7 a - 15\) , \( 8 a + 30\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-7a-15\right){x}+8a+30$
135.2-g1 135.2-g \(\Q(\sqrt{10}) \) \( 3^{3} \cdot 5 \) $1$ $\Z/6\Z$ $\mathrm{SU}(2)$ $1.661192439$ $16.24433986$ 2.844466074 \( \frac{1026304}{3645} a + \frac{949568}{729} \) \( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( -4 a - 1\) , \( -3 a + 1\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-4a-1\right){x}-3a+1$
135.2-g2 135.2-g \(\Q(\sqrt{10}) \) \( 3^{3} \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $2.491788659$ $3.609853302$ 2.844466074 \( -\frac{66006784}{375} a + \frac{226222784}{375} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -68 a - 266\) , \( -506 a - 1784\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-68a-266\right){x}-506a-1784$
135.2-g3 135.2-g \(\Q(\sqrt{10}) \) \( 3^{3} \cdot 5 \) $1$ $\Z/6\Z$ $\mathrm{SU}(2)$ $0.830596219$ $32.48867972$ 2.844466074 \( \frac{1217792}{135} a + \frac{4608704}{135} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -8 a - 26\) , \( 38 a + 120\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-8a-26\right){x}+38a+120$
135.2-g4 135.2-g \(\Q(\sqrt{10}) \) \( 3^{3} \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $4.983577319$ $1.804926651$ 2.844466074 \( \frac{74932775168}{225} a + \frac{47391625792}{45} \) \( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( -79 a - 241\) , \( -658 a - 2080\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-79a-241\right){x}-658a-2080$
135.2-h1 135.2-h \(\Q(\sqrt{10}) \) \( 3^{3} \cdot 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $5.140502805$ 0.812784859 \( \frac{336226}{135} a - \frac{1062059}{135} \) \( \bigl[a\) , \( a\) , \( 0\) , \( 7 a + 22\) , \( -154 a - 487\bigr] \) ${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(7a+22\right){x}-154a-487$
135.2-h2 135.2-h \(\Q(\sqrt{10}) \) \( 3^{3} \cdot 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $5.140502805$ 0.812784859 \( -\frac{156415766633}{3645} a + \frac{98945821613}{729} \) \( \bigl[a\) , \( a\) , \( 0\) , \( -213 a - 678\) , \( -3366 a - 10647\bigr] \) ${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(-213a-678\right){x}-3366a-10647$
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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.