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Results (27 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
48400.2-a1 48400.2-a \(\Q(\sqrt{-2}) \) \( 2^{4} \cdot 5^{2} \cdot 11^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.054095025$ $2.070993444$ 1.901219664 \( -\frac{16241202}{1375} \) \( \bigl[a\) , \( -1\) , \( 0\) , \( -16\) , \( -20\bigr] \) ${y}^2+a{x}{y}={x}^{3}-{x}^{2}-16{x}-20$
48400.2-b1 48400.2-b \(\Q(\sqrt{-2}) \) \( 2^{4} \cdot 5^{2} \cdot 11^{2} \) $2$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.046404488$ $1.581720524$ 4.152070585 \( \frac{314878832}{805255} a + \frac{1086200609}{805255} \) \( \bigl[a\) , \( a\) , \( 0\) , \( 12 a - 4\) , \( -16 a\bigr] \) ${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(12a-4\right){x}-16a$
48400.2-c1 48400.2-c \(\Q(\sqrt{-2}) \) \( 2^{4} \cdot 5^{2} \cdot 11^{2} \) $2$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.248068626$ $2.978126157$ 4.179168884 \( \frac{1048576}{605} \) \( \bigl[0\) , \( 1\) , \( 0\) , \( -5\) , \( -2\bigr] \) ${y}^2={x}^{3}+{x}^{2}-5{x}-2$
48400.2-c2 48400.2-c \(\Q(\sqrt{-2}) \) \( 2^{4} \cdot 5^{2} \cdot 11^{2} \) $2$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.992274504$ $2.978126157$ 4.179168884 \( \frac{94875856}{275} \) \( \bigl[a\) , \( 0\) , \( 0\) , \( -15\) , \( 25\bigr] \) ${y}^2+a{x}{y}={x}^{3}-15{x}+25$
48400.2-d1 48400.2-d \(\Q(\sqrt{-2}) \) \( 2^{4} \cdot 5^{2} \cdot 11^{2} \) $2$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.046404488$ $1.581720524$ 4.152070585 \( -\frac{314878832}{805255} a + \frac{1086200609}{805255} \) \( \bigl[a\) , \( -a\) , \( 0\) , \( -12 a - 4\) , \( 16 a\bigr] \) ${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(-12a-4\right){x}+16a$
48400.2-e1 48400.2-e \(\Q(\sqrt{-2}) \) \( 2^{4} \cdot 5^{2} \cdot 11^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.549489922$ 1.554192200 \( -\frac{76711450249}{851840} \) \( \bigl[a\) , \( 1\) , \( 0\) , \( -354\) , \( 2530\bigr] \) ${y}^2+a{x}{y}={x}^{3}+{x}^{2}-354{x}+2530$
48400.2-e2 48400.2-e \(\Q(\sqrt{-2}) \) \( 2^{4} \cdot 5^{2} \cdot 11^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.183163307$ 1.554192200 \( \frac{2882081488391}{2883584000} \) \( \bigl[a\) , \( 1\) , \( 0\) , \( 1186\) , \( 13618\bigr] \) ${y}^2+a{x}{y}={x}^{3}+{x}^{2}+1186{x}+13618$
48400.2-f1 48400.2-f \(\Q(\sqrt{-2}) \) \( 2^{4} \cdot 5^{2} \cdot 11^{2} \) $2$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.209374945$ $2.511961094$ 5.950351283 \( -\frac{117649}{440} \) \( \bigl[a\) , \( 1\) , \( 0\) , \( -4\) , \( 8\bigr] \) ${y}^2+a{x}{y}={x}^{3}+{x}^{2}-4{x}+8$
48400.2-f2 48400.2-f \(\Q(\sqrt{-2}) \) \( 2^{4} \cdot 5^{2} \cdot 11^{2} \) $2$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.023263882$ $0.837320364$ 5.950351283 \( \frac{80062991}{332750} \) \( \bigl[a\) , \( 1\) , \( 0\) , \( 36\) , \( -200\bigr] \) ${y}^2+a{x}{y}={x}^{3}+{x}^{2}+36{x}-200$
48400.2-g1 48400.2-g \(\Q(\sqrt{-2}) \) \( 2^{4} \cdot 5^{2} \cdot 11^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.449441034$ $3.446244963$ 3.532089493 \( \frac{55296}{275} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( 2\) , \( 3\bigr] \) ${y}^2={x}^{3}+2{x}+3$
48400.2-g2 48400.2-g \(\Q(\sqrt{-2}) \) \( 2^{4} \cdot 5^{2} \cdot 11^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.724720517$ $3.446244963$ 3.532089493 \( \frac{5256144}{605} \) \( \bigl[a\) , \( -1\) , \( 0\) , \( -5\) , \( -2\bigr] \) ${y}^2+a{x}{y}={x}^{3}-{x}^{2}-5{x}-2$
48400.2-h1 48400.2-h \(\Q(\sqrt{-2}) \) \( 2^{4} \cdot 5^{2} \cdot 11^{2} \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $2.697878822$ $0.158331435$ 3.624564542 \( -\frac{1957960715364}{29541015625} \) \( \bigl[a\) , \( -1\) , \( 0\) , \( -656\) , \( 34034\bigr] \) ${y}^2+a{x}{y}={x}^{3}-{x}^{2}-656{x}+34034$
48400.2-h2 48400.2-h \(\Q(\sqrt{-2}) \) \( 2^{4} \cdot 5^{2} \cdot 11^{2} \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $0.674469705$ $0.158331435$ 3.624564542 \( \frac{46424454082884}{26794860125} \) \( \bigl[a\) , \( -1\) , \( 0\) , \( -1886\) , \( -680\bigr] \) ${y}^2+a{x}{y}={x}^{3}-{x}^{2}-1886{x}-680$
48400.2-h3 48400.2-h \(\Q(\sqrt{-2}) \) \( 2^{4} \cdot 5^{2} \cdot 11^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1.348939411$ $0.316662871$ 3.624564542 \( \frac{55537159171536}{228765625} \) \( \bigl[a\) , \( -1\) , \( 0\) , \( -1261\) , \( 17820\bigr] \) ${y}^2+a{x}{y}={x}^{3}-{x}^{2}-1261{x}+17820$
48400.2-h4 48400.2-h \(\Q(\sqrt{-2}) \) \( 2^{4} \cdot 5^{2} \cdot 11^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $2.697878822$ $0.316662871$ 3.624564542 \( \frac{885956203616256}{15125} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -5042\) , \( -137801\bigr] \) ${y}^2={x}^{3}-5042{x}-137801$
48400.2-i1 48400.2-i \(\Q(\sqrt{-2}) \) \( 2^{4} \cdot 5^{2} \cdot 11^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.686309128$ $1.493096680$ 5.341108221 \( \frac{2122416}{171875} \) \( \bigl[a\) , \( -1\) , \( 0\) , \( 5\) , \( -42\bigr] \) ${y}^2+a{x}{y}={x}^{3}-{x}^{2}+5{x}-42$
48400.2-i2 48400.2-i \(\Q(\sqrt{-2}) \) \( 2^{4} \cdot 5^{2} \cdot 11^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.843154564$ $1.493096680$ 5.341108221 \( \frac{379275264}{15125} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -38\) , \( 87\bigr] \) ${y}^2={x}^{3}-38{x}+87$
48400.2-j1 48400.2-j \(\Q(\sqrt{-2}) \) \( 2^{4} \cdot 5^{2} \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $3.541244221$ 2.504037803 \( \frac{59319}{55} \) \( \bigl[a\) , \( -1\) , \( 0\) , \( 4\) , \( 0\bigr] \) ${y}^2+a{x}{y}={x}^{3}-{x}^{2}+4{x}$
48400.2-j2 48400.2-j \(\Q(\sqrt{-2}) \) \( 2^{4} \cdot 5^{2} \cdot 11^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.770622110$ 2.504037803 \( \frac{8120601}{3025} \) \( \bigl[a\) , \( -1\) , \( 0\) , \( -16\) , \( 24\bigr] \) ${y}^2+a{x}{y}={x}^{3}-{x}^{2}-16{x}+24$
48400.2-j3 48400.2-j \(\Q(\sqrt{-2}) \) \( 2^{4} \cdot 5^{2} \cdot 11^{2} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $0.885311055$ 2.504037803 \( \frac{2749884201}{73205} \) \( \bigl[a\) , \( -1\) , \( 0\) , \( -116\) , \( -416\bigr] \) ${y}^2+a{x}{y}={x}^{3}-{x}^{2}-116{x}-416$
48400.2-j4 48400.2-j \(\Q(\sqrt{-2}) \) \( 2^{4} \cdot 5^{2} \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.885311055$ 2.504037803 \( \frac{22930509321}{6875} \) \( \bigl[a\) , \( -1\) , \( 0\) , \( -236\) , \( 1520\bigr] \) ${y}^2+a{x}{y}={x}^{3}-{x}^{2}-236{x}+1520$
48400.2-k1 48400.2-k \(\Q(\sqrt{-2}) \) \( 2^{4} \cdot 5^{2} \cdot 11^{2} \) $2$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $6.733584661$ $0.137614587$ 10.48372894 \( -\frac{23178622194826561}{1610510} \) \( \bigl[a\) , \( 0\) , \( a\) , \( -23759\) , \( -1405718\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-23759{x}-1405718$
48400.2-k2 48400.2-k \(\Q(\sqrt{-2}) \) \( 2^{4} \cdot 5^{2} \cdot 11^{2} \) $2$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.269343386$ $0.688072939$ 10.48372894 \( \frac{109902239}{1100000} \) \( \bigl[a\) , \( 0\) , \( a\) , \( 41\) , \( -398\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+41{x}-398$
48400.2-l1 48400.2-l \(\Q(\sqrt{-2}) \) \( 2^{4} \cdot 5^{2} \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.437433019$ 6.098511811 \( \frac{436334416}{171875} \) \( \bigl[a\) , \( 1\) , \( a\) , \( -24\) , \( -31\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-24{x}-31$
48400.2-l2 48400.2-l \(\Q(\sqrt{-2}) \) \( 2^{4} \cdot 5^{2} \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.437433019$ 6.098511811 \( \frac{643956736}{15125} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( -45\) , \( -100\bigr] \) ${y}^2={x}^{3}-{x}^{2}-45{x}-100$
48400.2-l3 48400.2-l \(\Q(\sqrt{-2}) \) \( 2^{4} \cdot 5^{2} \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.479144339$ 6.098511811 \( \frac{610462990336}{8857805} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( -445\) , \( 3720\bigr] \) ${y}^2={x}^{3}-{x}^{2}-445{x}+3720$
48400.2-l4 48400.2-l \(\Q(\sqrt{-2}) \) \( 2^{4} \cdot 5^{2} \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.479144339$ 6.098511811 \( \frac{154639330142416}{33275} \) \( \bigl[a\) , \( 1\) , \( a\) , \( -1774\) , \( -29081\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-1774{x}-29081$
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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.