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Results (28 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
26244.2-a1 26244.2-a \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{8} \) $1$ $\Z/3\Z$ $\mathrm{SU}(2)$ $0.305934883$ $3.305583379$ 2.038575609 \( -\frac{35937}{4} \) \( \bigl[1\) , \( -1\) , \( 0\) , \( -6\) , \( 8\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}-6{x}+8$
26244.2-a2 26244.2-a \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{8} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.101978294$ $1.101861126$ 2.038575609 \( \frac{109503}{64} \) \( \bigl[1\) , \( -1\) , \( 0\) , \( 39\) , \( -19\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}+39{x}-19$
26244.2-b1 26244.2-b \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{8} \) $1$ $\Z/3\Z$ $\mathrm{SU}(2)$ $10.13703660$ $0.583485219$ 2.980784579 \( -\frac{189613868625}{128} \) \( \bigl[1\) , \( -1\) , \( 0\) , \( -1077\) , \( 13877\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}-1077{x}+13877$
26244.2-b2 26244.2-b \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{8} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.482716028$ $1.361465512$ 2.980784579 \( -\frac{140625}{8} \) \( \bigl[1\) , \( -1\) , \( 0\) , \( -42\) , \( -100\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}-42{x}-100$
26244.2-b3 26244.2-b \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{8} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $3.379012201$ $0.194495073$ 2.980784579 \( -\frac{1159088625}{2097152} \) \( \bigl[1\) , \( -1\) , \( 0\) , \( -852\) , \( 19664\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}-852{x}+19664$
26244.2-b4 26244.2-b \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{8} \) $1$ $\Z/3\Z$ $\mathrm{SU}(2)$ $1.448148086$ $4.084396538$ 2.980784579 \( \frac{3375}{2} \) \( \bigl[1\) , \( -1\) , \( 0\) , \( 3\) , \( -1\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}+3{x}-1$
26244.2-c1 26244.2-c \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{8} \) 0 $\Z/3\Z$ $\mathrm{SU}(2)$ $1$ $1.223113832$ 2.465565733 \( -\frac{3541149801}{16777216} a - \frac{7108840053}{8388608} \) \( \bigl[1\) , \( -1\) , \( a\) , \( 4 a - 27\) , \( -28 a + 95\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(4a-27\right){x}-28a+95$
26244.2-c2 26244.2-c \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{8} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.407704610$ 2.465565733 \( \frac{3499281}{32768} a + \frac{20975733}{32768} \) \( \bigl[1\) , \( -1\) , \( a\) , \( -41 a + 228\) , \( 587 a - 1598\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-41a+228\right){x}+587a-1598$
26244.2-d1 26244.2-d \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{8} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.820812680$ $0.407704610$ 5.059419044 \( \frac{3541149801}{16777216} a - \frac{17758829907}{16777216} \) \( \bigl[1\) , \( -1\) , \( a\) , \( -41 a - 204\) , \( -709 a - 1598\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-41a-204\right){x}-709a-1598$
26244.2-d2 26244.2-d \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{8} \) $1$ $\Z/3\Z$ $\mathrm{SU}(2)$ $0.273604226$ $1.223113832$ 5.059419044 \( -\frac{3499281}{32768} a + \frac{12237507}{16384} \) \( \bigl[1\) , \( -1\) , \( a\) , \( 4 a + 21\) , \( 20 a + 31\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(4a+21\right){x}+20a+31$
26244.2-e1 26244.2-e \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{8} \) $1$ $\Z/3\Z$ $\mathrm{SU}(2)$ $0.607627350$ $2.973335577$ 5.462886890 \( \frac{20817}{16} a + \frac{26271}{16} \) \( \bigl[1\) , \( -1\) , \( a\) , \( -5 a + 3\) , \( 2 a - 5\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-5a+3\right){x}+2a-5$
26244.2-e2 26244.2-e \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{8} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1.822882051$ $0.991111859$ 5.462886890 \( -\frac{11308041}{4096} a + \frac{12488499}{4096} \) \( \bigl[1\) , \( -1\) , \( a\) , \( 40 a - 42\) , \( 101 a + 22\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(40a-42\right){x}+101a+22$
26244.2-f1 26244.2-f \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{8} \) 0 $\Z/3\Z$ $\mathrm{SU}(2)$ $1$ $2.973335577$ 2.996840572 \( \frac{11308041}{4096} a + \frac{590229}{2048} \) \( \bigl[1\) , \( -1\) , \( a\) , \( -5 a\) , \( 5 a - 4\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}-5a{x}+5a-4$
26244.2-f2 26244.2-f \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{8} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.991111859$ 2.996840572 \( -\frac{20817}{16} a + 2943 \) \( \bigl[1\) , \( -1\) , \( a\) , \( 40 a - 15\) , \( 20 a + 103\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(40a-15\right){x}+20a+103$
26244.2-g1 26244.2-g \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{8} \) 0 $\Z/3\Z$ $\mathrm{SU}(2)$ $1$ $1.223113832$ 2.465565733 \( \frac{3541149801}{16777216} a - \frac{17758829907}{16777216} \) \( \bigl[1\) , \( -1\) , \( a + 1\) , \( -5 a - 23\) , \( 27 a + 67\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-5a-23\right){x}+27a+67$
26244.2-g2 26244.2-g \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{8} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.407704610$ 2.465565733 \( -\frac{3499281}{32768} a + \frac{12237507}{16384} \) \( \bigl[1\) , \( -1\) , \( a + 1\) , \( 40 a + 187\) , \( -588 a - 1011\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(40a+187\right){x}-588a-1011$
26244.2-h1 26244.2-h \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{8} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.820812680$ $0.407704610$ 5.059419044 \( -\frac{3541149801}{16777216} a - \frac{7108840053}{8388608} \) \( \bigl[1\) , \( -1\) , \( a + 1\) , \( 40 a - 245\) , \( 708 a - 2307\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(40a-245\right){x}+708a-2307$
26244.2-h2 26244.2-h \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{8} \) $1$ $\Z/3\Z$ $\mathrm{SU}(2)$ $0.273604226$ $1.223113832$ 5.059419044 \( \frac{3499281}{32768} a + \frac{20975733}{32768} \) \( \bigl[1\) , \( -1\) , \( a + 1\) , \( -5 a + 25\) , \( -21 a + 51\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-5a+25\right){x}-21a+51$
26244.2-i1 26244.2-i \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{8} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1.822882051$ $0.991111859$ 5.462886890 \( \frac{11308041}{4096} a + \frac{590229}{2048} \) \( \bigl[1\) , \( -1\) , \( a + 1\) , \( -41 a - 2\) , \( -102 a + 123\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-41a-2\right){x}-102a+123$
26244.2-i2 26244.2-i \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{8} \) $1$ $\Z/3\Z$ $\mathrm{SU}(2)$ $0.607627350$ $2.973335577$ 5.462886890 \( -\frac{20817}{16} a + 2943 \) \( \bigl[1\) , \( -1\) , \( a + 1\) , \( 4 a - 2\) , \( -3 a - 3\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(4a-2\right){x}-3a-3$
26244.2-j1 26244.2-j \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{8} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.991111859$ 2.996840572 \( \frac{20817}{16} a + \frac{26271}{16} \) \( \bigl[1\) , \( -1\) , \( a + 1\) , \( -41 a + 25\) , \( -21 a + 123\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-41a+25\right){x}-21a+123$
26244.2-j2 26244.2-j \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{8} \) 0 $\Z/3\Z$ $\mathrm{SU}(2)$ $1$ $2.973335577$ 2.996840572 \( -\frac{11308041}{4096} a + \frac{12488499}{4096} \) \( \bigl[1\) , \( -1\) , \( a + 1\) , \( 4 a - 5\) , \( -6 a + 1\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(4a-5\right){x}-6a+1$
26244.2-k1 26244.2-k \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{8} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1.373693536$ $1.101861126$ 9.153510392 \( -\frac{35937}{4} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( -56\) , \( -161\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-56{x}-161$
26244.2-k2 26244.2-k \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{8} \) $1$ $\Z/3\Z$ $\mathrm{SU}(2)$ $0.457897845$ $3.305583379$ 9.153510392 \( \frac{109503}{64} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( 4\) , \( -1\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+4{x}-1$
26244.2-l1 26244.2-l \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{8} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.719702593$ $0.194495073$ 10.36976045 \( -\frac{189613868625}{128} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( -9695\) , \( -364985\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-9695{x}-364985$
26244.2-l2 26244.2-l \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{8} \) $1$ $\Z/3\Z$ $\mathrm{SU}(2)$ $1.679306052$ $4.084396538$ 10.36976045 \( -\frac{140625}{8} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( -5\) , \( 5\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-5{x}+5$
26244.2-l3 26244.2-l \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{8} \) $1$ $\Z/3\Z$ $\mathrm{SU}(2)$ $0.239900864$ $0.583485219$ 10.36976045 \( -\frac{1159088625}{2097152} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( -95\) , \( -697\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-95{x}-697$
26244.2-l4 26244.2-l \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{8} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $5.037918157$ $1.361465512$ 10.36976045 \( \frac{3375}{2} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( 25\) , \( 1\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+25{x}+1$
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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.