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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
4356.5-a1 4356.5-a \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{2} \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.623134288$ 0.942090491 \( -\frac{7357983625}{127552392} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -41\) , \( -556\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-41{x}-556$
4356.5-a2 4356.5-a \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{2} \cdot 11^{2} \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $1.869402865$ 0.942090491 \( \frac{9938375}{176418} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( 4\) , \( 20\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+4{x}+20$
4356.5-a3 4356.5-a \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{2} \cdot 11^{2} \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $3.738805730$ 0.942090491 \( \frac{18609625}{1188} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -6\) , \( 4\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-6{x}+4$
4356.5-a4 4356.5-a \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{2} \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.246268576$ 0.942090491 \( \frac{57736239625}{255552} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -81\) , \( -284\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-81{x}-284$
4356.5-b1 4356.5-b \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{2} \cdot 11^{2} \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $0.523029338$ 2.372238099 \( \frac{229027231511}{680279424} a - \frac{24638577262535}{165307900032} \) \( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -79 a + 79\) , \( -325 a - 685\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-79a+79\right){x}-325a-685$
4356.5-b2 4356.5-b \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{2} \cdot 11^{2} \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $1.046058676$ 2.372238099 \( -\frac{2492457457997}{588791808} a + \frac{3282842124127}{588791808} \) \( \bigl[1\) , \( -a + 1\) , \( 0\) , \( 41 a - 1\) , \( -13 a - 125\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(41a-1\right){x}-13a-125$
4356.5-b3 4356.5-b \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{2} \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.348686225$ 2.372238099 \( \frac{105273133194758264123}{17561399718838272} a + \frac{342157997809516499975}{17561399718838272} \) \( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -424 a + 614\) , \( -1060 a - 6260\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-424a+614\right){x}-1060a-6260$
4356.5-b4 4356.5-b \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{2} \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.174343112$ 2.372238099 \( \frac{968213635965123841917}{3715232694272} a + \frac{9325769488561763242777}{33437094248448} \) \( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -6694 a + 9754\) , \( -54874 a - 409456\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-6694a+9754\right){x}-54874a-409456$
4356.5-c1 4356.5-c \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{2} \cdot 11^{2} \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $0.523029338$ 2.372238099 \( -\frac{229027231511}{680279424} a + \frac{15507519997319}{82653950016} \) \( \bigl[1\) , \( a\) , \( 0\) , \( 79 a\) , \( 325 a - 1010\bigr] \) ${y}^2+{x}{y}={x}^{3}+a{x}^{2}+79a{x}+325a-1010$
4356.5-c2 4356.5-c \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{2} \cdot 11^{2} \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $1.046058676$ 2.372238099 \( \frac{2492457457997}{588791808} a + \frac{395192333065}{294395904} \) \( \bigl[1\) , \( a\) , \( 0\) , \( -41 a + 40\) , \( 13 a - 138\bigr] \) ${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(-41a+40\right){x}+13a-138$
4356.5-c3 4356.5-c \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{2} \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.348686225$ 2.372238099 \( -\frac{105273133194758264123}{17561399718838272} a + \frac{223715565502137382049}{8780699859419136} \) \( \bigl[1\) , \( a\) , \( 0\) , \( 424 a + 190\) , \( 1060 a - 7320\bigr] \) ${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(424a+190\right){x}+1060a-7320$
4356.5-c4 4356.5-c \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{2} \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.174343112$ 2.372238099 \( -\frac{968213635965123841917}{3715232694272} a + \frac{9019846106123938910015}{16718547124224} \) \( \bigl[1\) , \( a\) , \( 0\) , \( 6694 a + 3060\) , \( 54874 a - 464330\bigr] \) ${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(6694a+3060\right){x}+54874a-464330$
4356.5-d1 4356.5-d \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{2} \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.209138112$ 3.656089994 \( -\frac{192100033}{2371842} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -12\) , \( -81\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-12{x}-81$
4356.5-d2 4356.5-d \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{2} \cdot 11^{2} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $4.836552448$ 3.656089994 \( \frac{912673}{528} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -2\) , \( -1\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-2{x}-1$
4356.5-d3 4356.5-d \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{2} \cdot 11^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.418276224$ 3.656089994 \( \frac{1180932193}{4356} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -22\) , \( -49\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-22{x}-49$
4356.5-d4 4356.5-d \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{2} \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.209138112$ 3.656089994 \( \frac{4824238966273}{66} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -352\) , \( -2689\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-352{x}-2689$
4356.5-e1 4356.5-e \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{2} \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.112045110$ 4.234907127 \( -\frac{112427521449300721}{466873642818} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( -10055\) , \( -390309\bigr] \) ${y}^2+{x}{y}={x}^{3}-10055{x}-390309$
4356.5-e2 4356.5-e \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{2} \cdot 11^{2} \) 0 $\Z/10\Z$ $\mathrm{SU}(2)$ $1$ $0.560225554$ 4.234907127 \( \frac{168105213359}{228637728} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( 115\) , \( 561\bigr] \) ${y}^2+{x}{y}={x}^{3}+115{x}+561$
4356.5-e3 4356.5-e \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{2} \cdot 11^{2} \) 0 $\Z/10\Z$ $\mathrm{SU}(2)$ $1$ $1.120451108$ 4.234907127 \( \frac{10091699281}{2737152} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( -45\) , \( 81\bigr] \) ${y}^2+{x}{y}={x}^{3}-45{x}+81$
4356.5-e4 4356.5-e \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{2} \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.224090221$ 4.234907127 \( \frac{112763292123580561}{1932612} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( -10065\) , \( -389499\bigr] \) ${y}^2+{x}{y}={x}^{3}-10065{x}-389499$
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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.