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Results (24 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
288.1-a1 288.1-a \(\Q(\sqrt{3}) \) \( 2^{5} \cdot 3^{2} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $10.04344473$ 1.449646380 \( -\frac{166016}{3} a + 95936 \) \( \bigl[0\) , \( -a\) , \( 0\) , \( 4063804 a - 7038714\) , \( -5839863922 a + 10114941022\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(4063804a-7038714\right){x}-5839863922a+10114941022$
288.1-a2 288.1-a \(\Q(\sqrt{3}) \) \( 2^{5} \cdot 3^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.510861184$ 1.449646380 \( -\frac{164847992914}{3} a + \frac{285525100658}{3} \) \( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 381758 a - 661224\) , \( 168866036 a - 292484554\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(381758a-661224\right){x}+168866036a-292484554$
288.1-a3 288.1-a \(\Q(\sqrt{3}) \) \( 2^{5} \cdot 3^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $10.04344473$ 1.449646380 \( -\frac{1122088}{9} a + \frac{1989808}{9} \) \( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 23873 a - 41349\) , \( 2630312 a - 4555834\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(23873a-41349\right){x}+2630312a-4555834$
288.1-a4 288.1-a \(\Q(\sqrt{3}) \) \( 2^{5} \cdot 3^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $10.04344473$ 1.449646380 \( \frac{9856}{3} a + \frac{22336}{3} \) \( \bigl[0\) , \( -a\) , \( 0\) , \( 113682 a - 196902\) , \( 3469554 a - 6009444\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(113682a-196902\right){x}+3469554a-6009444$
288.1-a5 288.1-a \(\Q(\sqrt{3}) \) \( 2^{5} \cdot 3^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $5.021722368$ 1.449646380 \( \frac{443186854}{81} a + \frac{767608522}{81} \) \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 77 a - 140\) , \( 1663 a - 2881\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(77a-140\right){x}+1663a-2881$
288.1-a6 288.1-a \(\Q(\sqrt{3}) \) \( 2^{5} \cdot 3^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $5.021722368$ 1.449646380 \( \frac{132636728}{3} a + 76579552 \) \( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -1569806 a + 2718984\) , \( 176681708 a - 306021695\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(-1569806a+2718984\right){x}+176681708a-306021695$
288.1-b1 288.1-b \(\Q(\sqrt{3}) \) \( 2^{5} \cdot 3^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $5.021722368$ 1.449646380 \( -\frac{443186854}{81} a + \frac{767608522}{81} \) \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -79 a - 140\) , \( -1664 a - 2881\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-79a-140\right){x}-1664a-2881$
288.1-b2 288.1-b \(\Q(\sqrt{3}) \) \( 2^{5} \cdot 3^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $5.021722368$ 1.449646380 \( -\frac{132636728}{3} a + 76579552 \) \( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( 10822 a - 18744\) , \( 809620 a - 1402303\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(10822a-18744\right){x}+809620a-1402303$
288.1-b3 288.1-b \(\Q(\sqrt{3}) \) \( 2^{5} \cdot 3^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $10.04344473$ 1.449646380 \( -\frac{9856}{3} a + \frac{22336}{3} \) \( \bigl[0\) , \( a\) , \( 0\) , \( 198 a - 342\) , \( 1746 a - 3024\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(198a-342\right){x}+1746a-3024$
288.1-b4 288.1-b \(\Q(\sqrt{3}) \) \( 2^{5} \cdot 3^{2} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $10.04344473$ 1.449646380 \( \frac{166016}{3} a + 95936 \) \( \bigl[0\) , \( a\) , \( 0\) , \( -668 a + 1158\) , \( 54226 a - 93922\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(-668a+1158\right){x}+54226a-93922$
288.1-b5 288.1-b \(\Q(\sqrt{3}) \) \( 2^{5} \cdot 3^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $10.04344473$ 1.449646380 \( \frac{1122088}{9} a + \frac{1989808}{9} \) \( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( 11 a - 21\) , \( -20 a + 34\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(11a-21\right){x}-20a+34$
288.1-b6 288.1-b \(\Q(\sqrt{3}) \) \( 2^{5} \cdot 3^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.510861184$ 1.449646380 \( \frac{164847992914}{3} a + \frac{285525100658}{3} \) \( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -34 a + 24\) , \( -164 a + 214\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-34a+24\right){x}-164a+214$
288.1-c1 288.1-c \(\Q(\sqrt{3}) \) \( 2^{5} \cdot 3^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.410195878$ $7.783091503$ 1.843243885 \( -\frac{166016}{3} a + 95936 \) \( \bigl[0\) , \( a\) , \( 0\) , \( 4063804 a - 7038714\) , \( 5839863922 a - 10114941022\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(4063804a-7038714\right){x}+5839863922a-10114941022$
288.1-c2 288.1-c \(\Q(\sqrt{3}) \) \( 2^{5} \cdot 3^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.820391757$ $7.783091503$ 1.843243885 \( -\frac{164847992914}{3} a + \frac{285525100658}{3} \) \( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( 381758 a - 661224\) , \( -168866036 a + 292484554\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(381758a-661224\right){x}-168866036a+292484554$
288.1-c3 288.1-c \(\Q(\sqrt{3}) \) \( 2^{5} \cdot 3^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.410195878$ $15.56618300$ 1.843243885 \( -\frac{1122088}{9} a + \frac{1989808}{9} \) \( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( 23873 a - 41349\) , \( -2630312 a + 4555834\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(23873a-41349\right){x}-2630312a+4555834$
288.1-c4 288.1-c \(\Q(\sqrt{3}) \) \( 2^{5} \cdot 3^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.205097939$ $15.56618300$ 1.843243885 \( \frac{9856}{3} a + \frac{22336}{3} \) \( \bigl[0\) , \( a\) , \( 0\) , \( 113682 a - 196902\) , \( -3469554 a + 6009444\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(113682a-196902\right){x}-3469554a+6009444$
288.1-c5 288.1-c \(\Q(\sqrt{3}) \) \( 2^{5} \cdot 3^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.820391757$ $3.891545751$ 1.843243885 \( \frac{443186854}{81} a + \frac{767608522}{81} \) \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 77 a - 140\) , \( -1664 a + 2879\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(77a-140\right){x}-1664a+2879$
288.1-c6 288.1-c \(\Q(\sqrt{3}) \) \( 2^{5} \cdot 3^{2} \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $0.410195878$ $15.56618300$ 1.843243885 \( \frac{132636728}{3} a + 76579552 \) \( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -1569806 a + 2718984\) , \( -176681708 a + 306021695\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-1569806a+2718984\right){x}-176681708a+306021695$
288.1-d1 288.1-d \(\Q(\sqrt{3}) \) \( 2^{5} \cdot 3^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.820391757$ $3.891545751$ 1.843243885 \( -\frac{443186854}{81} a + \frac{767608522}{81} \) \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -79 a - 140\) , \( 1663 a + 2879\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-79a-140\right){x}+1663a+2879$
288.1-d2 288.1-d \(\Q(\sqrt{3}) \) \( 2^{5} \cdot 3^{2} \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $0.410195878$ $15.56618300$ 1.843243885 \( -\frac{132636728}{3} a + 76579552 \) \( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 10822 a - 18744\) , \( -809620 a + 1402303\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(10822a-18744\right){x}-809620a+1402303$
288.1-d3 288.1-d \(\Q(\sqrt{3}) \) \( 2^{5} \cdot 3^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.205097939$ $15.56618300$ 1.843243885 \( -\frac{9856}{3} a + \frac{22336}{3} \) \( \bigl[0\) , \( -a\) , \( 0\) , \( 198 a - 342\) , \( -1746 a + 3024\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(198a-342\right){x}-1746a+3024$
288.1-d4 288.1-d \(\Q(\sqrt{3}) \) \( 2^{5} \cdot 3^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.410195878$ $7.783091503$ 1.843243885 \( \frac{166016}{3} a + 95936 \) \( \bigl[0\) , \( -a\) , \( 0\) , \( -668 a + 1158\) , \( -54226 a + 93922\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(-668a+1158\right){x}-54226a+93922$
288.1-d5 288.1-d \(\Q(\sqrt{3}) \) \( 2^{5} \cdot 3^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.410195878$ $15.56618300$ 1.843243885 \( \frac{1122088}{9} a + \frac{1989808}{9} \) \( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 11 a - 21\) , \( 20 a - 34\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(11a-21\right){x}+20a-34$
288.1-d6 288.1-d \(\Q(\sqrt{3}) \) \( 2^{5} \cdot 3^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.820391757$ $7.783091503$ 1.843243885 \( \frac{164847992914}{3} a + \frac{285525100658}{3} \) \( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -34 a + 24\) , \( 164 a - 214\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(-34a+24\right){x}+164a-214$
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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.