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Results (10 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
73.2-a2 73.2-a \(\Q(\sqrt{-3}) \) \( 73 \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $4.863501133$ 0.311993743 \( \frac{927841113}{5329} a - \frac{1323774856}{5329} \) \( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( -6 a - 1\) , \( 4 a\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-6a-1\right){x}+4a$
5329.3-a2 5329.3-a \(\Q(\sqrt{-3}) \) \( 73^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.657874373$ $0.569229752$ 2.179408166 \( \frac{927841113}{5329} a - \frac{1323774856}{5329} \) \( \bigl[1\) , \( 1\) , \( a + 1\) , \( -341 a - 76\) , \( -3390 a + 857\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-341a-76\right){x}-3390a+857$
12337.2-c2 12337.2-c \(\Q(\sqrt{-3}) \) \( 13^{2} \cdot 73 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.348892516$ 3.115133830 \( \frac{927841113}{5329} a - \frac{1323774856}{5329} \) \( \bigl[a + 1\) , \( a\) , \( 0\) , \( 40 a + 39\) , \( 226 a - 266\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(40a+39\right){x}+226a-266$
12337.6-a2 12337.6-a \(\Q(\sqrt{-3}) \) \( 13^{2} \cdot 73 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.517117678$ $1.348892516$ 3.221781549 \( \frac{927841113}{5329} a - \frac{1323774856}{5329} \) \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 77 a - 44\) , \( 178 a + 34\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(77a-44\right){x}+178a+34$
18688.2-e2 18688.2-e \(\Q(\sqrt{-3}) \) \( 2^{8} \cdot 73 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.215875283$ 2.807943688 \( \frac{927841113}{5329} a - \frac{1323774856}{5329} \) \( \bigl[0\) , \( a\) , \( 0\) , \( 83 a - 86\) , \( -345 a + 159\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(83a-86\right){x}-345a+159$
32193.2-b2 32193.2-b \(\Q(\sqrt{-3}) \) \( 3^{2} \cdot 7^{2} \cdot 73 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.061302956$ 2.450974190 \( \frac{927841113}{5329} a - \frac{1323774856}{5329} \) \( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -43 a + 125\) , \( -416 a + 68\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-43a+125\right){x}-416a+68$
32193.6-a2 32193.6-a \(\Q(\sqrt{-3}) \) \( 3^{2} \cdot 7^{2} \cdot 73 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.699718891$ $1.061302956$ 3.429985888 \( \frac{927841113}{5329} a - \frac{1323774856}{5329} \) \( \bigl[1\) , \( -a + 1\) , \( a\) , \( 50 a + 76\) , \( -443 a + 520\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(50a+76\right){x}-443a+520$
45625.2-a2 45625.2-a \(\Q(\sqrt{-3}) \) \( 5^{4} \cdot 73 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.036355966$ $0.972700226$ 4.656046711 \( \frac{927841113}{5329} a - \frac{1323774856}{5329} \) \( \bigl[1\) , \( a - 1\) , \( 0\) , \( 129 a - 134\) , \( 638 a - 374\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(129a-134\right){x}+638a-374$
99937.2-a2 99937.2-a \(\Q(\sqrt{-3}) \) \( 37^{2} \cdot 73 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.939469735$ $0.799554661$ 3.469447446 \( \frac{927841113}{5329} a - \frac{1323774856}{5329} \) \( \bigl[1\) , \( a + 1\) , \( a\) , \( -43 a - 169\) , \( 264 a + 771\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-43a-169\right){x}+264a+771$
99937.6-a2 99937.6-a \(\Q(\sqrt{-3}) \) \( 37^{2} \cdot 73 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.915664043$ $0.799554661$ 3.381533386 \( \frac{927841113}{5329} a - \frac{1323774856}{5329} \) \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 30 a - 208\) , \( 253 a - 1145\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(30a-208\right){x}+253a-1145$
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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.