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Base field Conductor norm Rank* Torsion order CM discriminant
Base field degree/signature Bad \(p\) $\Q$-curves Torsion structure CM
Analytic order of Ш* Cyclic isogeny degree Isogeny class size Reduction Galois image
j-invariant Regulator* Curves per isogeny class Isogeny class degree Nonmax$\ \ell$
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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
1.1-a1 1.1-a 4.4.2624.1 \( 1 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $10.73961278$ 0.471725361 \( 427641453408640 a^{3} + 331260963910720 a^{2} - 363800343820288 a - 154126073580480 \) \( \bigl[a^{3} - 2 a^{2} - 2 a + 1\) , \( a^{3} - 2 a^{2} - 3 a\) , \( a + 1\) , \( -16 a^{3} + 36 a^{2} + 39 a - 49\) , \( -57 a^{3} + 134 a^{2} + 126 a - 168\bigr] \) ${y}^2+\left(a^{3}-2a^{2}-2a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{3}-2a^{2}-3a\right){x}^{2}+\left(-16a^{3}+36a^{2}+39a-49\right){x}-57a^{3}+134a^{2}+126a-168$
49.3-a1 49.3-a 4.4.2624.1 \( 7^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.115090895$ $312.5508098$ 1.404460983 \( 427641453408640 a^{3} + 331260963910720 a^{2} - 363800343820288 a - 154126073580480 \) \( \bigl[a^{2} - a - 1\) , \( a^{2} - 2 a - 2\) , \( a^{3} - 2 a^{2} - a + 2\) , \( 15 a^{3} - 62 a^{2} + 53 a - 13\) , \( -93 a^{3} + 335 a^{2} - 211 a - 6\bigr] \) ${y}^2+\left(a^{2}-a-1\right){x}{y}+\left(a^{3}-2a^{2}-a+2\right){y}={x}^{3}+\left(a^{2}-2a-2\right){x}^{2}+\left(15a^{3}-62a^{2}+53a-13\right){x}-93a^{3}+335a^{2}-211a-6$
49.4-a3 49.4-a 4.4.2624.1 \( 7^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.057545447$ $312.5508098$ 1.404460983 \( 427641453408640 a^{3} + 331260963910720 a^{2} - 363800343820288 a - 154126073580480 \) \( \bigl[a^{3} - 2 a^{2} - 2 a + 1\) , \( -a^{3} + 2 a^{2} + 3 a - 2\) , \( a^{2} - 2 a\) , \( 4 a^{3} - 24 a^{2} - 22 a - 8\) , \( 4 a^{3} + 39 a^{2} + 126 a + 47\bigr] \) ${y}^2+\left(a^{3}-2a^{2}-2a+1\right){x}{y}+\left(a^{2}-2a\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+3a-2\right){x}^{2}+\left(4a^{3}-24a^{2}-22a-8\right){x}+4a^{3}+39a^{2}+126a+47$
256.1-e3 256.1-e 4.4.2624.1 \( 2^{8} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $35.20912159$ 1.546520898 \( 427641453408640 a^{3} + 331260963910720 a^{2} - 363800343820288 a - 154126073580480 \) \( \bigl[0\) , \( -a^{3} + 2 a^{2} + 2 a\) , \( 0\) , \( 80 a^{3} - 225 a^{2} - 8 a + 25\) , \( -316 a^{3} + 1348 a^{2} - 1083 a - 584\bigr] \) ${y}^2={x}^{3}+\left(-a^{3}+2a^{2}+2a\right){x}^{2}+\left(80a^{3}-225a^{2}-8a+25\right){x}-316a^{3}+1348a^{2}-1083a-584$
256.1-j2 256.1-j 4.4.2624.1 \( 2^{8} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $35.20912159$ 1.546520898 \( 427641453408640 a^{3} + 331260963910720 a^{2} - 363800343820288 a - 154126073580480 \) \( \bigl[0\) , \( a^{3} - 2 a^{2} - 2 a\) , \( 0\) , \( 80 a^{3} - 225 a^{2} - 8 a + 25\) , \( 316 a^{3} - 1348 a^{2} + 1083 a + 584\bigr] \) ${y}^2={x}^{3}+\left(a^{3}-2a^{2}-2a\right){x}^{2}+\left(80a^{3}-225a^{2}-8a+25\right){x}+316a^{3}-1348a^{2}+1083a+584$
256.1-n3 256.1-n 4.4.2624.1 \( 2^{8} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $461.7232551$ 2.253408053 \( 427641453408640 a^{3} + 331260963910720 a^{2} - 363800343820288 a - 154126073580480 \) \( \bigl[0\) , \( a^{3} - 2 a^{2} - 3 a + 2\) , \( 0\) , \( -60 a^{3} + 139 a^{2} + 142 a - 198\) , \( 318 a^{3} - 756 a^{2} - 701 a + 998\bigr] \) ${y}^2={x}^{3}+\left(a^{3}-2a^{2}-3a+2\right){x}^{2}+\left(-60a^{3}+139a^{2}+142a-198\right){x}+318a^{3}-756a^{2}-701a+998$
289.3-a3 289.3-a 4.4.2624.1 \( 17^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $34.15786525$ 3.000691301 \( 427641453408640 a^{3} + 331260963910720 a^{2} - 363800343820288 a - 154126073580480 \) \( \bigl[a^{3} - 2 a^{2} - 2 a + 1\) , \( -a^{3} + 2 a^{2} + 3 a\) , \( a^{2} - 2 a\) , \( -36 a^{3} + 56 a^{2} + 140 a - 130\) , \( 169 a^{3} - 364 a^{2} - 668 a + 690\bigr] \) ${y}^2+\left(a^{3}-2a^{2}-2a+1\right){x}{y}+\left(a^{2}-2a\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+3a\right){x}^{2}+\left(-36a^{3}+56a^{2}+140a-130\right){x}+169a^{3}-364a^{2}-668a+690$
289.4-a1 289.4-a 4.4.2624.1 \( 17^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $34.15786525$ 3.000691301 \( 427641453408640 a^{3} + 331260963910720 a^{2} - 363800343820288 a - 154126073580480 \) \( \bigl[a^{2} - a - 1\) , \( a^{2} - 2 a - 1\) , \( a^{3} - a^{2} - 4 a + 1\) , \( -26 a^{3} - 19 a^{2} + 12 a - 14\) , \( 195 a^{3} + 231 a^{2} - 46 a - 73\bigr] \) ${y}^2+\left(a^{2}-a-1\right){x}{y}+\left(a^{3}-a^{2}-4a+1\right){y}={x}^{3}+\left(a^{2}-2a-1\right){x}^{2}+\left(-26a^{3}-19a^{2}+12a-14\right){x}+195a^{3}+231a^{2}-46a-73$
625.2-a1 625.2-a 4.4.2624.1 \( 5^{4} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $10.71427532$ 0.941224884 \( 427641453408640 a^{3} + 331260963910720 a^{2} - 363800343820288 a - 154126073580480 \) \( \bigl[a^{2} - a - 1\) , \( -a^{2} + 3 a\) , \( a + 1\) , \( -11 a^{3} + 69 a^{2} - 51 a - 190\) , \( -667 a^{3} + 1058 a^{2} + 2194 a - 115\bigr] \) ${y}^2+\left(a^{2}-a-1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+3a\right){x}^{2}+\left(-11a^{3}+69a^{2}-51a-190\right){x}-667a^{3}+1058a^{2}+2194a-115$
625.3-a1 625.3-a 4.4.2624.1 \( 5^{4} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $10.71427532$ 0.941224884 \( 427641453408640 a^{3} + 331260963910720 a^{2} - 363800343820288 a - 154126073580480 \) \( \bigl[a^{2} - a - 1\) , \( -a^{3} + 2 a^{2} + 2 a\) , \( a^{2} - 2 a\) , \( 339 a^{3} - 418 a^{2} - 1326 a - 410\) , \( -10370 a^{3} + 12291 a^{2} + 41049 a + 12711\bigr] \) ${y}^2+\left(a^{2}-a-1\right){x}{y}+\left(a^{2}-2a\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+2a\right){x}^{2}+\left(339a^{3}-418a^{2}-1326a-410\right){x}-10370a^{3}+12291a^{2}+41049a+12711$
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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.