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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 (4 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
7.1-a1 7.1-a 6.6.1387029.1 \( 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2571.915476$ 1.09190 \( \frac{8057034}{2401} a^{4} - \frac{16114068}{2401} a^{3} - \frac{23703961}{2401} a^{2} + \frac{4537285}{343} a + \frac{5064062}{2401} \) \( \bigl[a^{5} - 2 a^{4} - 3 a^{3} + 5 a^{2} + a - 1\) , \( a^{4} - 2 a^{3} - 2 a^{2} + 3 a - 1\) , \( a + 1\) , \( -a^{5} + 7 a^{4} - 4 a^{3} - 10 a^{2} + 4 a\) , \( 2 a^{5} + 3 a^{4} - 13 a^{3} - a^{2} + 7 a - 2\bigr] \) ${y}^2+\left(a^{5}-2a^{4}-3a^{3}+5a^{2}+a-1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{4}-2a^{3}-2a^{2}+3a-1\right){x}^{2}+\left(-a^{5}+7a^{4}-4a^{3}-10a^{2}+4a\right){x}+2a^{5}+3a^{4}-13a^{3}-a^{2}+7a-2$
7.1-a2 7.1-a 6.6.1387029.1 \( 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $642.9788691$ 1.09190 \( -\frac{150188255755733}{5764801} a^{4} + \frac{300376511511466}{5764801} a^{3} + \frac{407543256494144}{5764801} a^{2} - \frac{79675930321411}{823543} a + \frac{116748450527349}{5764801} \) \( \bigl[a^{5} - 2 a^{4} - 3 a^{3} + 5 a^{2} + a - 1\) , \( a^{4} - 2 a^{3} - 2 a^{2} + 3 a - 1\) , \( a + 1\) , \( -6 a^{5} + 27 a^{4} - 4 a^{3} - 85 a^{2} + 79 a - 15\) , \( -33 a^{5} + 130 a^{4} - 26 a^{3} - 309 a^{2} + 258 a - 48\bigr] \) ${y}^2+\left(a^{5}-2a^{4}-3a^{3}+5a^{2}+a-1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{4}-2a^{3}-2a^{2}+3a-1\right){x}^{2}+\left(-6a^{5}+27a^{4}-4a^{3}-85a^{2}+79a-15\right){x}-33a^{5}+130a^{4}-26a^{3}-309a^{2}+258a-48$
7.1-b1 7.1-b 6.6.1387029.1 \( 7 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.012253140$ $21273.16609$ 2.65594 \( \frac{8057034}{2401} a^{4} - \frac{16114068}{2401} a^{3} - \frac{23703961}{2401} a^{2} + \frac{4537285}{343} a + \frac{5064062}{2401} \) \( \bigl[-2 a^{5} + 5 a^{4} + 7 a^{3} - 14 a^{2} - 6 a + 5\) , \( 3 a^{5} - 7 a^{4} - 9 a^{3} + 18 a^{2} + 5 a - 3\) , \( -a^{5} + 3 a^{4} + 3 a^{3} - 9 a^{2} - 3 a + 4\) , \( 22 a^{5} - 27 a^{4} - 71 a^{3} + 73 a^{2} + 41 a - 20\) , \( 101 a^{5} - 61 a^{4} - 321 a^{3} + 139 a^{2} + 154 a - 49\bigr] \) ${y}^2+\left(-2a^{5}+5a^{4}+7a^{3}-14a^{2}-6a+5\right){x}{y}+\left(-a^{5}+3a^{4}+3a^{3}-9a^{2}-3a+4\right){y}={x}^{3}+\left(3a^{5}-7a^{4}-9a^{3}+18a^{2}+5a-3\right){x}^{2}+\left(22a^{5}-27a^{4}-71a^{3}+73a^{2}+41a-20\right){x}+101a^{5}-61a^{4}-321a^{3}+139a^{2}+154a-49$
7.1-b2 7.1-b 6.6.1387029.1 \( 7 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.024506281$ $5318.291523$ 2.65594 \( -\frac{150188255755733}{5764801} a^{4} + \frac{300376511511466}{5764801} a^{3} + \frac{407543256494144}{5764801} a^{2} - \frac{79675930321411}{823543} a + \frac{116748450527349}{5764801} \) \( \bigl[-2 a^{5} + 5 a^{4} + 7 a^{3} - 14 a^{2} - 6 a + 5\) , \( 3 a^{5} - 7 a^{4} - 9 a^{3} + 18 a^{2} + 5 a - 3\) , \( -a^{5} + 3 a^{4} + 3 a^{3} - 9 a^{2} - 3 a + 4\) , \( -8 a^{5} - 12 a^{4} + 29 a^{3} + 28 a^{2} - 4 a\) , \( -246 a^{5} + 98 a^{4} + 780 a^{3} - 187 a^{2} - 339 a + 85\bigr] \) ${y}^2+\left(-2a^{5}+5a^{4}+7a^{3}-14a^{2}-6a+5\right){x}{y}+\left(-a^{5}+3a^{4}+3a^{3}-9a^{2}-3a+4\right){y}={x}^{3}+\left(3a^{5}-7a^{4}-9a^{3}+18a^{2}+5a-3\right){x}^{2}+\left(-8a^{5}-12a^{4}+29a^{3}+28a^{2}-4a\right){x}-246a^{5}+98a^{4}+780a^{3}-187a^{2}-339a+85$
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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.