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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 (5 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
61.1-a1 61.1-a 5.5.24217.1 \( 61 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $229.4499904$ 1.47444261 \( \frac{27040797}{61} a^{4} + \frac{28132769}{61} a^{3} - \frac{119092723}{61} a^{2} - \frac{136691009}{61} a - \frac{33340058}{61} \) \( \bigl[a\) , \( -5 a^{4} + 2 a^{3} + 24 a^{2} - 5 a - 11\) , \( 2 a^{4} - a^{3} - 9 a^{2} + 4 a + 3\) , \( 7 a^{4} - a^{3} - 34 a^{2} - 2 a + 16\) , \( -2 a^{4} + 3 a^{3} + 11 a^{2} - 12 a - 15\bigr] \) ${y}^2+a{x}{y}+\left(2a^{4}-a^{3}-9a^{2}+4a+3\right){y}={x}^{3}+\left(-5a^{4}+2a^{3}+24a^{2}-5a-11\right){x}^{2}+\left(7a^{4}-a^{3}-34a^{2}-2a+16\right){x}-2a^{4}+3a^{3}+11a^{2}-12a-15$
61.1-b1 61.1-b 5.5.24217.1 \( 61 \) 0 $\Z/5\Z$ $\mathrm{SU}(2)$ $1$ $4658.517381$ 1.19742285 \( \frac{266240}{61} a^{4} - \frac{512000}{61} a^{3} - \frac{385024}{61} a^{2} + \frac{397312}{61} a + \frac{188416}{61} \) \( \bigl[0\) , \( -2 a^{4} + 2 a^{3} + 9 a^{2} - 7 a - 5\) , \( a + 1\) , \( -3 a^{4} + 13 a^{2} + 3 a\) , \( a^{3} - 5 a - 2\bigr] \) ${y}^2+\left(a+1\right){y}={x}^{3}+\left(-2a^{4}+2a^{3}+9a^{2}-7a-5\right){x}^{2}+\left(-3a^{4}+13a^{2}+3a\right){x}+a^{3}-5a-2$
61.1-b2 61.1-b 5.5.24217.1 \( 61 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $1.490725562$ 1.19742285 \( \frac{814621975367829286400000}{844596301} a^{4} - \frac{588819537749162764800000}{844596301} a^{3} - \frac{3647503475859398758400000}{844596301} a^{2} + \frac{1821841937334970774327296}{844596301} a + \frac{1127015091876445279977472}{844596301} \) \( \bigl[0\) , \( a^{4} - a^{3} - 4 a^{2} + 4 a\) , \( 3 a^{4} - a^{3} - 14 a^{2} + 3 a + 6\) , \( -172 a^{4} + 72 a^{3} + 808 a^{2} - 126 a - 461\) , \( -1112 a^{4} + 465 a^{3} + 5243 a^{2} - 885 a - 2921\bigr] \) ${y}^2+\left(3a^{4}-a^{3}-14a^{2}+3a+6\right){y}={x}^{3}+\left(a^{4}-a^{3}-4a^{2}+4a\right){x}^{2}+\left(-172a^{4}+72a^{3}+808a^{2}-126a-461\right){x}-1112a^{4}+465a^{3}+5243a^{2}-885a-2921$
61.1-c1 61.1-c 5.5.24217.1 \( 61 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $139.6494849$ 0.897385747 \( -\frac{14149720466856}{61} a^{4} + \frac{5230874058759}{61} a^{3} + \frac{68814850746192}{61} a^{2} - \frac{11289779910942}{61} a - \frac{38275551231064}{61} \) \( \bigl[2 a^{4} - 9 a^{2} + 3\) , \( -a^{3} + 3 a\) , \( 2 a^{4} - a^{3} - 9 a^{2} + 4 a + 4\) , \( a^{4} - 2 a^{3} - 6 a^{2} + 7 a + 2\) , \( -2 a^{4} + 4 a^{3} + 7 a^{2} - 13 a - 6\bigr] \) ${y}^2+\left(2a^{4}-9a^{2}+3\right){x}{y}+\left(2a^{4}-a^{3}-9a^{2}+4a+4\right){y}={x}^{3}+\left(-a^{3}+3a\right){x}^{2}+\left(a^{4}-2a^{3}-6a^{2}+7a+2\right){x}-2a^{4}+4a^{3}+7a^{2}-13a-6$
61.1-d1 61.1-d 5.5.24217.1 \( 61 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.002786894$ $17875.95611$ 1.60066176 \( -\frac{31227904}{61} a^{4} + \frac{11927552}{61} a^{3} + \frac{152190976}{61} a^{2} - \frac{26697728}{61} a - \frac{86028288}{61} \) \( \bigl[0\) , \( -2 a^{4} + a^{3} + 10 a^{2} - 2 a - 5\) , \( a^{4} - 4 a^{2} + a + 1\) , \( 4 a^{4} - a^{3} - 18 a^{2} + 2 a + 6\) , \( -2 a^{4} + 8 a^{2} - 2\bigr] \) ${y}^2+\left(a^{4}-4a^{2}+a+1\right){y}={x}^{3}+\left(-2a^{4}+a^{3}+10a^{2}-2a-5\right){x}^{2}+\left(4a^{4}-a^{3}-18a^{2}+2a+6\right){x}-2a^{4}+8a^{2}-2$
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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.