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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
1.1-a1 1.1-a 6.6.434581.1 \( 1 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.014802157$ 0.641303 \( 14273264587780952609125805373809022 a^{5} - 33978664183724880412077066535252082 a^{4} - 44161420314998729136586656312921749 a^{3} + 88173325697661842578861191186611639 a^{2} + 23535955393860563533538162020788064 a - 37503869415369575938251635322944654 \) \( \bigl[3 a^{5} - 7 a^{4} - 8 a^{3} + 15 a^{2} + a - 3\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 2 a + 2\) , \( 2 a^{5} - 5 a^{4} - 5 a^{3} + 12 a^{2} - 3\) , \( -2015 a^{5} + 2317 a^{4} + 10491 a^{3} - 2078 a^{2} - 11628 a - 4340\) , \( -87669 a^{5} + 112368 a^{4} + 435832 a^{3} - 134018 a^{2} - 464939 a - 144427\bigr] \) ${y}^2+\left(3a^{5}-7a^{4}-8a^{3}+15a^{2}+a-3\right){x}{y}+\left(2a^{5}-5a^{4}-5a^{3}+12a^{2}-3\right){y}={x}^{3}+\left(a^{4}-2a^{3}-3a^{2}+2a+2\right){x}^{2}+\left(-2015a^{5}+2317a^{4}+10491a^{3}-2078a^{2}-11628a-4340\right){x}-87669a^{5}+112368a^{4}+435832a^{3}-134018a^{2}-464939a-144427$
1.1-a2 1.1-a 6.6.434581.1 \( 1 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.014802157$ 0.641303 \( -299441694155033880148130654153024 a^{5} - 187917845986491657242090310571049 a^{4} + 704001225414123443403572247320027 a^{3} + 352597497846354900118604631201756 a^{2} - 271295440361411180696560081353475 a - 113961855027594415883614627224113 \) \( \bigl[2 a^{5} - 4 a^{4} - 6 a^{3} + 7 a^{2} + a - 1\) , \( a^{5} - 4 a^{4} + 11 a^{2} - 2 a - 3\) , \( 2 a^{5} - 4 a^{4} - 6 a^{3} + 7 a^{2} + 2 a\) , \( 670 a^{5} - 2194 a^{4} + 16 a^{3} + 3065 a^{2} - 90 a - 1279\) , \( 20194 a^{5} - 68427 a^{4} + 14638 a^{3} + 73555 a^{2} - 10467 a - 21619\bigr] \) ${y}^2+\left(2a^{5}-4a^{4}-6a^{3}+7a^{2}+a-1\right){x}{y}+\left(2a^{5}-4a^{4}-6a^{3}+7a^{2}+2a\right){y}={x}^{3}+\left(a^{5}-4a^{4}+11a^{2}-2a-3\right){x}^{2}+\left(670a^{5}-2194a^{4}+16a^{3}+3065a^{2}-90a-1279\right){x}+20194a^{5}-68427a^{4}+14638a^{3}+73555a^{2}-10467a-21619$
1.1-a3 1.1-a 6.6.434581.1 \( 1 \) 0 $\Z/13\Z$ $\mathrm{SU}(2)$ $1$ $71447.18768$ 0.641303 \( 7824861 a^{5} - 5363852 a^{4} - 38334375 a^{3} - 11300754 a^{2} + 16416844 a + 5946574 \) \( \bigl[3 a^{5} - 7 a^{4} - 8 a^{3} + 15 a^{2} + a - 4\) , \( a^{5} - 3 a^{4} - 2 a^{3} + 8 a^{2} - 3\) , \( a^{5} - 3 a^{4} - 2 a^{3} + 8 a^{2} - 2\) , \( -3 a^{4} + 4 a^{3} + 12 a^{2} - 3 a - 4\) , \( 10 a^{5} - 28 a^{4} - 19 a^{3} + 67 a^{2} - 8 a - 15\bigr] \) ${y}^2+\left(3a^{5}-7a^{4}-8a^{3}+15a^{2}+a-4\right){x}{y}+\left(a^{5}-3a^{4}-2a^{3}+8a^{2}-2\right){y}={x}^{3}+\left(a^{5}-3a^{4}-2a^{3}+8a^{2}-3\right){x}^{2}+\left(-3a^{4}+4a^{3}+12a^{2}-3a-4\right){x}+10a^{5}-28a^{4}-19a^{3}+67a^{2}-8a-15$
1.1-a4 1.1-a 6.6.434581.1 \( 1 \) 0 $\Z/13\Z$ $\mathrm{SU}(2)$ $1$ $71447.18768$ 0.641303 \( -23419364 a^{5} + 64630767 a^{4} + 44556569 a^{3} - 150905488 a^{2} + 21033374 a + 30775655 \) \( \bigl[2 a^{5} - 4 a^{4} - 7 a^{3} + 8 a^{2} + 4 a - 1\) , \( a^{5} - 3 a^{4} - 2 a^{3} + 8 a^{2} - 4\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 3 a + 1\) , \( -3 a^{5} + 4 a^{4} + 15 a^{3} - 6 a^{2} - 17 a - 3\) , \( 3 a^{5} - 4 a^{4} - 15 a^{3} + 5 a^{2} + 16 a + 4\bigr] \) ${y}^2+\left(2a^{5}-4a^{4}-7a^{3}+8a^{2}+4a-1\right){x}{y}+\left(a^{4}-2a^{3}-3a^{2}+3a+1\right){y}={x}^{3}+\left(a^{5}-3a^{4}-2a^{3}+8a^{2}-4\right){x}^{2}+\left(-3a^{5}+4a^{4}+15a^{3}-6a^{2}-17a-3\right){x}+3a^{5}-4a^{4}-15a^{3}+5a^{2}+16a+4$
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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.