Elliptic curves over 4.4.6125.1 of conductor 71.3

Results (8 matches)

 

Label	Class	Class size	Class degree	Base field	Field degree	Field signature	Conductor	Conductor norm	Discriminant norm	Root analytic conductor	Bad primes	Rank	Torsion	CM	CM	Sato-Tate	$\Q$-curve	Base change	Semistable	Potentially good	Nonmax $\ell$	mod-$\ell$ images	$Ш_{\textrm{an}}$	Tamagawa	Regulator	Period	Leading coeff	j-invariant	Weierstrass coefficients	Weierstrass equation
71.3-a1	71.3-a	$1$	$1$	4.4.6125.1	$4$	$[4, 0]$	71.3	\( 71 \)	\( 71 \)	$11.91513$	$(5a^3+7a^2-28a-24)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓				$1$	\( 1 \)	$0.880646448$	$82.10556773$	3.695567517	\( \frac{14499836867}{71} a^{3} - \frac{55487831122}{71} a^{2} + \frac{26243447485}{71} a + \frac{56492779821}{71} \)	\( \bigl[2 a^{3} + 3 a^{2} - 11 a - 12\) , \( -a^{3} - a^{2} + 6 a + 4\) , \( a^{3} + a^{2} - 5 a - 3\) , \( -a^{2} - 2 a + 1\) , \( -2 a^{3} - 4 a^{2} + 8 a + 7\bigr] \)	${y}^2+\left(2a^{3}+3a^{2}-11a-12\right){x}{y}+\left(a^{3}+a^{2}-5a-3\right){y}={x}^{3}+\left(-a^{3}-a^{2}+6a+4\right){x}^{2}+\left(-a^{2}-2a+1\right){x}-2a^{3}-4a^{2}+8a+7$
71.3-b1	71.3-b	$1$	$1$	4.4.6125.1	$4$	$[4, 0]$	71.3	\( 71 \)	\( 71^{3} \)	$11.91513$	$(5a^3+7a^2-28a-24)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓				$1$	\( 3 \)	$0.278940957$	$74.56956939$	3.189349568	\( \frac{171505521527}{357911} a^{3} + \frac{230646737948}{357911} a^{2} - \frac{982547272228}{357911} a - \frac{796389209025}{357911} \)	\( \bigl[1\) , \( -a^{2} - a + 5\) , \( a^{3} + 2 a^{2} - 5 a - 7\) , \( a^{3} - 8 a^{2} + 5 a + 17\) , \( 3 a^{3} - 24 a^{2} + 24 a + 30\bigr] \)	${y}^2+{x}{y}+\left(a^{3}+2a^{2}-5a-7\right){y}={x}^{3}+\left(-a^{2}-a+5\right){x}^{2}+\left(a^{3}-8a^{2}+5a+17\right){x}+3a^{3}-24a^{2}+24a+30$
71.3-c1	71.3-c	$1$	$1$	4.4.6125.1	$4$	$[4, 0]$	71.3	\( 71 \)	\( 71^{2} \)	$11.91513$	$(5a^3+7a^2-28a-24)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓				$1$	\( 2 \)	$1.350817753$	$24.25015266$	3.348483607	\( \frac{13630521344}{5041} a^{3} + \frac{59020271616}{5041} a^{2} - \frac{66721566720}{5041} a - \frac{352246767616}{5041} \)	\( \bigl[0\) , \( a^{2} - 5\) , \( 1\) , \( a^{3} - 9 a\) , \( 610 a^{3} + 832 a^{2} - 3525 a - 2843\bigr] \)	${y}^2+{y}={x}^{3}+\left(a^{2}-5\right){x}^{2}+\left(a^{3}-9a\right){x}+610a^{3}+832a^{2}-3525a-2843$
71.3-d1	71.3-d	$1$	$1$	4.4.6125.1	$4$	$[4, 0]$	71.3	\( 71 \)	\( 71 \)	$11.91513$	$(5a^3+7a^2-28a-24)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓				$1$	\( 1 \)	$0.077631787$	$821.9823011$	3.261437020	\( \frac{5520752072949}{71} a^{3} + \frac{7531137764446}{71} a^{2} - \frac{31882024190872}{71} a - \frac{25687141194430}{71} \)	\( \bigl[2 a^{3} + 3 a^{2} - 12 a - 12\) , \( a^{2} + a - 4\) , \( a^{3} + 2 a^{2} - 6 a - 7\) , \( 10 a^{3} + 12 a^{2} - 62 a - 46\) , \( 35 a^{3} + 41 a^{2} - 221 a - 165\bigr] \)	${y}^2+\left(2a^{3}+3a^{2}-12a-12\right){x}{y}+\left(a^{3}+2a^{2}-6a-7\right){y}={x}^{3}+\left(a^{2}+a-4\right){x}^{2}+\left(10a^{3}+12a^{2}-62a-46\right){x}+35a^{3}+41a^{2}-221a-165$
71.3-e1	71.3-e	$1$	$1$	4.4.6125.1	$4$	$[4, 0]$	71.3	\( 71 \)	\( 71^{3} \)	$11.91513$	$(5a^3+7a^2-28a-24)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓				$1$	\( 3 \)	$0.012087042$	$1375.479221$	2.549190457	\( \frac{171505521527}{357911} a^{3} + \frac{230646737948}{357911} a^{2} - \frac{982547272228}{357911} a - \frac{796389209025}{357911} \)	\( \bigl[2 a^{3} + 3 a^{2} - 12 a - 11\) , \( -1\) , \( a^{3} + a^{2} - 5 a - 4\) , \( 12 a^{3} + 15 a^{2} - 77 a - 64\) , \( 24 a^{3} + 28 a^{2} - 152 a - 116\bigr] \)	${y}^2+\left(2a^{3}+3a^{2}-12a-11\right){x}{y}+\left(a^{3}+a^{2}-5a-4\right){y}={x}^{3}-{x}^{2}+\left(12a^{3}+15a^{2}-77a-64\right){x}+24a^{3}+28a^{2}-152a-116$
71.3-f1	71.3-f	$1$	$1$	4.4.6125.1	$4$	$[4, 0]$	71.3	\( 71 \)	\( 71 \)	$11.91513$	$(5a^3+7a^2-28a-24)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓				$1$	\( 1 \)	$0.316585081$	$168.4566808$	2.725747549	\( \frac{5520752072949}{71} a^{3} + \frac{7531137764446}{71} a^{2} - \frac{31882024190872}{71} a - \frac{25687141194430}{71} \)	\( \bigl[2 a^{3} + 3 a^{2} - 11 a - 11\) , \( 2 a^{3} + 3 a^{2} - 13 a - 13\) , \( a\) , \( 2 a^{3} + 4 a^{2} - 11 a - 8\) , \( 5 a^{3} + 7 a^{2} - 28 a - 33\bigr] \)	${y}^2+\left(2a^{3}+3a^{2}-11a-11\right){x}{y}+a{y}={x}^{3}+\left(2a^{3}+3a^{2}-13a-13\right){x}^{2}+\left(2a^{3}+4a^{2}-11a-8\right){x}+5a^{3}+7a^{2}-28a-33$
71.3-g1	71.3-g	$1$	$1$	4.4.6125.1	$4$	$[4, 0]$	71.3	\( 71 \)	\( 71 \)	$11.91513$	$(5a^3+7a^2-28a-24)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓				$1$	\( 1 \)	$0.021483562$	$2332.543676$	2.561197211	\( \frac{14499836867}{71} a^{3} - \frac{55487831122}{71} a^{2} + \frac{26243447485}{71} a + \frac{56492779821}{71} \)	\( \bigl[a\) , \( a^{2} - a - 3\) , \( 2 a^{3} + 3 a^{2} - 11 a - 11\) , \( 4 a^{2} - 5 a - 17\) , \( -18 a^{2} - 16 a + 129\bigr] \)	${y}^2+a{x}{y}+\left(2a^{3}+3a^{2}-11a-11\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(4a^{2}-5a-17\right){x}-18a^{2}-16a+129$
71.3-h1	71.3-h	$1$	$1$	4.4.6125.1	$4$	$[4, 0]$	71.3	\( 71 \)	\( 71^{2} \)	$11.91513$	$(5a^3+7a^2-28a-24)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓				$1$	\( 2 \)	$0.021909019$	$1115.169704$	2.497473303	\( \frac{13630521344}{5041} a^{3} + \frac{59020271616}{5041} a^{2} - \frac{66721566720}{5041} a - \frac{352246767616}{5041} \)	\( \bigl[0\) , \( -a^{3} - a^{2} + 7 a + 5\) , \( a\) , \( 3 a^{2} + 2 a - 19\) , \( 2 a^{3} - 3 a^{2} - 15 a + 25\bigr] \)	${y}^2+a{y}={x}^{3}+\left(-a^{3}-a^{2}+7a+5\right){x}^{2}+\left(3a^{2}+2a-19\right){x}+2a^{3}-3a^{2}-15a+25$

 

  *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.