Elliptic curves over $\Q$ of conductor 14

Conductor	j-invariant	Rank	Torsion	Complex multiplication
Bad$\ p$	Discriminant	Regulator	Analytic order of Ш	Galois image
Isogeny class size	Isogeny class degree	Cyclic isogeny degree	$p\ $div$\ $|Ш|	Nonmax$\ \ell$
Curves per isogeny class	Reduction	Integral points	Faltings height

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Results (6 matches)

 

Label	Cremona label	Class	Cremona class	Class size	Class degree	Conductor	Discriminant	Rank	Torsion	$\textrm{End}^0(E_{\overline\Q})$	CM	Sato-Tate	Semistable	Potentially good	Nonmax $\ell$	$\ell$-adic images	mod-$\ell$ images	Regulator	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	Weierstrass coefficients	Weierstrass equation
14.a1	14a5	14.a	14a	$6$	$18$	\( 2 \cdot 7 \)	\( 2^{9} \cdot 7^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2, 3$	8.6.0.6, 9.24.0.3	2B, 3B.1.2	$1$	$1$		$0$	$6$	$0.413101$	$2251439055699625/25088$	$[1, 0, 1, -2731, -55146]$	\(y^2+xy+y=x^3-2731x-55146\)
14.a2	14a3	14.a	14a	$6$	$18$	\( 2 \cdot 7 \)	\( - 2^{18} \cdot 7 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2, 3$	8.6.0.1, 9.24.0.3	2B, 3B.1.2	$1$	$1$		$1$	$3$	$0.066527$	$-548347731625/1835008$	$[1, 0, 1, -171, -874]$	\(y^2+xy+y=x^3-171x-874\)
14.a3	14a2	14.a	14a	$6$	$18$	\( 2 \cdot 7 \)	\( 2^{3} \cdot 7^{6} \)	$0$	$\Z/6\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2, 3$	8.6.0.6, 3.24.0.1	2B, 3Cs.1.1	$1$	$1$		$4$	$2$	$-0.136205$	$4956477625/941192$	$[1, 0, 1, -36, -70]$	\(y^2+xy+y=x^3-36x-70\)
14.a4	14a6	14.a	14a	$6$	$18$	\( 2 \cdot 7 \)	\( 2 \cdot 7^{2} \)	$0$	$\Z/6\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2, 3$	8.6.0.6, 9.24.0.1	2B, 3B.1.1	$1$	$1$		$4$	$6$	$-0.685512$	$128787625/98$	$[1, 0, 1, -11, 12]$	\(y^2+xy+y=x^3-11x+12\)
14.a5	14a4	14.a	14a	$6$	$18$	\( 2 \cdot 7 \)	\( - 2^{2} \cdot 7 \)	$0$	$\Z/6\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2, 3$	8.6.0.1, 9.24.0.1	2B, 3B.1.1	$1$	$1$		$5$	$3$	$-1.032085$	$-15625/28$	$[1, 0, 1, -1, 0]$	\(y^2+xy+y=x^3-x\)
14.a6	14a1	14.a	14a	$6$	$18$	\( 2 \cdot 7 \)	\( - 2^{6} \cdot 7^{3} \)	$0$	$\Z/6\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2, 3$	8.6.0.1, 3.24.0.1	2B, 3Cs.1.1	$1$	$1$		$5$	$1$	$-0.482779$	$9938375/21952$	$[1, 0, 1, 4, -6]$	\(y^2+xy+y=x^3+4x-6\)