Elliptic curves over $\Q$ of conductor 1342

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	Adelic level	Adelic index	Adelic genus	Regulator	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	$abc$ quality	Szpiro ratio	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
1342.a1	1342a1	1342.a	1342a	$1$	$1$	\( 2 \cdot 11 \cdot 61 \)	\( 2 \cdot 11^{3} \cdot 61 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$5368$	$2$	$0$	$1.155153717$	$1$		$4$	$144$	$-0.223773$	$5386984777/162382$	$0.83155$	$3.11129$	$[1, 0, 1, -37, -86]$	\(y^2+xy+y=x^3-37x-86\)	5368.2.0.?	$[(-4, 2)]$
1342.b1	1342c3	1342.b	1342c	$3$	$25$	\( 2 \cdot 11 \cdot 61 \)	\( 2 \cdot 11 \cdot 61 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓		$5$	25.120.0.3	5B.1.2	$134200$	$1200$	$37$	$1$	$25$	$5$	$0$	$80000$	$2.645401$	$178296503348692983836197044001/1342$	$1.04540$	$9.35213$	$[1, 1, 1, -117257250, -488766109679]$	\(y^2+xy+y=x^3+x^2-117257250x-488766109679\)	5.24.0-5.a.2.2, 25.120.0-25.a.2.2, 5368.2.0.?, 16775.600.12.?, 26840.48.1.?, $\ldots$	$[]$
1342.b2	1342c2	1342.b	1342c	$3$	$25$	\( 2 \cdot 11 \cdot 61 \)	\( 2^{5} \cdot 11^{5} \cdot 61^{5} \)	$0$	$\Z/5\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$5$	5.120.0.1	5Cs.1.1	$134200$	$1200$	$37$	$1$	$1$		$4$	$16000$	$1.840681$	$733441552889589371521/4352738523915232$	$1.02828$	$6.67104$	$[1, 1, 1, -187880, -31262199]$	\(y^2+xy+y=x^3+x^2-187880x-31262199\)	5.120.0-5.a.1.2, 5368.2.0.?, 16775.600.12.?, 26840.240.5.?, 134200.1200.37.?	$[]$
1342.b3	1342c1	1342.b	1342c	$3$	$25$	\( 2 \cdot 11 \cdot 61 \)	\( 2^{25} \cdot 11 \cdot 61 \)	$0$	$\Z/5\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$5$	25.120.0.1	5B.1.1	$134200$	$1200$	$37$	$1$	$1$		$4$	$3200$	$1.035963$	$300872095888141441/22515023872$	$1.04210$	$5.58816$	$[1, 1, 1, -13960, 629001]$	\(y^2+xy+y=x^3+x^2-13960x+629001\)	5.24.0-5.a.1.2, 25.120.0-25.a.1.2, 5368.2.0.?, 16775.600.12.?, 26840.48.1.?, $\ldots$	$[]$
1342.c1	1342b1	1342.c	1342b	$1$	$1$	\( 2 \cdot 11 \cdot 61 \)	\( 2^{11} \cdot 11 \cdot 61 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$5368$	$2$	$0$	$0.123350681$	$1$		$8$	$176$	$-0.132199$	$2433138625/1374208$	$0.88405$	$3.00093$	$[1, 1, 1, -28, -3]$	\(y^2+xy+y=x^3+x^2-28x-3\)	5368.2.0.?	$[(-3, 9)]$
1342.d1	1342d1	1342.d	1342d	$1$	$1$	\( 2 \cdot 11 \cdot 61 \)	\( 2 \cdot 11 \cdot 61 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$5368$	$2$	$0$	$1$	$1$		$0$	$128$	$-0.541275$	$350402625/1342$	$0.80690$	$2.73186$	$[1, -1, 1, -15, 25]$	\(y^2+xy+y=x^3-x^2-15x+25\)	5368.2.0.?	$[]$