Elliptic curves over $\Q$ of conductor 114

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 (10 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
114.a1	114b1	114.a	114b	$2$	$2$	\( 2 \cdot 3 \cdot 19 \)	\( 2^{2} \cdot 3^{5} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.6.0.4	2B	$1$	$1$		$1$	$20$	$-0.180691$	$96386901625/18468$	$[1, 1, 0, -95, -399]$	\(y^2+xy=x^3+x^2-95x-399\)
114.a2	114b2	114.a	114b	$2$	$2$	\( 2 \cdot 3 \cdot 19 \)	\( - 2 \cdot 3^{10} \cdot 19^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.6.0.5	2B	$1$	$1$		$0$	$40$	$0.165883$	$-69173457625/42633378$	$[1, 1, 0, -85, -473]$	\(y^2+xy=x^3+x^2-85x-473\)
114.b1	114c3	114.b	114c	$4$	$4$	\( 2 \cdot 3 \cdot 19 \)	\( 2^{5} \cdot 3^{3} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.24.0.102	2B	$1$	$4$	$2$	$0$	$240$	$1.101439$	$74220219816682217473/16416$	$[1, 1, 1, -87552, -10007679]$	\(y^2+xy+y=x^3+x^2-87552x-10007679\)
114.b2	114c2	114.b	114c	$4$	$4$	\( 2 \cdot 3 \cdot 19 \)	\( 2^{10} \cdot 3^{6} \cdot 19^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.24.0.4	2Cs	$1$	$1$		$2$	$120$	$0.754866$	$18120364883707393/269485056$	$[1, 1, 1, -5472, -158079]$	\(y^2+xy+y=x^3+x^2-5472x-158079\)
114.b3	114c4	114.b	114c	$4$	$4$	\( 2 \cdot 3 \cdot 19 \)	\( - 2^{5} \cdot 3^{12} \cdot 19^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.24.0.59	2B	$1$	$1$		$0$	$240$	$1.101439$	$-16576888679672833/2216253521952$	$[1, 1, 1, -5312, -167551]$	\(y^2+xy+y=x^3+x^2-5312x-167551\)
114.b4	114c1	114.b	114c	$4$	$4$	\( 2 \cdot 3 \cdot 19 \)	\( 2^{20} \cdot 3^{3} \cdot 19 \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.24.0.53	2B	$1$	$1$		$3$	$60$	$0.408292$	$4824238966273/537919488$	$[1, 1, 1, -352, -2431]$	\(y^2+xy+y=x^3+x^2-352x-2431\)
114.c1	114a3	114.c	114a	$4$	$6$	\( 2 \cdot 3 \cdot 19 \)	\( 2^{2} \cdot 3 \cdot 19^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2, 3$	8.6.0.4, 3.8.0.2	2B, 3B.1.2	$1$	$1$		$1$	$36$	$0.105502$	$8671983378625/82308$	$[1, 0, 0, -428, -3444]$	\(y^2+xy=x^3-428x-3444\)
114.c2	114a4	114.c	114a	$4$	$6$	\( 2 \cdot 3 \cdot 19 \)	\( - 2 \cdot 3^{2} \cdot 19^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2, 3$	8.6.0.5, 3.8.0.2	2B, 3B.1.2	$1$	$1$		$0$	$72$	$0.452075$	$-8078253774625/846825858$	$[1, 0, 0, -418, -3610]$	\(y^2+xy=x^3-418x-3610\)
114.c3	114a1	114.c	114a	$4$	$6$	\( 2 \cdot 3 \cdot 19 \)	\( 2^{6} \cdot 3^{3} \cdot 19 \)	$0$	$\Z/6\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2, 3$	8.6.0.4, 3.8.0.1	2B, 3B.1.1	$1$	$1$		$5$	$12$	$-0.443804$	$57066625/32832$	$[1, 0, 0, -8, 0]$	\(y^2+xy=x^3-8x\)
114.c4	114a2	114.c	114a	$4$	$6$	\( 2 \cdot 3 \cdot 19 \)	\( - 2^{3} \cdot 3^{6} \cdot 19^{2} \)	$0$	$\Z/6\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2, 3$	8.6.0.5, 3.8.0.1	2B, 3B.1.1	$1$	$1$		$4$	$24$	$-0.097231$	$3616805375/2105352$	$[1, 0, 0, 32, 8]$	\(y^2+xy=x^3+32x+8\)