Elliptic curves over $\Q$ of conductor 4025

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 (14 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
4025.a1	4025d1	4025.a	4025d	$1$	$1$	\( 5^{2} \cdot 7 \cdot 23 \)	\( - 5^{7} \cdot 7^{3} \cdot 23^{2} \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$0.064723565$	$1$		$34$	$8640$	$0.633570$	$-242970624/907235$	$[0, 0, 1, -325, 6156]$	\(y^2+y=x^3-325x+6156\)
4025.b1	4025e1	4025.b	4025e	$1$	$1$	\( 5^{2} \cdot 7 \cdot 23 \)	\( - 5^{11} \cdot 7^{11} \cdot 23^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$0.168464283$	$1$		$8$	$137280$	$2.465557$	$1346216501445963776/3268768272021875$	$[0, 1, 1, 575092, 300275344]$	\(y^2+y=x^3+x^2+575092x+300275344\)
4025.c1	4025g1	4025.c	4025g	$1$	$1$	\( 5^{2} \cdot 7 \cdot 23 \)	\( - 5^{3} \cdot 7 \cdot 23^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$0.210484398$	$1$		$6$	$544$	$0.119613$	$-35806478336/3703$	$[0, -1, 1, -343, 2563]$	\(y^2+y=x^3-x^2-343x+2563\)
4025.d1	4025f1	4025.d	4025f	$1$	$1$	\( 5^{2} \cdot 7 \cdot 23 \)	\( - 5^{9} \cdot 7 \cdot 23^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$0.657925041$	$1$		$4$	$2720$	$0.924332$	$-35806478336/3703$	$[0, 1, 1, -8583, 303244]$	\(y^2+y=x^3+x^2-8583x+303244\)
4025.e1	4025a3	4025.e	4025a	$4$	$4$	\( 5^{2} \cdot 7 \cdot 23 \)	\( 5^{6} \cdot 7^{4} \cdot 23 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1$	$1$		$0$	$2560$	$0.699085$	$209267191953/55223$	$[1, -1, 0, -3092, 66941]$	\(y^2+xy=x^3-x^2-3092x+66941\)
4025.e2	4025a2	4025.e	4025a	$4$	$4$	\( 5^{2} \cdot 7 \cdot 23 \)	\( 5^{6} \cdot 7^{2} \cdot 23^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$1$	$1$		$2$	$1280$	$0.352511$	$72511713/25921$	$[1, -1, 0, -217, 816]$	\(y^2+xy=x^3-x^2-217x+816\)
4025.e3	4025a1	4025.e	4025a	$4$	$4$	\( 5^{2} \cdot 7 \cdot 23 \)	\( 5^{6} \cdot 7 \cdot 23 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1$	$1$		$1$	$640$	$0.005938$	$5545233/161$	$[1, -1, 0, -92, -309]$	\(y^2+xy=x^3-x^2-92x-309\)
4025.e4	4025a4	4025.e	4025a	$4$	$4$	\( 5^{2} \cdot 7 \cdot 23 \)	\( - 5^{6} \cdot 7 \cdot 23^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1$	$1$		$0$	$2560$	$0.699085$	$2014698447/1958887$	$[1, -1, 0, 658, 5191]$	\(y^2+xy=x^3-x^2+658x+5191\)
4025.f1	4025c4	4025.f	4025c	$4$	$4$	\( 5^{2} \cdot 7 \cdot 23 \)	\( 5^{14} \cdot 7^{3} \cdot 23 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1$	$1$		$0$	$34560$	$1.976631$	$8244966675515989329/3081640625$	$[1, -1, 0, -1052192, 415686091]$	\(y^2+xy=x^3-x^2-1052192x+415686091\)
4025.f2	4025c3	4025.f	4025c	$4$	$4$	\( 5^{2} \cdot 7 \cdot 23 \)	\( 5^{8} \cdot 7^{12} \cdot 23 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1$	$1$		$0$	$34560$	$1.976631$	$18577831198352049/7958740140575$	$[1, -1, 0, -137942, -10015159]$	\(y^2+xy=x^3-x^2-137942x-10015159\)
4025.f3	4025c2	4025.f	4025c	$4$	$4$	\( 5^{2} \cdot 7 \cdot 23 \)	\( 5^{10} \cdot 7^{6} \cdot 23^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$1$	$1$		$2$	$17280$	$1.630058$	$2041085246738049/38897700625$	$[1, -1, 0, -66067, 6444216]$	\(y^2+xy=x^3-x^2-66067x+6444216\)
4025.f4	4025c1	4025.f	4025c	$4$	$4$	\( 5^{2} \cdot 7 \cdot 23 \)	\( - 5^{8} \cdot 7^{3} \cdot 23^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1$	$1$		$1$	$8640$	$1.283484$	$1367631/2399636575$	$[1, -1, 0, 58, 294591]$	\(y^2+xy=x^3-x^2+58x+294591\)
4025.g1	4025b1	4025.g	4025b	$2$	$2$	\( 5^{2} \cdot 7 \cdot 23 \)	\( 5^{8} \cdot 7^{3} \cdot 23 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$3456$	$0.782702$	$476196576129/197225$	$[1, -1, 0, -4067, -98784]$	\(y^2+xy=x^3-x^2-4067x-98784\)
4025.g2	4025b2	4025.g	4025b	$2$	$2$	\( 5^{2} \cdot 7 \cdot 23 \)	\( - 5^{7} \cdot 7^{6} \cdot 23^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$0$	$6912$	$1.129276$	$-288673724529/311181605$	$[1, -1, 0, -3442, -130659]$	\(y^2+xy=x^3-x^2-3442x-130659\)