Elliptic curves over $\Q$ of conductor 6760

Results (20 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
6760.a1	6760e1	6760.a	6760e	$1$	$1$	\( 2^{3} \cdot 5 \cdot 13^{2} \)	\( 2^{4} \cdot 5^{8} \cdot 13^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2$	4.4.0.2	2Cn	$52$	$12$	$0$	$1.585314648$	$1$		$4$	$99840$	$1.837515$	$44302512384/390625$	$0.99127$	$5.42099$	$[0, 0, 0, -173563, 27618487]$	\(y^2=x^3-173563x+27618487\)	2.2.0.a.1, 4.4.0-2.a.1.1, 26.6.0.a.1, 52.12.0-26.a.1.3	$[(211, 625)]$
6760.b1	6760m1	6760.b	6760m	$1$	$1$	\( 2^{3} \cdot 5 \cdot 13^{2} \)	\( 2^{4} \cdot 5^{8} \cdot 13^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2$	2.2.0.1	2Cn	$52$	$12$	$0$	$0.082995496$	$1$		$10$	$7680$	$0.555040$	$44302512384/390625$	$0.99127$	$3.67588$	$[0, 0, 0, -1027, 12571]$	\(y^2=x^3-1027x+12571\)	2.2.0.a.1, 26.6.0.a.1, 52.12.0-26.a.1.1	$[(-3, 125)]$
6760.c1	6760h1	6760.c	6760h	$1$	$1$	\( 2^{3} \cdot 5 \cdot 13^{2} \)	\( 2^{4} \cdot 5^{2} \cdot 13^{4} \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2$	2.2.0.1	2Cn	$260$	$12$	$0$	$0.178903348$	$1$		$16$	$1152$	$0.043772$	$43264/25$	$1.09219$	$2.68829$	$[0, -1, 0, -56, 25]$	\(y^2=x^3-x^2-56x+25\)	2.2.0.a.1, 20.4.0-2.a.1.1, 26.6.0.a.1, 260.12.0.?	$[(-4, 13), (-3/2, 65/2)]$
6760.d1	6760b1	6760.d	6760b	$1$	$1$	\( 2^{3} \cdot 5 \cdot 13^{2} \)	\( 2^{4} \cdot 5^{2} \cdot 13^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2$	2.2.0.1	2Cn	$260$	$12$	$0$	$0.251968725$	$1$		$4$	$14976$	$1.379604$	$3037375744/25$	$1.18153$	$5.11709$	$[0, -1, 0, -71036, 7310965]$	\(y^2=x^3-x^2-71036x+7310965\)	2.2.0.a.1, 20.4.0-2.a.1.1, 26.6.0.a.1, 260.12.0.?	$[(113, 845)]$
6760.e1	6760a1	6760.e	6760a	$1$	$1$	\( 2^{3} \cdot 5 \cdot 13^{2} \)	\( 2^{4} \cdot 5^{2} \cdot 13^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2$	2.2.0.1	2Cn	$260$	$12$	$0$	$0.230291196$	$1$		$6$	$768$	$-0.209718$	$7311616/25$	$0.98811$	$2.68829$	$[0, -1, 0, -56, 181]$	\(y^2=x^3-x^2-56x+181\)	2.2.0.a.1, 26.6.0.a.1, 260.12.0.?	$[(6, 5)]$
6760.f1	6760k1	6760.f	6760k	$1$	$1$	\( 2^{3} \cdot 5 \cdot 13^{2} \)	\( 2^{4} \cdot 5^{2} \cdot 13^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2$	2.2.0.1	2Cn	$260$	$12$	$0$	$0.290637684$	$1$		$6$	$9984$	$1.072758$	$7311616/25$	$0.98811$	$4.43340$	$[0, -1, 0, -9520, 359657]$	\(y^2=x^3-x^2-9520x+359657\)	2.2.0.a.1, 20.4.0-2.a.1.1, 26.6.0.a.1, 260.12.0.?	$[(-56, 845)]$
6760.g1	6760j1	6760.g	6760j	$1$	$1$	\( 2^{3} \cdot 5 \cdot 13^{2} \)	\( 2^{4} \cdot 5^{2} \cdot 13^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2$	2.2.0.1	2Cn	$260$	$12$	$0$	$0.310116679$	$1$		$6$	$1152$	$0.097129$	$3037375744/25$	$1.18153$	$3.37198$	$[0, -1, 0, -420, 3457]$	\(y^2=x^3-x^2-420x+3457\)	2.2.0.a.1, 26.6.0.a.1, 260.12.0.?	$[(12, 1)]$
6760.h1	6760f1	6760.h	6760f	$1$	$1$	\( 2^{3} \cdot 5 \cdot 13^{2} \)	\( 2^{4} \cdot 5^{2} \cdot 13^{10} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2$	2.2.0.1	2Cn	$260$	$12$	$0$	$1$	$1$		$0$	$14976$	$1.326246$	$43264/25$	$1.09219$	$4.43340$	$[0, -1, 0, -9520, 16925]$	\(y^2=x^3-x^2-9520x+16925\)	2.2.0.a.1, 26.6.0.a.1, 260.12.0.?	$[]$
6760.i1	6760g3	6760.i	6760g	$4$	$4$	\( 2^{3} \cdot 5 \cdot 13^{2} \)	\( 2^{10} \cdot 5 \cdot 13^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.15	2B	$1040$	$192$	$3$	$1$	$4$	$2$	$1$	$9216$	$1.080261$	$132304644/5$	$1.13632$	$4.65164$	$[0, 0, 0, -18083, -935922]$	\(y^2=x^3-18083x-935922\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.o.1, 10.6.0.a.1, 16.24.0.i.1, $\ldots$	$[]$
6760.i2	6760g2	6760.i	6760g	$4$	$4$	\( 2^{3} \cdot 5 \cdot 13^{2} \)	\( 2^{8} \cdot 5^{2} \cdot 13^{6} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.35	2Cs	$520$	$192$	$3$	$1$	$1$		$3$	$4608$	$0.733687$	$148176/25$	$1.09175$	$3.72399$	$[0, 0, 0, -1183, -13182]$	\(y^2=x^3-1183x-13182\)	2.6.0.a.1, 4.12.0.a.1, 8.24.0.g.1, 20.24.0.b.1, 40.96.3.bk.1, $\ldots$	$[]$
6760.i3	6760g1	6760.i	6760g	$4$	$4$	\( 2^{3} \cdot 5 \cdot 13^{2} \)	\( 2^{4} \cdot 5 \cdot 13^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.15	2B	$1040$	$192$	$3$	$1$	$1$		$1$	$2304$	$0.387114$	$55296/5$	$1.01898$	$3.29782$	$[0, 0, 0, -338, 2197]$	\(y^2=x^3-338x+2197\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.o.1, 10.6.0.a.1, 16.24.0.i.1, $\ldots$	$[]$
6760.i4	6760g4	6760.i	6760g	$4$	$4$	\( 2^{3} \cdot 5 \cdot 13^{2} \)	\( - 2^{10} \cdot 5^{4} \cdot 13^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.24.0.2	2B	$1040$	$192$	$3$	$1$	$1$		$1$	$9216$	$1.080261$	$237276/625$	$1.04671$	$4.07829$	$[0, 0, 0, 2197, -74698]$	\(y^2=x^3+2197x-74698\)	2.3.0.a.1, 4.24.0.c.1, 40.48.1.dk.1, 52.48.0-4.c.1.1, 80.96.3.?, $\ldots$	$[]$
6760.j1	6760i3	6760.j	6760i	$4$	$4$	\( 2^{3} \cdot 5 \cdot 13^{2} \)	\( 2^{11} \cdot 5^{4} \cdot 13^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$520$	$48$	$0$	$3.919059190$	$1$		$3$	$21504$	$1.595594$	$9636491538/8125$	$0.94289$	$5.21650$	$[0, 0, 0, -95147, -11288186]$	\(y^2=x^3-95147x-11288186\)	2.3.0.a.1, 4.12.0-4.c.1.2, 40.24.0-40.y.1.7, 104.24.0.?, 520.48.0.?	$[(3978, 250120)]$
6760.j2	6760i2	6760.j	6760i	$4$	$4$	\( 2^{3} \cdot 5 \cdot 13^{2} \)	\( 2^{10} \cdot 5^{2} \cdot 13^{8} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$520$	$48$	$0$	$7.838118380$	$1$		$3$	$10752$	$1.249022$	$8586756/4225$	$0.96662$	$4.34152$	$[0, 0, 0, -7267, -92274]$	\(y^2=x^3-7267x-92274\)	2.6.0.a.1, 4.12.0-2.a.1.1, 40.24.0-40.b.1.5, 104.24.0.?, 260.24.0.?, $\ldots$	$[(-1694/5, 37296/5)]$
6760.j3	6760i1	6760.j	6760i	$4$	$4$	\( 2^{3} \cdot 5 \cdot 13^{2} \)	\( 2^{8} \cdot 5 \cdot 13^{7} \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$520$	$48$	$0$	$3.919059190$	$1$		$5$	$5376$	$0.902448$	$5256144/65$	$0.85145$	$4.12867$	$[0, 0, 0, -3887, 92274]$	\(y^2=x^3-3887x+92274\)	2.3.0.a.1, 4.12.0-4.c.1.1, 40.24.0-40.y.1.15, 104.24.0.?, 130.6.0.?, $\ldots$	$[(-61, 320)]$
6760.j4	6760i4	6760.j	6760i	$4$	$4$	\( 2^{3} \cdot 5 \cdot 13^{2} \)	\( - 2^{11} \cdot 5 \cdot 13^{10} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.6	2B	$520$	$48$	$0$	$15.67623676$	$1$		$1$	$21504$	$1.595594$	$208974222/142805$	$0.95226$	$4.78207$	$[0, 0, 0, 26533, -707434]$	\(y^2=x^3+26533x-707434\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 40.24.0-40.s.1.7, 104.24.0.?, $\ldots$	$[(1905914/185, 6147954288/185)]$
6760.k1	6760c1	6760.k	6760c	$2$	$2$	\( 2^{3} \cdot 5 \cdot 13^{2} \)	\( 2^{8} \cdot 5 \cdot 13^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.3	2B	$520$	$48$	$0$	$8.419848493$	$1$		$1$	$5376$	$0.888139$	$3631696/65$	$0.75998$	$4.08674$	$[0, -1, 0, -3436, -75180]$	\(y^2=x^3-x^2-3436x-75180\)	2.3.0.a.1, 4.6.0.b.1, 40.12.0-4.b.1.1, 104.12.0.?, 130.6.0.?, $\ldots$	$[(-6159/13, 38676/13)]$
6760.k2	6760c2	6760.k	6760c	$2$	$2$	\( 2^{3} \cdot 5 \cdot 13^{2} \)	\( - 2^{10} \cdot 5^{2} \cdot 13^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.5	2B	$520$	$48$	$0$	$4.209924246$	$1$		$1$	$10752$	$1.234713$	$-4/4225$	$1.09431$	$4.32312$	$[0, -1, 0, -56, -219844]$	\(y^2=x^3-x^2-56x-219844\)	2.3.0.a.1, 4.6.0.a.1, 20.12.0-4.a.1.2, 52.12.0-4.a.1.1, 260.24.0.?, $\ldots$	$[(2122/3, 96668/3)]$
6760.l1	6760d1	6760.l	6760d	$1$	$1$	\( 2^{3} \cdot 5 \cdot 13^{2} \)	\( - 2^{11} \cdot 5 \cdot 13^{4} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$40$	$2$	$0$	$2.496215047$	$1$		$2$	$2880$	$0.305920$	$-338/5$	$0.82681$	$3.06017$	$[0, -1, 0, -56, -820]$	\(y^2=x^3-x^2-56x-820\)	40.2.0.a.1	$[(61, 468)]$
6760.m1	6760l1	6760.m	6760l	$1$	$1$	\( 2^{3} \cdot 5 \cdot 13^{2} \)	\( - 2^{11} \cdot 5 \cdot 13^{10} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$40$	$2$	$0$	$27.58671101$	$1$		$0$	$37440$	$1.588394$	$-338/5$	$0.82681$	$4.80527$	$[0, -1, 0, -9520, -1839540]$	\(y^2=x^3-x^2-9520x-1839540\)	40.2.0.a.1	$[(956640860457/449, 935671376935889742/449)]$