Elliptic curves over $\Q$ of conductor 405

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	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
405.a1	405f1	405.a	405f	$1$	$1$	\( 3^{4} \cdot 5 \)	\( 3^{4} \cdot 5 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$10$	$2$	$0$	$0.272277013$	$1$		$6$	$24$	$-0.772497$	$36864/5$	$0.77778$	$2.48330$	$[0, 0, 1, -3, -2]$	\(y^2+y=x^3-3x-2\)	10.2.0.a.1	$[(-1, 0)]$
405.b1	405d2	405.b	405d	$2$	$7$	\( 3^{4} \cdot 5 \)	\( - 3^{10} \cdot 5^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$7$	7.8.0.1	7B	$1260$	$96$	$2$	$0.043718464$	$1$		$12$	$252$	$0.701672$	$-15590912409/78125$	$1.00703$	$5.74040$	$[1, -1, 1, -2027, 35776]$	\(y^2+xy+y=x^3-x^2-2027x+35776\)	7.8.0.a.1, 20.2.0.a.1, 21.16.0-7.a.1.1, 63.48.0-63.b.1.3, 140.16.0.?, $\ldots$	$[(76, 524)]$
405.b2	405d1	405.b	405d	$2$	$7$	\( 3^{4} \cdot 5 \)	\( - 3^{10} \cdot 5 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$7$	7.8.0.1	7B	$1260$	$96$	$2$	$0.306029253$	$1$		$8$	$36$	$-0.271284$	$-9/5$	$1.00480$	$3.33972$	$[1, -1, 1, -2, -26]$	\(y^2+xy+y=x^3-x^2-2x-26\)	7.8.0.a.1, 20.2.0.a.1, 21.16.0-7.a.1.2, 63.48.0-63.b.2.2, 140.16.0.?, $\ldots$	$[(4, 2)]$
405.c1	405b2	405.c	405b	$2$	$3$	\( 3^{4} \cdot 5 \)	\( 3^{10} \cdot 5^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.2	3B.1.2	$30$	$16$	$0$	$0.355512380$	$1$		$6$	$72$	$0.074670$	$2359296/125$	$1.10725$	$4.27390$	$[0, 0, 1, -108, -412]$	\(y^2+y=x^3-108x-412\)	3.8.0-3.a.1.1, 10.2.0.a.1, 30.16.0-30.a.1.1	$[(-6, 4)]$
405.c2	405b1	405.c	405b	$2$	$3$	\( 3^{4} \cdot 5 \)	\( 3^{6} \cdot 5 \)	$1$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.1	3B.1.1	$30$	$16$	$0$	$1.066537142$	$1$		$6$	$24$	$-0.474636$	$884736/5$	$1.04562$	$3.37860$	$[0, 0, 1, -18, 29]$	\(y^2+y=x^3-18x+29\)	3.8.0-3.a.1.2, 10.2.0.a.1, 30.16.0-30.a.1.4	$[(1, 3)]$
405.d1	405a2	405.d	405a	$2$	$3$	\( 3^{4} \cdot 5 \)	\( 3^{12} \cdot 5 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.2	3B.1.2	$30$	$16$	$0$	$1$	$1$		$0$	$72$	$0.074670$	$884736/5$	$1.04562$	$4.47650$	$[0, 0, 1, -162, -790]$	\(y^2+y=x^3-162x-790\)	3.8.0-3.a.1.1, 10.2.0.a.1, 30.16.0-30.a.1.1	$[]$
405.d2	405a1	405.d	405a	$2$	$3$	\( 3^{4} \cdot 5 \)	\( 3^{4} \cdot 5^{3} \)	$0$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.1	3B.1.1	$30$	$16$	$0$	$1$	$1$		$2$	$24$	$-0.474636$	$2359296/125$	$1.10725$	$3.17600$	$[0, 0, 1, -12, 15]$	\(y^2+y=x^3-12x+15\)	3.8.0-3.a.1.2, 10.2.0.a.1, 30.16.0-30.a.1.4	$[]$
405.e1	405c2	405.e	405c	$2$	$7$	\( 3^{4} \cdot 5 \)	\( - 3^{4} \cdot 5^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$7$	7.16.0.2	7B.2.3	$1260$	$96$	$2$	$3.274202297$	$1$		$2$	$84$	$0.152365$	$-15590912409/78125$	$1.00703$	$4.64250$	$[1, -1, 0, -225, -1250]$	\(y^2+xy=x^3-x^2-225x-1250\)	7.16.0-7.a.1.1, 20.2.0.a.1, 63.48.0-63.b.1.2, 140.32.0.?, 1260.96.2.?	$[(18, 8)]$
405.e2	405c1	405.e	405c	$2$	$7$	\( 3^{4} \cdot 5 \)	\( - 3^{4} \cdot 5 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$7$	7.16.0.1	7B.2.1	$1260$	$96$	$2$	$0.467743185$	$1$		$2$	$12$	$-0.820590$	$-9/5$	$1.00480$	$2.24182$	$[1, -1, 0, 0, 1]$	\(y^2+xy=x^3-x^2+1\)	7.16.0-7.a.1.2, 20.2.0.a.1, 63.48.0-63.b.2.3, 140.32.0.?, 1260.96.2.?	$[(0, 1)]$
405.f1	405e1	405.f	405e	$1$	$1$	\( 3^{4} \cdot 5 \)	\( 3^{10} \cdot 5 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$10$	$2$	$0$	$1$	$1$		$0$	$72$	$-0.223191$	$36864/5$	$0.77778$	$3.58120$	$[0, 0, 1, -27, 47]$	\(y^2+y=x^3-27x+47\)	10.2.0.a.1	$[]$