Elliptic curves over $\Q$ of conductor 3185

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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
3185.a1	3185g1	3185.a	3185g	$1$	$1$	\( 5 \cdot 7^{2} \cdot 13 \)	\( - 5^{11} \cdot 7^{4} \cdot 13^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$20$	$2$	$0$	$0.098347377$	$1$		$10$	$29040$	$1.700691$	$-688691336801860161/8251953125$	$1.03647$	$6.05703$	$[1, -1, 1, -246357, 47126706]$	\(y^2+xy+y=x^3-x^2-246357x+47126706\)	20.2.0.a.1	$[(416, 3854)]$
3185.b1	3185b1	3185.b	3185b	$1$	$1$	\( 5 \cdot 7^{2} \cdot 13 \)	\( - 5^{2} \cdot 7^{2} \cdot 13 \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$52$	$2$	$0$	$0.319670521$	$1$		$14$	$240$	$-0.514276$	$-2401/325$	$0.91119$	$2.12425$	$[1, 0, 0, -1, 6]$	\(y^2+xy=x^3-x+6\)	52.2.0.a.1	$[(1, 2), (-1, 3)]$
3185.c1	3185a3	3185.c	3185a	$4$	$4$	\( 5 \cdot 7^{2} \cdot 13 \)	\( 5 \cdot 7^{14} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.18	2B	$7280$	$192$	$3$	$1$	$1$		$0$	$6144$	$1.374084$	$6903498885921/374712065$	$1.05880$	$5.11250$	$[1, -1, 1, -19438, 997812]$	\(y^2+xy+y=x^3-x^2-19438x+997812\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.o.1, 16.24.0-8.o.1.2, 28.12.0-4.c.1.1, $\ldots$	$[ ]$
3185.c2	3185a2	3185.c	3185a	$4$	$4$	\( 5 \cdot 7^{2} \cdot 13 \)	\( 5^{2} \cdot 7^{10} \cdot 13^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.34	2Cs	$3640$	$192$	$3$	$1$	$1$		$2$	$3072$	$1.027510$	$40743095121/10144225$	$1.04116$	$4.47621$	$[1, -1, 1, -3513, -59608]$	\(y^2+xy+y=x^3-x^2-3513x-59608\)	2.6.0.a.1, 4.12.0.a.1, 8.24.0-4.a.1.2, 28.24.0-4.a.1.1, 56.48.0-56.j.1.4, $\ldots$	$[ ]$
3185.c3	3185a1	3185.c	3185a	$4$	$4$	\( 5 \cdot 7^{2} \cdot 13 \)	\( 5 \cdot 7^{8} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.18	2B	$7280$	$192$	$3$	$1$	$1$		$1$	$1536$	$0.680937$	$32798729601/3185$	$0.88277$	$4.44932$	$[1, -1, 1, -3268, -71074]$	\(y^2+xy+y=x^3-x^2-3268x-71074\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.o.1, 16.24.0-8.o.1.2, 28.12.0-4.c.1.2, $\ldots$	$[ ]$
3185.c4	3185a4	3185.c	3185a	$4$	$4$	\( 5 \cdot 7^{2} \cdot 13 \)	\( - 5^{4} \cdot 7^{8} \cdot 13^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.75	2B	$7280$	$192$	$3$	$1$	$1$		$0$	$6144$	$1.374084$	$575722725759/874680625$	$0.94006$	$4.86475$	$[1, -1, 1, 8492, -386144]$	\(y^2+xy+y=x^3-x^2+8492x-386144\)	2.3.0.a.1, 4.12.0.d.1, 8.24.0-4.d.1.4, 28.24.0-4.d.1.1, 56.48.0-56.x.1.2, $\ldots$	$[ ]$
3185.d1	3185f1	3185.d	3185f	$1$	$1$	\( 5 \cdot 7^{2} \cdot 13 \)	\( - 5^{2} \cdot 7^{8} \cdot 13 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$52$	$2$	$0$	$0.787654773$	$1$		$4$	$1680$	$0.458680$	$-2401/325$	$0.91119$	$3.57170$	$[1, 1, 1, -50, -2108]$	\(y^2+xy+y=x^3+x^2-50x-2108\)	52.2.0.a.1	$[(20, 63)]$
3185.e1	3185i1	3185.e	3185i	$2$	$2$	\( 5 \cdot 7^{2} \cdot 13 \)	\( 5 \cdot 7^{6} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.3	2B	$3640$	$48$	$0$	$1$	$1$		$1$	$576$	$0.011340$	$117649/65$	$0.95681$	$2.89491$	$[1, 1, 1, -50, -50]$	\(y^2+xy+y=x^3+x^2-50x-50\)	2.3.0.a.1, 4.6.0.b.1, 56.12.0-4.b.1.2, 130.6.0.?, 260.24.0.?, $\ldots$	$[ ]$
3185.e2	3185i2	3185.e	3185i	$2$	$2$	\( 5 \cdot 7^{2} \cdot 13 \)	\( - 5^{2} \cdot 7^{6} \cdot 13^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.5	2B	$3640$	$48$	$0$	$1$	$1$		$0$	$1152$	$0.357913$	$6967871/4225$	$0.89914$	$3.40089$	$[1, 1, 1, 195, -148]$	\(y^2+xy+y=x^3+x^2+195x-148\)	2.3.0.a.1, 4.6.0.a.1, 56.12.0-4.a.1.1, 260.12.0.?, 520.24.0.?, $\ldots$	$[ ]$
3185.f1	3185c1	3185.f	3185c	$1$	$1$	\( 5 \cdot 7^{2} \cdot 13 \)	\( - 5^{11} \cdot 7^{10} \cdot 13^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$20$	$2$	$0$	$1$	$25$	$5$	$0$	$203280$	$2.673645$	$-688691336801860161/8251953125$	$1.03647$	$7.50448$	$[1, -1, 1, -12071478, -16140317294]$	\(y^2+xy+y=x^3-x^2-12071478x-16140317294\)	20.2.0.a.1	$[ ]$
3185.g1	3185d1	3185.g	3185d	$1$	$1$	\( 5 \cdot 7^{2} \cdot 13 \)	\( - 5^{3} \cdot 7^{2} \cdot 13^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$20$	$2$	$0$	$0.838911260$	$1$		$2$	$720$	$-0.166339$	$251559/21125$	$0.89820$	$2.64038$	$[1, -1, 0, 5, -50]$	\(y^2+xy=x^3-x^2+5x-50\)	20.2.0.a.1	$[(6, 10)]$
3185.h1	3185h3	3185.h	3185h	$4$	$4$	\( 5 \cdot 7^{2} \cdot 13 \)	\( 5^{3} \cdot 7^{7} \cdot 13^{4} \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$3640$	$48$	$0$	$1$	$1$		$2$	$9216$	$1.638031$	$11264882429818809/24990875$	$0.98096$	$6.02959$	$[1, -1, 0, -228839, 42192198]$	\(y^2+xy=x^3-x^2-228839x+42192198\)	2.3.0.a.1, 4.12.0-4.c.1.1, 140.24.0.?, 520.24.0.?, 728.24.0.?, $\ldots$	$[ ]$
3185.h2	3185h2	3185.h	3185h	$4$	$4$	\( 5 \cdot 7^{2} \cdot 13 \)	\( 5^{6} \cdot 7^{8} \cdot 13^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$1820$	$48$	$0$	$1$	$1$		$2$	$4608$	$1.291458$	$2844576388809/129390625$	$0.96596$	$5.00259$	$[1, -1, 0, -14464, 646323]$	\(y^2+xy=x^3-x^2-14464x+646323\)	2.6.0.a.1, 4.12.0-2.a.1.1, 140.24.0.?, 260.24.0.?, 364.24.0.?, $\ldots$	$[ ]$
3185.h3	3185h1	3185.h	3185h	$4$	$4$	\( 5 \cdot 7^{2} \cdot 13 \)	\( 5^{3} \cdot 7^{10} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.6	2B	$3640$	$48$	$0$	$1$	$1$		$1$	$2304$	$0.944884$	$13980103929/3901625$	$0.88564$	$4.34360$	$[1, -1, 0, -2459, -33160]$	\(y^2+xy=x^3-x^2-2459x-33160\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 130.6.0.?, 140.12.0.?, $\ldots$	$[ ]$
3185.h4	3185h4	3185.h	3185h	$4$	$4$	\( 5 \cdot 7^{2} \cdot 13 \)	\( - 5^{12} \cdot 7^{7} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$3640$	$48$	$0$	$1$	$1$		$0$	$9216$	$1.638031$	$451394172711/22216796875$	$1.03650$	$5.32375$	$[1, -1, 0, 7831, 2443300]$	\(y^2+xy=x^3-x^2+7831x+2443300\)	2.3.0.a.1, 4.12.0-4.c.1.2, 182.6.0.?, 280.24.0.?, 364.24.0.?, $\ldots$	$[ ]$
3185.i1	3185e1	3185.i	3185e	$1$	$1$	\( 5 \cdot 7^{2} \cdot 13 \)	\( - 5^{3} \cdot 7^{8} \cdot 13^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$20$	$2$	$0$	$1$	$1$		$0$	$5040$	$0.806616$	$251559/21125$	$0.89820$	$4.08783$	$[1, -1, 0, 236, 16673]$	\(y^2+xy=x^3-x^2+236x+16673\)	20.2.0.a.1	$[ ]$

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