Elliptic curves over Q\Q of conductor 21

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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
21.a1	21a5	21.a	21a	$6$	$8$	$3 \cdot 7$	$3 \cdot 7^{2}$	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	16.48.0.48	2B	$336$	$192$	$1$	$1$	$1$		$0$	$4$	$0.074205$	$53297461115137/147$	$1.05087$	$10.38157$	$[1, 0, 0, -784, -8515]$	$y^2+xy=x^3-784x-8515$	2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.n.1.6, 12.24.0-12.h.1.1, 16.48.0-16.e.2.5, $\ldots$	$[]$
21.a2	21a2	21.a	21a	$6$	$8$	$3 \cdot 7$	$3^{2} \cdot 7^{4}$	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.48.0.34	2Cs	$168$	$192$	$1$	$1$	$1$		$2$	$2$	$-0.272368$	$13027640977/21609$	$1.08149$	$7.64992$	$[1, 0, 0, -49, -136]$	$y^2+xy=x^3-49x-136$	2.6.0.a.1, 4.24.0-4.b.1.1, 8.48.0-8.e.1.1, 12.48.0-12.c.1.3, 24.96.0-24.j.2.5, $\ldots$	$[]$
21.a3	21a3	21.a	21a	$6$	$8$	$3 \cdot 7$	$3^{8} \cdot 7$	$0$	$\Z/8\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.48.0.159	2B	$336$	$192$	$1$	$1$	$1$		$6$	$2$	$-0.272368$	$6570725617/45927$	$1.00160$	$7.42510$	$[1, 0, 0, -39, 90]$	$y^2+xy=x^3-39x+90$	2.3.0.a.1, 4.12.0-4.c.1.1, 8.48.0-8.bb.1.1, 28.24.0-28.h.1.2, 48.96.0-48.bf.1.3, $\ldots$	$[]$
21.a4	21a6	21.a	21a	$6$	$8$	$3 \cdot 7$	$- 3 \cdot 7^{8}$	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.48.0.177	2B	$336$	$192$	$1$	$1$	$1$		$0$	$4$	$0.074205$	$-4354703137/17294403$	$1.04266$	$7.96731$	$[1, 0, 0, -34, -217]$	$y^2+xy=x^3-34x-217$	2.3.0.a.1, 4.12.0-4.c.1.2, 6.6.0.a.1, 8.48.0-8.bb.2.3, 12.24.0-12.g.1.1, $\ldots$	$[]$
21.a5	21a1	21.a	21a	$6$	$8$	$3 \cdot 7$	$3^{4} \cdot 7^{2}$	$0$	$\Z/2\Z\oplus\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.48.0.24	2Cs	$168$	$192$	$1$	$1$	$1$		$6$	$1$	$-0.618942$	$7189057/3969$	$1.14862$	$5.18573$	$[1, 0, 0, -4, -1]$	$y^2+xy=x^3-4x-1$	2.6.0.a.1, 4.24.0-4.b.1.3, 8.48.0-8.e.2.2, 24.96.0-24.w.2.6, 28.48.0-28.c.1.1, $\ldots$	$[]$
21.a6	21a4	21.a	21a	$6$	$8$	$3 \cdot 7$	$- 3^{2} \cdot 7$	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	16.48.0.27	2B	$336$	$192$	$1$	$1$	$1$		$3$	$2$	$-0.965515$	$103823/63$	$0.97868$	$3.79384$	$[1, 0, 0, 1, 0]$	$y^2+xy=x^3+x$	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.n.1.2, 14.6.0.b.1, 16.48.0-16.e.1.2, $\ldots$	$[]$

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