Elliptic curves over $\Q$ of conductor 42

Results (6 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
42.a1	42a4	42.a	42a	$6$	$8$	\( 2 \cdot 3 \cdot 7 \)	\( 2^{2} \cdot 3^{2} \cdot 7 \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	16.96.0.103	2B	$112$	$192$	$1$	$1$	$1$		$2$	$16$	$0.189101$	$268498407453697/252$	$1.05727$	$8.88893$	$[1, 1, 1, -1344, 18405]$	\(y^2+xy+y=x^3+x^2-1344x+18405\)	2.3.0.a.1, 4.12.0-4.c.1.1, 8.48.0-8.bb.2.4, 16.96.0-16.z.2.3, 28.24.0-28.h.1.2, $\ldots$	$[]$
42.a2	42a5	42.a	42a	$6$	$8$	\( 2 \cdot 3 \cdot 7 \)	\( 2 \cdot 3^{4} \cdot 7^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.96.0.164	2B	$112$	$192$	$1$	$1$	$1$		$0$	$32$	$0.535675$	$84448510979617/933897762$	$1.05309$	$8.57945$	$[1, 1, 1, -914, -10915]$	\(y^2+xy+y=x^3+x^2-914x-10915\)	2.3.0.a.1, 4.12.0-4.c.1.2, 8.96.0-8.p.1.4, 112.192.1.?	$[]$
42.a3	42a3	42.a	42a	$6$	$8$	\( 2 \cdot 3 \cdot 7 \)	\( 2^{2} \cdot 3^{8} \cdot 7^{4} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.96.0.50	2Cs	$56$	$192$	$1$	$1$	$1$		$2$	$16$	$0.189101$	$124475734657/63011844$	$1.06499$	$6.83511$	$[1, 1, 1, -104, 101]$	\(y^2+xy+y=x^3+x^2-104x+101\)	2.6.0.a.1, 4.24.0-4.b.1.1, 8.96.0-8.f.1.1, 56.192.1-56.bp.2.4	$[]$
42.a4	42a2	42.a	42a	$6$	$8$	\( 2 \cdot 3 \cdot 7 \)	\( 2^{4} \cdot 3^{4} \cdot 7^{2} \)	$0$	$\Z/2\Z\oplus\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.96.0.37	2Cs	$56$	$192$	$1$	$1$	$1$		$6$	$8$	$-0.157472$	$65597103937/63504$	$1.01692$	$6.66372$	$[1, 1, 1, -84, 261]$	\(y^2+xy+y=x^3+x^2-84x+261\)	2.6.0.a.1, 4.24.0-4.b.1.3, 8.96.0-8.i.1.2, 28.48.0-28.c.1.1, 56.192.1-56.by.1.7	$[]$
42.a5	42a1	42.a	42a	$6$	$8$	\( 2 \cdot 3 \cdot 7 \)	\( - 2^{8} \cdot 3^{2} \cdot 7 \)	$0$	$\Z/8\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	16.96.0.98	2B	$112$	$192$	$1$	$1$	$1$		$7$	$4$	$-0.504046$	$-7189057/16128$	$0.98224$	$4.64796$	$[1, 1, 1, -4, 5]$	\(y^2+xy+y=x^3+x^2-4x+5\)	2.3.0.a.1, 4.12.0-4.c.1.1, 8.48.0-8.bb.1.1, 14.6.0.b.1, 16.96.0-16.z.1.2, $\ldots$	$[]$
42.a6	42a6	42.a	42a	$6$	$8$	\( 2 \cdot 3 \cdot 7 \)	\( - 2 \cdot 3^{16} \cdot 7^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	16.96.0.137	2B	$112$	$192$	$1$	$1$	$1$		$0$	$32$	$0.535675$	$6359387729183/4218578658$	$1.08314$	$7.88752$	$[1, 1, 1, 386, 1277]$	\(y^2+xy+y=x^3+x^2+386x+1277\)	2.3.0.a.1, 4.12.0-4.c.1.2, 8.48.0-8.k.1.6, 16.96.0-16.e.1.6, 56.96.0-56.bc.1.4, $\ldots$	$[]$