Elliptic curves over $\Q$ of conductor 30

Results (8 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
30.a1	30a7	30.a	30a	$8$	$12$	\( 2 \cdot 3 \cdot 5 \)	\( 2^{3} \cdot 3^{4} \cdot 5^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2, 3$	8.12.0.7, 3.8.0.2	2B, 3B.1.2	$120$	$384$	$5$	$1$	$1$		$0$	$24$	$0.564166$	$16778985534208729/81000$	$1.08181$	$10.98404$	$[1, 0, 1, -5334, -150368]$	\(y^2+xy+y=x^3-5334x-150368\)	2.3.0.a.1, 3.8.0-3.a.1.1, 4.6.0.c.1, 6.24.0-6.a.1.2, 8.12.0-4.c.1.3, $\ldots$	$[]$
30.a2	30a8	30.a	30a	$8$	$12$	\( 2 \cdot 3 \cdot 5 \)	\( 2^{3} \cdot 3 \cdot 5^{12} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2, 3$	8.12.0.8, 3.8.0.2	2B, 3B.1.2	$120$	$384$	$5$	$1$	$1$		$0$	$24$	$0.564166$	$10316097499609/5859375000$	$1.13600$	$8.81005$	$[1, 0, 1, -454, -544]$	\(y^2+xy+y=x^3-454x-544\)	2.3.0.a.1, 3.8.0-3.a.1.1, 4.6.0.c.1, 6.24.0-6.a.1.2, 8.12.0-4.c.1.4, $\ldots$	$[]$
30.a3	30a6	30.a	30a	$8$	$12$	\( 2 \cdot 3 \cdot 5 \)	\( 2^{6} \cdot 3^{2} \cdot 5^{6} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2, 3$	8.12.0.1, 3.8.0.2	2Cs, 3B.1.2	$120$	$384$	$5$	$1$	$1$		$2$	$12$	$0.217592$	$4102915888729/9000000$	$1.05221$	$8.53897$	$[1, 0, 1, -334, -2368]$	\(y^2+xy+y=x^3-334x-2368\)	2.6.0.a.1, 3.8.0-3.a.1.1, 6.48.0-6.a.1.2, 8.12.0-2.a.1.1, 12.96.0-12.a.1.15, $\ldots$	$[]$
30.a4	30a5	30.a	30a	$8$	$12$	\( 2 \cdot 3 \cdot 5 \)	\( 2 \cdot 3^{3} \cdot 5^{4} \)	$0$	$\Z/6\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2, 3$	8.12.0.8, 3.8.0.1	2B, 3B.1.1	$120$	$384$	$5$	$1$	$1$		$4$	$8$	$0.014860$	$2656166199049/33750$	$1.05017$	$8.41113$	$[1, 0, 1, -289, 1862]$	\(y^2+xy+y=x^3-289x+1862\)	2.3.0.a.1, 3.8.0-3.a.1.2, 4.6.0.c.1, 6.24.0-6.a.1.4, 8.12.0-4.c.1.4, $\ldots$	$[]$
30.a5	30a4	30.a	30a	$8$	$12$	\( 2 \cdot 3 \cdot 5 \)	\( 2 \cdot 3^{12} \cdot 5 \)	$0$	$\Z/6\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2, 3$	8.12.0.7, 3.8.0.1	2B, 3B.1.1	$120$	$384$	$5$	$1$	$1$		$4$	$8$	$0.014860$	$35578826569/5314410$	$1.03393$	$7.14308$	$[1, 0, 1, -69, -194]$	\(y^2+xy+y=x^3-69x-194\)	2.3.0.a.1, 3.8.0-3.a.1.2, 4.6.0.c.1, 6.24.0-6.a.1.4, 8.12.0-4.c.1.3, $\ldots$	$[]$
30.a6	30a2	30.a	30a	$8$	$12$	\( 2 \cdot 3 \cdot 5 \)	\( 2^{2} \cdot 3^{6} \cdot 5^{2} \)	$0$	$\Z/2\Z\oplus\Z/6\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2, 3$	8.12.0.1, 3.8.0.1	2Cs, 3B.1.1	$120$	$384$	$5$	$1$	$1$		$10$	$4$	$-0.331714$	$702595369/72900$	$1.00457$	$5.98915$	$[1, 0, 1, -19, 26]$	\(y^2+xy+y=x^3-19x+26\)	2.6.0.a.1, 3.8.0-3.a.1.2, 6.48.0-6.a.1.1, 8.12.0-2.a.1.1, 12.96.0-12.a.2.13, $\ldots$	$[]$
30.a7	30a3	30.a	30a	$8$	$12$	\( 2 \cdot 3 \cdot 5 \)	\( - 2^{12} \cdot 3 \cdot 5^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2, 3$	8.12.0.12, 3.8.0.2	2B, 3B.1.2	$120$	$384$	$5$	$1$	$1$		$1$	$6$	$-0.128981$	$-273359449/1536000$	$1.04920$	$6.40875$	$[1, 0, 1, -14, -64]$	\(y^2+xy+y=x^3-14x-64\)	2.3.0.a.1, 3.8.0-3.a.1.1, 4.6.0.c.1, 6.24.0-6.a.1.2, 8.12.0-4.c.1.2, $\ldots$	$[]$
30.a8	30a1	30.a	30a	$8$	$12$	\( 2 \cdot 3 \cdot 5 \)	\( - 2^{4} \cdot 3^{3} \cdot 5 \)	$0$	$\Z/6\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2, 3$	8.12.0.12, 3.8.0.1	2B, 3B.1.1	$120$	$384$	$5$	$1$	$1$		$5$	$2$	$-0.678288$	$357911/2160$	$0.99689$	$4.41955$	$[1, 0, 1, 1, 2]$	\(y^2+xy+y=x^3+x+2\)	2.3.0.a.1, 3.8.0-3.a.1.2, 4.6.0.c.1, 6.24.0-6.a.1.4, 8.12.0-4.c.1.2, $\ldots$	$[]$