Elliptic curve isogeny class with Cremona label 30a (LMFDB label 30.a)

• Label: 30a
• Number of curves: $8$
• Conductor: $30$
• CM: no
• Rank: $0$

Elliptic curves in class 30a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
30.a8	30a1	$[1, 0, 1, 1, 2]$	$357911/2160$	$-2160$	$[6]$	$2$	$-0.67829$	$\Gamma_0(N)$-optimal
30.a6	30a2	$[1, 0, 1, -19, 26]$	$702595369/72900$	$72900$	$[2, 6]$	$4$	$-0.33171$
30.a7	30a3	$[1, 0, 1, -14, -64]$	$-273359449/1536000$	$-1536000$	$[2]$	$6$	$-0.12898$
30.a5	30a4	$[1, 0, 1, -69, -194]$	$35578826569/5314410$	$5314410$	$[6]$	$8$	$0.014860$
30.a4	30a5	$[1, 0, 1, -289, 1862]$	$2656166199049/33750$	$33750$	$[6]$	$8$	$0.014860$
30.a3	30a6	$[1, 0, 1, -334, -2368]$	$4102915888729/9000000$	$9000000$	$[2, 2]$	$12$	$0.21759$
30.a1	30a7	$[1, 0, 1, -5334, -150368]$	$16778985534208729/81000$	$81000$	$[2]$	$24$	$0.56417$
30.a2	30a8	$[1, 0, 1, -454, -544]$	$10316097499609/5859375000$	$5859375000$	$[2]$	$24$	$0.56417$

Rank

The elliptic curves in class 30a have rank $0$.

Complex multiplication

The elliptic curves in class 30a do not have complex multiplication.

Modular form 30.2.a.a

Isogeny matrix

The $i,j$ entry is the smallest degree of a cyclic isogeny between the $i$-th and $j$-th curve in the isogeny class, in the Cremona numbering.

$\left(\begin{array}{rrrrrrrr} 1 & 2 & 3 & 4 & 4 & 6 & 12 & 12 \\ 2 & 1 & 6 & 2 & 2 & 3 & 6 & 6 \\ 3 & 6 & 1 & 12 & 12 & 2 & 4 & 4 \\ 4 & 2 & 12 & 1 & 4 & 6 & 3 & 12 \\ 4 & 2 & 12 & 4 & 1 & 6 & 12 & 3 \\ 6 & 3 & 2 & 6 & 6 & 1 & 2 & 2 \\ 12 & 6 & 4 & 3 & 12 & 2 & 1 & 4 \\ 12 & 6 & 4 & 12 & 3 & 2 & 4 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with Cremona labels.