Elliptic Curve Isogeny Class with LMFDB label 30030.p (Cremona label 30030r)

• Label: 30030.p
• Number of curves: 8
• Conductor: 30030
• CM: no
• Rank: 1

Elliptic curves in class 30030.p

LMFDB label	Cremona label	Weierstrass coefficients	Torsion structure	Modular degree	Optimality
30030.p1	30030r8	[1, 0, 1, -105752574, -418583571128]	[2]	5971968
30030.p2	30030r6	[1, 0, 1, -6887574, -5960607128]	[2, 2]	2985984
30030.p3	30030r5	[1, 0, 1, -2313909, 426827206]	[6]	1990656
30030.p4	30030r3	[1, 0, 1, -1887574, 907392872]	[2]	1492992
30030.p5	30030r2	[1, 0, 1, -1840059, 959624146]	[2, 6]	995328
30030.p6	30030r1	[1, 0, 1, -1839559, 960172346]	[6]	497664	\(\Gamma_0(N)\)-optimal
30030.p7	30030r4	[1, 0, 1, -1374209, 1457338286]	[6]	1990656
30030.p8	30030r7	[1, 0, 1, 11977426, -32869643128]	[2]	5971968

Rank

The elliptic curves in class 30030.p have rank \(1\).

Modular form 30030.2.a.p

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 LMFDB numbering.

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

Isogeny graph

The vertices are labelled with LMFDB labels.