Elliptic curve isogeny class with Cremona label 30030o (LMFDB label 30030.o)

• Label: 30030o
• Number of curves: $4$
• Conductor: $30030$
• CM: no
• Rank: $0$

Elliptic curves in class 30030o

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
30030.o4	30030o1	\([1, 0, 1, 2281, 5205242]\)	\(1313328092999831/11704749246590400\)	\(-11704749246590400\)	\([6]\)	\(248832\)	\(1.7621\)	\(\Gamma_0(N)\)-optimal
30030.o2	30030o2	\([1, 0, 1, -437119, 109079402]\)	\(9236795664301877985769/201861773047214280\)	\(201861773047214280\)	\([6]\)	\(497664\)	\(2.1087\)
30030.o3	30030o3	\([1, 0, 1, -20534, -140546104]\)	\(-957445322254221529/8532623683584000000\)	\(-8532623683584000000\)	\([2]\)	\(746496\)	\(2.3115\)
30030.o1	30030o4	\([1, 0, 1, -4180534, -3245570104]\)	\(8080139196092838808461529/126414009350620992000\)	\(126414009350620992000\)	\([2]\)	\(1492992\)	\(2.6580\)

Rank

The elliptic curves in class 30030o have rank \(0\).

Complex multiplication

The elliptic curves in class 30030o do not have complex multiplication.

Modular form 30030.2.a.o

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.