Elliptic curve isogeny class with Cremona label 302016r (LMFDB label 302016.r)

• Label: 302016r
• Number of curves: $4$
• Conductor: $302016$
• CM: no
• Rank: $1$

Elliptic curves in class 302016r

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
302016.r3	302016r1	\([0, -1, 0, -371389, -63740147]\)	\(3122884507648/835956693\)	\(1516491033607959552\)	\([2]\)	\(5160960\)	\(2.1969\)	\(\Gamma_0(N)\)-optimal
302016.r2	302016r2	\([0, -1, 0, -2135569, 1150368529]\)	\(37109806448848/1803785841\)	\(52355344765219651584\)	\([2, 2]\)	\(10321920\)	\(2.5434\)
302016.r1	302016r3	\([0, -1, 0, -33760129, 75512358913]\)	\(36652193922790372/93308787\)	\(10833245503914442752\)	\([2]\)	\(20643840\)	\(2.8900\)
302016.r4	302016r4	\([0, -1, 0, 1262111, 4463106529]\)	\(1915049403068/75239967231\)	\(-8735437067892660043776\)	\([2]\)	\(20643840\)	\(2.8900\)

Rank

The elliptic curves in class 302016r have rank \(1\).

Complex multiplication

The elliptic curves in class 302016r do not have complex multiplication.

Modular form 302016.2.a.r

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.