Elliptic curve isogeny class with LMFDB label 221760.r (Cremona label 221760fh)

• Label: 221760.r
• Number of curves: $4$
• Conductor: $221760$
• CM: no
• Rank: $1$

Elliptic curves in class 221760.r

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
221760.r1	221760fh4	\([0, 0, 0, -3168588, -2170934512]\)	\(73639964854838596/9904125\)	\(473176940544000\)	\([2]\)	\(3932160\)	\(2.2292\)
221760.r2	221760fh3	\([0, 0, 0, -364908, 31009232]\)	\(112477694831716/56396484375\)	\(2694384000000000000\)	\([2]\)	\(3932160\)	\(2.2292\)
221760.r3	221760fh2	\([0, 0, 0, -198588, -33722512]\)	\(72516235474384/833765625\)	\(9958443264000000\)	\([2, 2]\)	\(1966080\)	\(1.8827\)
221760.r4	221760fh1	\([0, 0, 0, -2568, -1340008]\)	\(-2508888064/1037680875\)	\(-774624622464000\)	\([2]\)	\(983040\)	\(1.5361\)	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curves in class 221760.r have rank \(1\).

Complex multiplication

The elliptic curves in class 221760.r do not have complex multiplication.

Modular form 221760.2.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 LMFDB numbering.

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

Isogeny graph

The vertices are labelled with LMFDB labels.