Elliptic curve isogeny class with LMFDB label 229320.i (Cremona label 229320bf)

• Label: 229320.i
• Number of curves: $4$
• Conductor: $229320$
• CM: no
• Rank: $2$

Elliptic curves in class 229320.i

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
229320.i1	229320bf4	\([0, 0, 0, -730443, -239377642]\)	\(490757540836/2142075\)	\(188126682768460800\)	\([2]\)	\(3538944\)	\(2.1676\)
229320.i2	229320bf2	\([0, 0, 0, -68943, 482258]\)	\(1650587344/950625\)	\(20872043206560000\)	\([2, 2]\)	\(1769472\)	\(1.8210\)
229320.i3	229320bf1	\([0, 0, 0, -49098, 4177397]\)	\(9538484224/26325\)	\(36124690165200\)	\([2]\)	\(884736\)	\(1.4744\)	\(\Gamma_0(N)\)-optimal
229320.i4	229320bf3	\([0, 0, 0, 275037, 3853262]\)	\(26198797244/15234375\)	\(-1337951487600000000\)	\([2]\)	\(3538944\)	\(2.1676\)

Rank

The elliptic curves in class 229320.i have rank \(2\).

Complex multiplication

The elliptic curves in class 229320.i do not have complex multiplication.

Modular form 229320.2.a.i

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.