Elliptic curve isogeny class with LMFDB label 397800.f (Cremona label 397800f)

• Label: 397800.f
• Number of curves: $4$
• Conductor: $397800$
• CM: no
• Rank: $1$

Elliptic curves in class 397800.f

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
397800.f1	397800f3	\([0, 0, 0, -57285075, 166882324750]\)	\(891190736491222802/3729375\)	\(86998860000000000\)	\([2]\)	\(23592960\)	\(2.8819\)
397800.f2	397800f2	\([0, 0, 0, -3582075, 2604847750]\)	\(435792975088324/890127225\)	\(10382443952400000000\)	\([2, 2]\)	\(11796480\)	\(2.5353\)
397800.f3	397800f4	\([0, 0, 0, -2367075, 4399402750]\)	\(-62875617222962/322034842935\)	\(-7512428815987680000000\)	\([2]\)	\(23592960\)	\(2.8819\)
397800.f4	397800f1	\([0, 0, 0, -301575, 9972250]\)	\(1040212820176/587242305\)	\(1712398561380000000\)	\([2]\)	\(5898240\)	\(2.1887\)	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curves in class 397800.f have rank \(1\).

Complex multiplication

The elliptic curves in class 397800.f do not have complex multiplication.

Modular form 397800.2.a.f

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.