Elliptic curve isogeny class with Cremona label 381150df (LMFDB label 381150.df)

• Label: 381150df
• Number of curves: $4$
• Conductor: $381150$
• CM: no
• Rank: $1$

Elliptic curves in class 381150df

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
381150.df4	381150df1	\([1, -1, 0, -5445567, -4236204659]\)	\(885012508801/127733760\)	\(2577563431248960000000\)	\([2]\)	\(17694720\)	\(2.8338\)	\(\Gamma_0(N)\)-optimal
381150.df2	381150df2	\([1, -1, 0, -83853567, -295521924659]\)	\(3231355012744321/85377600\)	\(1722850557345225000000\)	\([2, 2]\)	\(35389440\)	\(3.1804\)
381150.df3	381150df3	\([1, -1, 0, -80586567, -319609515659]\)	\(-2868190647517441/527295615000\)	\(-10640396827603998984375000\)	\([2]\)	\(70778880\)	\(3.5269\)
381150.df1	381150df4	\([1, -1, 0, -1341648567, -18914661309659]\)	\(13235378341603461121/9240\)	\(186455688024375000\)	\([2]\)	\(70778880\)	\(3.5269\)

Rank

The elliptic curves in class 381150df have rank \(1\).

Complex multiplication

The elliptic curves in class 381150df do not have complex multiplication.

Modular form 381150.2.a.df

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.