Elliptic curve isogeny class with Cremona label 68400eq (LMFDB label 68400.gc)

• Label: 68400eq
• Number of curves: $4$
• Conductor: $68400$
• CM: no
• Rank: $1$

Elliptic curves in class 68400eq

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
68400.gc4	68400eq1	\([0, 0, 0, -6840075, 7196440250]\)	\(-758575480593601/40535043840\)	\(-1891203005399040000000\)	\([2]\)	\(4423680\)	\(2.8415\)	\(\Gamma_0(N)\)-optimal
68400.gc3	68400eq2	\([0, 0, 0, -110808075, 448956472250]\)	\(3225005357698077121/8526675600\)	\(397820576793600000000\)	\([2, 2]\)	\(8847360\)	\(3.1881\)
68400.gc2	68400eq3	\([0, 0, 0, -112176075, 437302480250]\)	\(3345930611358906241/165622259047500\)	\(7727272118120160000000000\)	\([2]\)	\(17694720\)	\(3.5347\)
68400.gc1	68400eq4	\([0, 0, 0, -1772928075, 28733252512250]\)	\(13209596798923694545921/92340\)	\(4308215040000000\)	\([4]\)	\(17694720\)	\(3.5347\)

Rank

The elliptic curves in class 68400eq have rank \(1\).

Complex multiplication

The elliptic curves in class 68400eq do not have complex multiplication.

Modular form 68400.2.a.eq

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.