Elliptic curve isogeny class with Cremona label 138675s (LMFDB label 138675.o)

• Label: 138675s
• Number of curves: $4$
• Conductor: $138675$
• CM: no
• Rank: $0$

Elliptic curves in class 138675s

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
138675.o4	138675s1	\([1, 1, 0, 68375, -62696000]\)	\(357911/17415\)	\(-1720102148411484375\)	\([2]\)	\(1951488\)	\(2.1788\)	\(\Gamma_0(N)\)-optimal
138675.o3	138675s2	\([1, 1, 0, -2011750, -1054915625]\)	\(9116230969/416025\)	\(41091329100941015625\)	\([2, 2]\)	\(3902976\)	\(2.5254\)
138675.o2	138675s3	\([1, 1, 0, -5478625, 3552561250]\)	\(184122897769/51282015\)	\(5065191167175995859375\)	\([2]\)	\(7805952\)	\(2.8720\)
138675.o1	138675s4	\([1, 1, 0, -31826875, -69122846000]\)	\(36097320816649/80625\)	\(7963435872275390625\)	\([2]\)	\(7805952\)	\(2.8720\)

Rank

The elliptic curves in class 138675s have rank \(0\).

Complex multiplication

The elliptic curves in class 138675s do not have complex multiplication.

Modular form 138675.2.a.s

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.