Elliptic curve isogeny class with Cremona label 260100c (LMFDB label 260100.c)

• Label: 260100c
• Number of curves: $2$
• Conductor: $260100$
• CM: \(\Q(\sqrt{-3}) \)
• Rank: $1$

Elliptic curves in class 260100c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
260100.c2	260100c1	\([0, 0, 0, 0, 3612500]\)	\(0\)	\(-5637667500000000\)	\([]\)	\(1438560\)	\(1.7012\)	\(\Gamma_0(N)\)-optimal	\(-3\)
260100.c1	260100c2	\([0, 0, 0, 0, -97537500]\)	\(0\)	\(-4109859607500000000\)	\([]\)	\(4315680\)	\(2.2505\)		\(-3\)

Rank

The elliptic curves in class 260100c have rank \(1\).

Complex multiplication

Each elliptic curve in class 260100c has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-3}) \).

Modular form 260100.2.a.c

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.