Elliptic curve isogeny class with Cremona label 15600be (LMFDB label 15600.b)

• Label: 15600be
• Number of curves: $4$
• Conductor: $15600$
• CM: no
• Rank: $2$

Elliptic curves in class 15600be

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
15600.b4	15600be1	\([0, -1, 0, 192, 2112]\)	\(12167/39\)	\(-2496000000\)	\([2]\)	\(8192\)	\(0.48635\)	\(\Gamma_0(N)\)-optimal
15600.b3	15600be2	\([0, -1, 0, -1808, 26112]\)	\(10218313/1521\)	\(97344000000\)	\([2, 2]\)	\(16384\)	\(0.83293\)
15600.b2	15600be3	\([0, -1, 0, -7808, -237888]\)	\(822656953/85683\)	\(5483712000000\)	\([2]\)	\(32768\)	\(1.1795\)
15600.b1	15600be4	\([0, -1, 0, -27808, 1794112]\)	\(37159393753/1053\)	\(67392000000\)	\([2]\)	\(32768\)	\(1.1795\)

Rank

The elliptic curves in class 15600be have rank \(2\).

Complex multiplication

The elliptic curves in class 15600be do not have complex multiplication.

Modular form 15600.2.a.be

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.