Elliptic curve isogeny class with Cremona label 900e (LMFDB label 900.b)

• Label: 900e
• Number of curves: $4$
• Conductor: $900$
• CM: no
• Rank: $1$

Elliptic curves in class 900e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
900.b3	900e1	\([0, 0, 0, -300, -1375]\)	\(16384/5\)	\(911250000\)	\([2]\)	\(288\)	\(0.42408\)	\(\Gamma_0(N)\)-optimal
900.b4	900e2	\([0, 0, 0, 825, -9250]\)	\(21296/25\)	\(-72900000000\)	\([2]\)	\(576\)	\(0.77065\)
900.b1	900e3	\([0, 0, 0, -9300, 345125]\)	\(488095744/125\)	\(22781250000\)	\([2]\)	\(864\)	\(0.97338\)
900.b2	900e4	\([0, 0, 0, -8175, 431750]\)	\(-20720464/15625\)	\(-45562500000000\)	\([2]\)	\(1728\)	\(1.3200\)

Rank

The elliptic curves in class 900e have rank \(1\).

Complex multiplication

The elliptic curves in class 900e do not have complex multiplication.

Modular form 900.2.a.e

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.