Elliptic curve isogeny class with Cremona label 50a (LMFDB label 50.a)

• Label: 50a
• Number of curves: $4$
• Conductor: $50$
• CM: no
• Rank: $0$

Elliptic curves in class 50a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
50.a3	50a1	\([1, 0, 1, -1, -2]\)	\(-25/2\)	\(-1250\)	\([3]\)	\(2\)	\(-0.72610\)	\(\Gamma_0(N)\)-optimal
50.a1	50a2	\([1, 0, 1, -126, -552]\)	\(-349938025/8\)	\(-5000\)	\([]\)	\(6\)	\(-0.17679\)
50.a2	50a3	\([1, 0, 1, -76, 298]\)	\(-121945/32\)	\(-12500000\)	\([3]\)	\(10\)	\(0.078619\)
50.a4	50a4	\([1, 0, 1, 549, -2202]\)	\(46969655/32768\)	\(-12800000000\)	\([]\)	\(30\)	\(0.62793\)

Rank

The elliptic curves in class 50a have rank \(0\).

Complex multiplication

The elliptic curves in class 50a do not have complex multiplication.

Modular form 50.2.a.a

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.

\(\left(\begin{array}{rrrr} 1 & 3 & 5 & 15 \\ 3 & 1 & 15 & 5 \\ 5 & 15 & 1 & 3 \\ 15 & 5 & 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.