Elliptic Curve Isogeny Class with Cremona label 100a (LMFDB label 100.a)

• Label: 100a
• Number of curves: 4
• Conductor: 100
• CM: no
• Rank: 0

Elliptic curves in class 100a

LMFDB label	Cremona label	Weierstrass coefficients	Torsion structure	Modular degree	Optimality
100.a3	100a1	[0, -1, 0, -33, 62]	[2]	12	\(\Gamma_0(N)\)-optimal
100.a4	100a2	[0, -1, 0, 92, 312]	[2]	24
100.a1	100a3	[0, -1, 0, -1033, -12438]	[2]	36
100.a2	100a4	[0, -1, 0, -908, -15688]	[2]	72

Rank

The elliptic curves in class 100a have rank \(0\).

Modular form 100.2.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.

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

Isogeny graph

The vertices are labelled with Cremona labels.