Elliptic Curve Isogeny Class with Cremona label 315b (LMFDB label 315.a)

• Label: 315b
• Number of curves: 4
• Conductor: 315
• CM: no
• Rank: 1

Elliptic curves in class 315b

LMFDB label	Cremona label	Weierstrass coefficients	Torsion structure	Modular degree	Optimality
315.a3	315b1	[1, -1, 1, -23, -34]	[2]	32	\(\Gamma_0(N)\)-optimal
315.a2	315b2	[1, -1, 1, -68, 182]	[2, 2]	64
315.a1	315b3	[1, -1, 1, -1013, 12656]	[2]	128
315.a4	315b4	[1, -1, 1, 157, 992]	[2]	128

Rank

The elliptic curves in class 315b have rank \(1\).

Modular form 315.2.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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.