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 \(1\).

Complex multiplication

The elliptic curves in class 315b do not have complex multiplication.

Modular form 315.2.a.b

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.