Elliptic curve isogeny class with LMFDB label 63945.j (Cremona label 63945be)

• Label: 63945.j
• Number of curves: $4$
• Conductor: $63945$
• CM: no
• Rank: $0$

Elliptic curves in class 63945.j

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
63945.j1	63945be4	\([1, -1, 1, -113567, -14486286]\)	\(1888690601881/31827645\)	\(2729733652215045\)	\([2]\)	\(442368\)	\(1.7599\)
63945.j2	63945be2	\([1, -1, 1, -14342, 318084]\)	\(3803721481/1703025\)	\(146061848216025\)	\([2, 2]\)	\(221184\)	\(1.4133\)
63945.j3	63945be1	\([1, -1, 1, -12137, 517416]\)	\(2305199161/1305\)	\(111924787905\)	\([2]\)	\(110592\)	\(1.0668\)	\(\Gamma_0(N)\)-optimal
63945.j4	63945be3	\([1, -1, 1, 49603, 2338746]\)	\(157376536199/118918125\)	\(-10199146297843125\)	\([2]\)	\(442368\)	\(1.7599\)

Rank

The elliptic curves in class 63945.j have rank \(0\).

Complex multiplication

The elliptic curves in class 63945.j do not have complex multiplication.

Modular form 63945.2.a.j

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 LMFDB 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 LMFDB labels.