Elliptic curve isogeny class with LMFDB label 11970.cb (Cremona label 11970cg)

• Label: 11970.cb
• Number of curves: $4$
• Conductor: $11970$
• CM: no
• Rank: $1$

Elliptic curves in class 11970.cb

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
11970.cb1	11970cg3	\([1, -1, 1, -638537, -196233739]\)	\(39496057701398850889/7068165300\)	\(5152692503700\)	\([2]\)	\(98304\)	\(1.8351\)
11970.cb2	11970cg2	\([1, -1, 1, -40037, -3037939]\)	\(9735776569434889/128952810000\)	\(94006598490000\)	\([2, 2]\)	\(49152\)	\(1.4885\)
11970.cb3	11970cg4	\([1, -1, 1, -6017, -8059291]\)	\(-33042169120969/38485420312500\)	\(-28055871407812500\)	\([2]\)	\(98304\)	\(1.8351\)
11970.cb4	11970cg1	\([1, -1, 1, -4757, 52589]\)	\(16327137318409/7882963200\)	\(5746680172800\)	\([4]\)	\(24576\)	\(1.1419\)	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curves in class 11970.cb have rank \(1\).

Complex multiplication

The elliptic curves in class 11970.cb do not have complex multiplication.

Modular form 11970.2.a.cb

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.