Elliptic curve isogeny class with Cremona label 11970bp (LMFDB label 11970.bg)

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

Elliptic curves in class 11970bp

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
11970.bg3	11970bp1	\([1, -1, 1, -118598, 15747797]\)	\(253060782505556761/41184460800\)	\(30023471923200\)	\([4]\)	\(49152\)	\(1.5951\)	\(\Gamma_0(N)\)-optimal
11970.bg2	11970bp2	\([1, -1, 1, -130118, 12512981]\)	\(334199035754662681/101099003040000\)	\(73701173216160000\)	\([2, 2]\)	\(98304\)	\(1.9417\)
11970.bg1	11970bp3	\([1, -1, 1, -800438, -265803883]\)	\(77799851782095807001/3092322318750000\)	\(2254302970368750000\)	\([2]\)	\(196608\)	\(2.2882\)
11970.bg4	11970bp4	\([1, -1, 1, 355882, 83663381]\)	\(6837784281928633319/8113766016106800\)	\(-5914935425741857200\)	\([2]\)	\(196608\)	\(2.2882\)

Rank

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

Complex multiplication

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

Modular form 11970.2.a.bp

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.