Elliptic curve isogeny class with LMFDB label 21294.k (Cremona label 21294bi)

• Label: 21294.k
• Number of curves: $4$
• Conductor: $21294$
• CM: no
• Rank: $1$

Elliptic curves in class 21294.k

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
21294.k1	21294bi4	\([1, -1, 0, -2975868, -1974774060]\)	\(828279937799497/193444524\)	\(680681711924614764\)	\([2]\)	\(516096\)	\(2.4124\)
21294.k2	21294bi2	\([1, -1, 0, -207648, -23178960]\)	\(281397674377/96589584\)	\(339873996077585424\)	\([2, 2]\)	\(258048\)	\(2.0658\)
21294.k3	21294bi1	\([1, -1, 0, -85968, 9455616]\)	\(19968681097/628992\)	\(2213261675718912\)	\([2]\)	\(129024\)	\(1.7193\)	\(\Gamma_0(N)\)-optimal
21294.k4	21294bi3	\([1, -1, 0, 613692, -161656884]\)	\(7264187703863/7406095788\)	\(-26060153347393378668\)	\([2]\)	\(516096\)	\(2.4124\)

Rank

The elliptic curves in class 21294.k have rank \(1\).

Complex multiplication

The elliptic curves in class 21294.k do not have complex multiplication.

Modular form 21294.2.a.k

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.