Elliptic curve isogeny class with Cremona label 10470a (LMFDB label 10470.a)

• Label: 10470a
• Number of curves: $4$
• Conductor: $10470$
• CM: no
• Rank: $1$

Elliptic curves in class 10470a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
10470.a4	10470a1	\([1, 1, 0, 3543, 52101]\)	\(4916382075769319/3952292659200\)	\(-3952292659200\)	\([2]\)	\(31104\)	\(1.1050\)	\(\Gamma_0(N)\)-optimal
10470.a3	10470a2	\([1, 1, 0, -16937, 433029]\)	\(537369779909439001/227309898240000\)	\(227309898240000\)	\([2, 2]\)	\(62208\)	\(1.4516\)
10470.a2	10470a3	\([1, 1, 0, -128617, -17502779]\)	\(235301185027835613721/4636822725000000\)	\(4636822725000000\)	\([2]\)	\(124416\)	\(1.7981\)
10470.a1	10470a4	\([1, 1, 0, -232937, 43157829]\)	\(1397790417785316543001/640892891563200\)	\(640892891563200\)	\([4]\)	\(124416\)	\(1.7981\)

Rank

The elliptic curves in class 10470a have rank \(1\).

Complex multiplication

The elliptic curves in class 10470a do not have complex multiplication.

Modular form 10470.2.a.a

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.