Elliptic curve isogeny class with Cremona label 453152s (LMFDB label 453152.s)

• Label: 453152s
• Number of curves: $2$
• Conductor: $453152$
• CM: \(\Q(\sqrt{-1}) \)
• Rank: $0$

Elliptic curves in class 453152s

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
453152.s2	453152s1	\([0, 0, 0, 2023, 0]\)	\(1728\)	\(-529867914688\)	\([2]\)	\(532480\)	\(0.93913\)	\(\Gamma_0(N)\)-optimal^*	\(-4\)
453152.s1	453152s2	\([0, 0, 0, -8092, 0]\)	\(1728\)	\(33911546540032\)	\([2]\)	\(1064960\)	\(1.2857\)	\(\Gamma_0(N)\)-optimal^*	\(-4\)

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 453152s1.

Rank

The elliptic curves in class 453152s have rank \(0\).

Complex multiplication

Each elliptic curve in class 453152s has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-1}) \).

Modular form 453152.2.a.s

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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.