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

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

Elliptic curves in class 453152.ba

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
453152.ba1	453152ba2	\([0, 0, 0, -137564, 0]\)	\(1728\)	\(166607428151177216\)	\([2]\)	\(3063808\)	\(1.9940\)	\(\Gamma_0(N)\)-optimal^*	\(-4\)
453152.ba2	453152ba1	\([0, 0, 0, 34391, 0]\)	\(1728\)	\(-2603241064862144\)	\([2]\)	\(1531904\)	\(1.6474\)	\(\Gamma_0(N)\)-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 453152.ba1.

Rank

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

Complex multiplication

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

Modular form 453152.2.a.ba

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.