Elliptic curve isogeny class with Cremona label 435344bc (LMFDB label 435344.bc)

• Label: 435344bc
• Number of curves: $4$
• Conductor: $435344$
• CM: no
• Rank: $0$

Elliptic curves in class 435344bc

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
435344.bc3	435344bc1	\([0, 0, 0, -1532999, -730568410]\)	\(322440248841552/27209\)	\(33621157396736\)	\([2]\)	\(3010560\)	\(2.0376\)	\(\Gamma_0(N)\)-optimal^*
435344.bc2	435344bc2	\([0, 0, 0, -1536379, -727185030]\)	\(81144432781668/740329681\)	\(3659192286431159296\)	\([2, 2]\)	\(6021120\)	\(2.3841\)	\(\Gamma_0(N)\)-optimal^*
435344.bc1	435344bc3	\([0, 0, 0, -2678819, 499567042]\)	\(215062038362754/113550802729\)	\(1122484298894462486528\)	\([2]\)	\(12042240\)	\(2.7307\)	\(\Gamma_0(N)\)-optimal^*
435344.bc4	435344bc4	\([0, 0, 0, -448019, -1737400782]\)	\(-1006057824354/131332646081\)	\(-1298263240903855163392\)	\([2]\)	\(12042240\)	\(2.7307\)

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 3 curves highlighted, and conditionally curve 435344bc1.

Rank

The elliptic curves in class 435344bc have rank \(0\).

Complex multiplication

The elliptic curves in class 435344bc do not have complex multiplication.

Modular form 435344.2.a.bc

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.