Elliptic curve isogeny class with Cremona label 430950be (LMFDB label 430950.be)

• Label: 430950be
• Number of curves: $2$
• Conductor: $430950$
• CM: no
• Rank: $2$

Elliptic curves in class 430950be

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
430950.be2	430950be1	\([1, 1, 0, -24625, 2135125]\)	\(-48109395853/30081024\)	\(-1032625152000000\)	\([2]\)	\(2211840\)	\(1.5826\)	\(\Gamma_0(N)\)-optimal^*
430950.be1	430950be2	\([1, 1, 0, -440625, 112375125]\)	\(275602131611533/53934336\)	\(1851464628000000\)	\([2]\)	\(4423680\)	\(1.9291\)	\(\Gamma_0(N)\)-optimal^*

^*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 430950be1.

Rank

The elliptic curves in class 430950be have rank \(2\).

Complex multiplication

The elliptic curves in class 430950be do not have complex multiplication.

Modular form 430950.2.a.be

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.