Elliptic curve isogeny class with LMFDB label 415150.bp (Cremona label 415150bp)

• Label: 415150.bp
• Number of curves: $2$
• Conductor: $415150$
• CM: no
• Rank: $1$

Elliptic curves in class 415150.bp

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
415150.bp1	415150bp2	\([1, 1, 1, -26290013, 51873148531]\)	\(109348914285625/1472\)	\(27051381575000000\)	\([]\)	\(15513120\)	\(2.7100\)	\(\Gamma_0(N)\)-optimal^*
415150.bp2	415150bp1	\([1, 1, 1, -343138, 62428531]\)	\(243135625/48668\)	\(894386303323437500\)	\([]\)	\(5171040\)	\(2.1607\)	\(\Gamma_0(N)\)-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 415150.bp1.

Rank

The elliptic curves in class 415150.bp have rank \(1\).

Complex multiplication

The elliptic curves in class 415150.bp do not have complex multiplication.

Modular form 415150.2.a.bp

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.