Elliptic curve isogeny class with LMFDB label 42350.ba (Cremona label 42350u)

• Label: 42350.ba
• Number of curves: $4$
• Conductor: $42350$
• CM: no
• Rank: $1$

Elliptic curves in class 42350.ba

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
42350.ba1	42350u4	\([1, -1, 0, -63250292, 193632103616]\)	\(1010962818911303721/57392720\)	\(1588667256811250000\)	\([2]\)	\(2949120\)	\(2.9591\)
42350.ba2	42350u3	\([1, -1, 0, -6622292, -1545252384]\)	\(1160306142246441/634128110000\)	\(17553072323120468750000\)	\([2]\)	\(2949120\)	\(2.9591\)
42350.ba3	42350u2	\([1, -1, 0, -3960292, 3014753616]\)	\(248158561089321/1859334400\)	\(51467567328100000000\)	\([2, 2]\)	\(1474560\)	\(2.6125\)
42350.ba4	42350u1	\([1, -1, 0, -88292, 106881616]\)	\(-2749884201/176619520\)	\(-4888941460480000000\)	\([2]\)	\(737280\)	\(2.2659\)	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curves in class 42350.ba have rank \(1\).

Complex multiplication

The elliptic curves in class 42350.ba do not have complex multiplication.

Modular form 42350.2.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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.