Elliptic curve isogeny class with LMFDB label 20535.f (Cremona label 20535a)

• Label: 20535.f
• Number of curves: $8$
• Conductor: $20535$
• CM: no
• Rank: $1$

Elliptic curves in class 20535.f

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
20535.f1	20535a7	\([1, 1, 0, -2957068, -1958454593]\)	\(1114544804970241/405\)	\(1039119195645\)	\([2]\)	\(193536\)	\(2.0963\)
20535.f2	20535a5	\([1, 1, 0, -184843, -30649328]\)	\(272223782641/164025\)	\(420843274236225\)	\([2, 2]\)	\(96768\)	\(1.7498\)
20535.f3	20535a8	\([1, 1, 0, -150618, -42306363]\)	\(-147281603041/215233605\)	\(-552230544452774445\)	\([2]\)	\(193536\)	\(2.0963\)
20535.f4	20535a4	\([1, 1, 0, -109548, 13910253]\)	\(56667352321/15\)	\(38485896135\)	\([2]\)	\(48384\)	\(1.4032\)
20535.f5	20535a3	\([1, 1, 0, -13718, -291753]\)	\(111284641/50625\)	\(129889899455625\)	\([2, 2]\)	\(48384\)	\(1.4032\)
20535.f6	20535a2	\([1, 1, 0, -6873, 213408]\)	\(13997521/225\)	\(577288442025\)	\([2, 2]\)	\(24192\)	\(1.0566\)
20535.f7	20535a1	\([1, 1, 0, -28, 9427]\)	\(-1/15\)	\(-38485896135\)	\([2]\)	\(12096\)	\(0.71003\)	\(\Gamma_0(N)\)-optimal
20535.f8	20535a6	\([1, 1, 0, 47887, -2127582]\)	\(4733169839/3515625\)	\(-9020131906640625\)	\([2]\)	\(96768\)	\(1.7498\)

Rank

The elliptic curves in class 20535.f have rank \(1\).

Complex multiplication

The elliptic curves in class 20535.f do not have complex multiplication.

Modular form 20535.2.a.f

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 16 & 4 & 8 & 16 & 8 \\ 2 & 1 & 2 & 8 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 16 & 4 & 8 & 16 & 8 \\ 16 & 8 & 16 & 1 & 4 & 2 & 4 & 8 \\ 4 & 2 & 4 & 4 & 1 & 2 & 4 & 2 \\ 8 & 4 & 8 & 2 & 2 & 1 & 2 & 4 \\ 16 & 8 & 16 & 4 & 4 & 2 & 1 & 8 \\ 8 & 4 & 8 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.