Elliptic curve isogeny class with LMFDB label 33135.j (Cremona label 33135h)

• Label: 33135.j
• Number of curves: $4$
• Conductor: $33135$
• CM: no
• Rank: $1$

Elliptic curves in class 33135.j

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
33135.j1	33135h4	\([1, 0, 1, -2380244, 1066993817]\)	\(138356873478361/34423828125\)	\(371061855807861328125\)	\([2]\)	\(953856\)	\(2.6571\)
33135.j2	33135h2	\([1, 0, 1, -822899, -273568759]\)	\(5717095008841/310640625\)	\(3348462186810140625\)	\([2, 2]\)	\(476928\)	\(2.3105\)
33135.j3	33135h1	\([1, 0, 1, -811854, -281622773]\)	\(5489965305721/17625\)	\(189983670173625\)	\([2]\)	\(238464\)	\(1.9640\)	\(\Gamma_0(N)\)-optimal
33135.j4	33135h3	\([1, 0, 1, 557726, -1098630259]\)	\(1779919481159/49406770125\)	\(-532566213887779246125\)	\([2]\)	\(953856\)	\(2.6571\)

Rank

The elliptic curves in class 33135.j have rank \(1\).

Complex multiplication

The elliptic curves in class 33135.j do not have complex multiplication.

Modular form 33135.2.a.j

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.