Elliptic curve isogeny class with Cremona label 1785i (LMFDB label 1785.m)

• Label: 1785i
• Number of curves: $4$
• Conductor: $1785$
• CM: no
• Rank: $0$

Elliptic curves in class 1785i

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
1785.m4	1785i1	\([1, 0, 1, 41, -1123]\)	\(7892485271/552491415\)	\(-552491415\)	\([2]\)	\(768\)	\(0.35706\)	\(\Gamma_0(N)\)-optimal
1785.m3	1785i2	\([1, 0, 1, -1404, -19619]\)	\(305759741604409/12646127025\)	\(12646127025\)	\([2, 2]\)	\(1536\)	\(0.70364\)
1785.m1	1785i3	\([1, 0, 1, -22229, -1277449]\)	\(1214661886599131209/2213451765\)	\(2213451765\)	\([2]\)	\(3072\)	\(1.0502\)
1785.m2	1785i4	\([1, 0, 1, -3699, 60247]\)	\(5595100866606889/1653777286875\)	\(1653777286875\)	\([2]\)	\(3072\)	\(1.0502\)

Rank

The elliptic curves in class 1785i have rank \(0\).

Complex multiplication

The elliptic curves in class 1785i do not have complex multiplication.

Modular form 1785.2.a.i

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.