Elliptic curve isogeny class with Cremona label 1800h (LMFDB label 1800.c)

• Label: 1800h
• Number of curves: $4$
• Conductor: $1800$
• CM: no
• Rank: $0$

Elliptic curves in class 1800h

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
1800.c4	1800h1	\([0, 0, 0, 825, 4250]\)	\(21296/15\)	\(-43740000000\)	\([2]\)	\(1536\)	\(0.73028\)	\(\Gamma_0(N)\)-optimal
1800.c3	1800h2	\([0, 0, 0, -3675, 35750]\)	\(470596/225\)	\(2624400000000\)	\([2, 2]\)	\(3072\)	\(1.0769\)
1800.c2	1800h3	\([0, 0, 0, -30675, -2043250]\)	\(136835858/1875\)	\(43740000000000\)	\([2]\)	\(6144\)	\(1.4234\)
1800.c1	1800h4	\([0, 0, 0, -48675, 4130750]\)	\(546718898/405\)	\(9447840000000\)	\([2]\)	\(6144\)	\(1.4234\)

Rank

The elliptic curves in class 1800h have rank \(0\).

Complex multiplication

The elliptic curves in class 1800h do not have complex multiplication.

Modular form 1800.2.a.h

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.