Elliptic curve isogeny class with Cremona label 58800dn (LMFDB label 58800.fp)

• Label: 58800dn
• Number of curves: $4$
• Conductor: $58800$
• CM: no
• Rank: $1$

Elliptic curves in class 58800dn

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
58800.fp3	58800dn1	\([0, 1, 0, -387508, -92971012]\)	\(13674725584/945\)	\(444713220000000\)	\([2]\)	\(442368\)	\(1.8644\)	\(\Gamma_0(N)\)-optimal
58800.fp2	58800dn2	\([0, 1, 0, -412008, -80574012]\)	\(4108974916/893025\)	\(1681015971600000000\)	\([2, 2]\)	\(884736\)	\(2.2110\)
58800.fp4	58800dn3	\([0, 1, 0, 910992, -490704012]\)	\(22208984782/40516875\)	\(-152536634460000000000\)	\([2]\)	\(1769472\)	\(2.5576\)
58800.fp1	58800dn4	\([0, 1, 0, -2127008, 1123355988]\)	\(282678688658/18600435\)	\(70026322474080000000\)	\([4]\)	\(1769472\)	\(2.5576\)

Rank

The elliptic curves in class 58800dn have rank \(1\).

Complex multiplication

The elliptic curves in class 58800dn do not have complex multiplication.

Modular form 58800.2.a.dn

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.