Elliptic curve isogeny class with LMFDB label 5184.r (Cremona label 5184a)

• Label: 5184.r
• Number of curves: $4$
• Conductor: $5184$
• CM: no
• Rank: $1$

Elliptic curves in class 5184.r

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
5184.r1	5184a4	\([0, 0, 0, -620460, -188113104]\)	\(-189613868625/128\)	\(-17832200896512\)	\([]\)	\(24192\)	\(1.8584\)
5184.r2	5184a3	\([0, 0, 0, -6060, -368848]\)	\(-1159088625/2097152\)	\(-44530220924928\)	\([]\)	\(8064\)	\(1.3091\)
5184.r3	5184a1	\([0, 0, 0, -300, 2096]\)	\(-140625/8\)	\(-169869312\)	\([]\)	\(1152\)	\(0.33613\)	\(\Gamma_0(N)\)-optimal
5184.r4	5184a2	\([0, 0, 0, 1620, 3888]\)	\(3375/2\)	\(-278628139008\)	\([]\)	\(3456\)	\(0.88544\)

Rank

The elliptic curves in class 5184.r have rank \(1\).

Complex multiplication

The elliptic curves in class 5184.r do not have complex multiplication.

Modular form 5184.2.a.r

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.

\(\left(\begin{array}{rrrr} 1 & 3 & 21 & 7 \\ 3 & 1 & 7 & 21 \\ 21 & 7 & 1 & 3 \\ 7 & 21 & 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.