Elliptic curve isogeny class with LMFDB label 55470.r (Cremona label 55470t)

• Label: 55470.r
• Number of curves: $4$
• Conductor: $55470$
• CM: no
• Rank: $1$

Elliptic curves in class 55470.r

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
55470.r1	55470t4	\([1, 1, 1, -9582481, 9847709639]\)	\(15393836938735081/2275690697640\)	\(14385467087014527504360\)	\([2]\)	\(5322240\)	\(2.9764\)
55470.r2	55470t3	\([1, 1, 1, -9212681, 10758748919]\)	\(13679527032530281/381633600\)	\(2412444537296846400\)	\([2]\)	\(2661120\)	\(2.6298\)
55470.r3	55470t2	\([1, 1, 1, -2510056, -1530074881]\)	\(276670733768281/336980250\)	\(2130174500592782250\)	\([2]\)	\(1774080\)	\(2.4271\)
55470.r4	55470t1	\([1, 1, 1, -198806, -10196881]\)	\(137467988281/72562500\)	\(458693906243062500\)	\([2]\)	\(887040\)	\(2.0805\)	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curves in class 55470.r have rank \(1\).

Complex multiplication

The elliptic curves in class 55470.r do not have complex multiplication.

Modular form 55470.2.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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.