Elliptic curve isogeny class with Cremona label 60690r (LMFDB label 60690.r)

• Label: 60690r
• Number of curves: $4$
• Conductor: $60690$
• CM: no
• Rank: $0$

Elliptic curves in class 60690r

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
60690.r4	60690r1	\([1, 0, 1, -7183824, 4496851102]\)	\(1698623579042432281/620987846492160\)	\(14989136992865919959040\)	\([2]\)	\(4423680\)	\(2.9555\)	\(\Gamma_0(N)\)-optimal
60690.r2	60690r2	\([1, 0, 1, -101883344, 395719508126]\)	\(4845512858070228485401/1370018429337600\)	\(33068914369407944294400\)	\([2, 2]\)	\(8847360\)	\(3.3020\)
60690.r3	60690r3	\([1, 0, 1, -88936144, 500001435806]\)	\(-3223035316613162194201/2609328690805052160\)	\(-62982851317986612060599040\)	\([2]\)	\(17694720\)	\(3.6486\)
60690.r1	60690r4	\([1, 0, 1, -1630022864, 25330066428062]\)	\(19843180007106582309156121/1586964960000\)	\(38305476222582240000\)	\([2]\)	\(17694720\)	\(3.6486\)

Rank

The elliptic curves in class 60690r have rank \(0\).

Complex multiplication

The elliptic curves in class 60690r do not have complex multiplication.

Modular form 60690.2.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 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.