Elliptic curve isogeny class with Cremona label 585f (LMFDB label 585.g)

• Label: 585f
• Number of curves: $8$
• Conductor: $585$
• CM: no
• Rank: $1$

Elliptic curves in class 585f

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
585.g6	585f1	\([1, -1, 0, -990, -11745]\)	\(147281603041/5265\)	\(3838185\)	\([2]\)	\(192\)	\(0.35243\)	\(\Gamma_0(N)\)-optimal
585.g5	585f2	\([1, -1, 0, -1035, -10584]\)	\(168288035761/27720225\)	\(20208044025\)	\([2, 2]\)	\(384\)	\(0.69900\)
585.g4	585f3	\([1, -1, 0, -4680, 114075]\)	\(15551989015681/1445900625\)	\(1054061555625\)	\([2, 2]\)	\(768\)	\(1.0456\)
585.g7	585f4	\([1, -1, 0, 1890, -61479]\)	\(1023887723039/2798036865\)	\(-2039768874585\)	\([2]\)	\(768\)	\(1.0456\)
585.g2	585f5	\([1, -1, 0, -73125, 7629336]\)	\(59319456301170001/594140625\)	\(433128515625\)	\([2, 2]\)	\(1536\)	\(1.3921\)
585.g8	585f6	\([1, -1, 0, 5445, 533250]\)	\(24487529386319/183539412225\)	\(-133800231512025\)	\([2]\)	\(1536\)	\(1.3921\)
585.g1	585f7	\([1, -1, 0, -1170000, 487402461]\)	\(242970740812818720001/24375\)	\(17769375\)	\([2]\)	\(3072\)	\(1.7387\)
585.g3	585f8	\([1, -1, 0, -71370, 8011575]\)	\(-55150149867714721/5950927734375\)	\(-4338226318359375\)	\([2]\)	\(3072\)	\(1.7387\)

Rank

The elliptic curves in class 585f have rank \(1\).

Complex multiplication

The elliptic curves in class 585f do not have complex multiplication.

Modular form 585.2.a.f

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 4 & 8 & 8 & 16 & 16 \\ 2 & 1 & 2 & 2 & 4 & 4 & 8 & 8 \\ 4 & 2 & 1 & 4 & 2 & 2 & 4 & 4 \\ 4 & 2 & 4 & 1 & 8 & 8 & 16 & 16 \\ 8 & 4 & 2 & 8 & 1 & 4 & 2 & 2 \\ 8 & 4 & 2 & 8 & 4 & 1 & 8 & 8 \\ 16 & 8 & 4 & 16 & 2 & 8 & 1 & 4 \\ 16 & 8 & 4 & 16 & 2 & 8 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.