Elliptic curve isogeny class with Cremona label 86490cm (LMFDB label 86490.cq)

• Label: 86490cm
• Number of curves: $4$
• Conductor: $86490$
• CM: no
• Rank: $1$

Elliptic curves in class 86490cm

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
86490.cq3	86490cm1	\([1, -1, 1, -938597, -310935139]\)	\(141339344329/17141760\)	\(11090550447038730240\)	\([2]\)	\(2211840\)	\(2.3849\)	\(\Gamma_0(N)\)-optimal
86490.cq2	86490cm2	\([1, -1, 1, -3706277, 2422425629]\)	\(8702409880009/1120910400\)	\(725218025325891969600\)	\([2, 2]\)	\(4423680\)	\(2.7315\)
86490.cq4	86490cm3	\([1, -1, 1, 5634643, 12656337581]\)	\(30579142915511/124675335000\)	\(-80663717863215530415000\)	\([2]\)	\(8847360\)	\(3.0780\)
86490.cq1	86490cm4	\([1, -1, 1, -57330077, 167090390669]\)	\(32208729120020809/658986840\)	\(426358016502076811160\)	\([2]\)	\(8847360\)	\(3.0780\)

Rank

The elliptic curves in class 86490cm have rank \(1\).

Complex multiplication

The elliptic curves in class 86490cm do not have complex multiplication.

Modular form 86490.2.a.cm

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.