# Properties

 Label 35280.r Number of curves $3$ Conductor $35280$ CM no Rank $0$ Graph # Learn more

Show commands for: SageMath
sage: E = EllipticCurve("r1")

sage: E.isogeny_class()

## Elliptic curves in class 35280.r

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
35280.r1 35280ek3 $$[0, 0, 0, -926688, 359184112]$$ $$-250523582464/13671875$$ $$-4802902776000000000$$ $$[]$$ $$622080$$ $$2.3429$$
35280.r2 35280ek1 $$[0, 0, 0, -9408, -389648]$$ $$-262144/35$$ $$-12295431106560$$ $$[]$$ $$69120$$ $$1.2443$$ $$\Gamma_0(N)$$-optimal
35280.r3 35280ek2 $$[0, 0, 0, 61152, 993328]$$ $$71991296/42875$$ $$-15061903105536000$$ $$[]$$ $$207360$$ $$1.7936$$

## Rank

sage: E.rank()

The elliptic curves in class 35280.r have rank $$0$$.

## Complex multiplication

The elliptic curves in class 35280.r do not have complex multiplication.

## Modular form 35280.2.a.r

sage: E.q_eigenform(10)

$$q - q^{5} - 3q^{11} - 5q^{13} + 3q^{17} + 2q^{19} + O(q^{20})$$ ## Isogeny matrix

sage: E.isogeny_class().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.

$$\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels. 