# Properties

 Label 8280.r Number of curves $4$ Conductor $8280$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 8280.r

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8280.r1 8280k4 $$[0, 0, 0, -19441587, 32994813166]$$ $$544328872410114151778/14166950625$$ $$21151143947520000$$ $$$$ $$196608$$ $$2.6479$$
8280.r2 8280k3 $$[0, 0, 0, -1887267, -115818626]$$ $$497927680189263938/284271240234375$$ $$424414687500000000000$$ $$$$ $$196608$$ $$2.6479$$
8280.r3 8280k2 $$[0, 0, 0, -1216587, 514218166]$$ $$266763091319403556/1355769140625$$ $$1012076240400000000$$ $$[2, 2]$$ $$98304$$ $$2.3013$$
8280.r4 8280k1 $$[0, 0, 0, -35607, 16553194]$$ $$-26752376766544/618796614375$$ $$-115482299361120000$$ $$$$ $$49152$$ $$1.9547$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 8280.r have rank $$0$$.

## Complex multiplication

The elliptic curves in class 8280.r do not have complex multiplication.

## Modular form8280.2.a.r

sage: E.q_eigenform(10)

$$q + q^{5} - 2 q^{13} + 6 q^{17} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 