# Properties

 Label 8280.c Number of curves $2$ Conductor $8280$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
E = EllipticCurve("c1")

E.isogeny_class()

## Elliptic curves in class 8280.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8280.c1 8280o2 $$[0, 0, 0, -13203, 583902]$$ $$12628458252/575$$ $$11589350400$$ $$$$ $$7680$$ $$1.0071$$
8280.c2 8280o1 $$[0, 0, 0, -783, 10098]$$ $$-10536048/2645$$ $$-13327752960$$ $$$$ $$3840$$ $$0.66054$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 8280.c have rank $$1$$.

## Complex multiplication

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

## Modular form8280.2.a.c

sage: E.q_eigenform(10)

$$q - q^{5} - 2 q^{7} - 2 q^{13} + 2 q^{17} - 4 q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 