# Properties

 Label 28899c Number of curves $3$ Conductor $28899$ CM no Rank $0$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 28899c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
28899.k3 28899c1 $$[0, 0, 1, 1014, 549]$$ $$32768/19$$ $$-66856131459$$ $$[]$$ $$17280$$ $$0.76661$$ $$\Gamma_0(N)$$-optimal
28899.k2 28899c2 $$[0, 0, 1, -14196, 692604]$$ $$-89915392/6859$$ $$-24135063456699$$ $$[]$$ $$51840$$ $$1.3159$$
28899.k1 28899c3 $$[0, 0, 1, -1170156, 487207269]$$ $$-50357871050752/19$$ $$-66856131459$$ $$[]$$ $$155520$$ $$1.8652$$

## Rank

sage: E.rank()

The elliptic curves in class 28899c have rank $$0$$.

## Complex multiplication

The elliptic curves in class 28899c do not have complex multiplication.

## Modular form 28899.2.a.c

sage: E.q_eigenform(10)

$$q - 2q^{4} + 3q^{5} + q^{7} + 3q^{11} + 4q^{16} + 3q^{17} - q^{19} + O(q^{20})$$

## 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 Cremona numbering.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.