# Properties

 Label 69828.v Number of curves 2 Conductor 69828 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("69828.v1")

sage: E.isogeny_class()

## Elliptic curves in class 69828.v

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
69828.v1 69828y2 [0, 1, 0, -6524, 94260]  152064
69828.v2 69828y1 [0, 1, 0, 1411, 11736]  76032 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 69828.v have rank $$0$$.

## Modular form 69828.2.a.v

sage: E.q_eigenform(10)

$$q + q^{3} - 2q^{5} + 2q^{7} + q^{9} - q^{11} - 2q^{13} - 2q^{15} - 4q^{17} + 6q^{19} + O(q^{20})$$

## 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. 