# Properties

 Label 69696.fz Number of curves 2 Conductor 69696 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("69696.fz1")

sage: E.isogeny_class()

## Elliptic curves in class 69696.fz

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
69696.fz1 69696ci2 [0, 0, 0, -53724, -2278672]  368640
69696.fz2 69696ci1 [0, 0, 0, 11616, -266200]  184320 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 69696.fz have rank $$1$$.

## Modular form 69696.2.a.fz

sage: E.q_eigenform(10)

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

## 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. 