# Properties

 Label 69696fn Number of curves 4 Conductor 69696 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("69696.ea1")

sage: E.isogeny_class()

## Elliptic curves in class 69696fn

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
69696.ea3 69696fn1 [0, 0, 0, -384780, -86653424] [2] 737280 $$\Gamma_0(N)$$-optimal
69696.ea4 69696fn2 [0, 0, 0, 312180, -365716208] [2] 1474560
69696.ea1 69696fn3 [0, 0, 0, -5611980, 5097474448] [2] 2211840
69696.ea2 69696fn4 [0, 0, 0, -2824140, 10163537296] [2] 4423680

## Rank

sage: E.rank()

The elliptic curves in class 69696fn have rank $$0$$.

## Modular form 69696.2.a.ea

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.