# Properties

 Label 69696.ey Number of curves $2$ Conductor $69696$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("ey1")

sage: E.isogeny_class()

## Elliptic curves in class 69696.ey

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
69696.ey1 69696bo2 [0, 0, 0, -175692, -110803088] [] 811008
69696.ey2 69696bo1 [0, 0, 0, -17292, 875248] [] 73728 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

The elliptic curves in class 69696.ey do not have complex multiplication.

## Modular form 69696.2.a.ey

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.