# Properties

 Label 69696gj Number of curves 2 Conductor 69696 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("69696.fj1")

sage: E.isogeny_class()

## Elliptic curves in class 69696gj

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
69696.fj2 69696gj1 [0, 0, 0, 11616, 266200] [2] 184320 $$\Gamma_0(N)$$-optimal
69696.fj1 69696gj2 [0, 0, 0, -53724, 2278672] [2] 368640

## Rank

sage: E.rank()

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

## Modular form 69696.2.a.fj

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 Cremona 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 Cremona labels.