# Properties

 Label 69696.cb Number of curves 4 Conductor 69696 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("69696.cb1")
sage: E.isogeny_class()

## Elliptic curves in class 69696.cb

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
69696.cb1 69696gp4 [0, 0, 0, -10211916, -12548220784] 2 2949120
69696.cb2 69696gp2 [0, 0, 0, -802956, -86994160] 4 1474560
69696.cb3 69696gp1 [0, 0, 0, -454476, 116936336] 2 737280 $$\Gamma_0(N)$$-optimal
69696.cb4 69696gp3 [0, 0, 0, 3030324, -677319280] 2 2949120

## Rank

sage: E.rank()

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

## Modular form 69696.2.a.cb

sage: E.q_eigenform(10)
$$q - 2q^{5} + 4q^{7} - 2q^{13} - 2q^{17} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 