# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("69696.fu1")

sage: E.isogeny_class()

## Elliptic curves in class 69696.fu

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
69696.fu1 69696gh4 [0, 0, 0, -2057484, -1135779568]  983040
69696.fu2 69696gh2 [0, 0, 0, -140844, -14161840] [2, 2] 491520
69696.fu3 69696gh1 [0, 0, 0, -53724, 4621232]  245760 $$\Gamma_0(N)$$-optimal
69696.fu4 69696gh3 [0, 0, 0, 381876, -94660720]  983040

## Rank

sage: E.rank()

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

## Modular form 69696.2.a.fu

sage: E.q_eigenform(10)

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

## 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. 