# Properties

 Label 3920.s Number of curves 4 Conductor 3920 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("3920.s1")

sage: E.isogeny_class()

## Elliptic curves in class 3920.s

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3920.s1 3920d3 [0, 0, 0, -5243, -146118] [2] 2304
3920.s2 3920d2 [0, 0, 0, -343, -2058] [2, 2] 1152
3920.s3 3920d1 [0, 0, 0, -98, 343] [2] 576 $$\Gamma_0(N)$$-optimal
3920.s4 3920d4 [0, 0, 0, 637, -11662] [2] 2304

## Rank

sage: E.rank()

The elliptic curves in class 3920.s have rank $$0$$.

## Modular form3920.2.a.s

sage: E.q_eigenform(10)

$$q - q^{5} - 3q^{9} - 4q^{11} + 2q^{13} - 2q^{17} + 4q^{19} + O(q^{20})$$

## 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 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.