# Properties

 Label 3920ba Number of curves $4$ Conductor $3920$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("3920.t1")

sage: E.isogeny_class()

## Elliptic curves in class 3920ba

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3920.t4 3920ba1 [0, 0, 0, 1813, -47334]  4608 $$\Gamma_0(N)$$-optimal
3920.t3 3920ba2 [0, 0, 0, -13867, -508326] [2, 2] 9216
3920.t1 3920ba3 [0, 0, 0, -209867, -37003526]  18432
3920.t2 3920ba4 [0, 0, 0, -68747, 6483386]  18432

## Rank

sage: E.rank()

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

## Modular form3920.2.a.t

sage: E.q_eigenform(10)

$$q + q^{5} - 3q^{9} - 4q^{11} + 6q^{13} - 2q^{17} + O(q^{20})$$

## 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 Cremona 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 Cremona labels. 