# Properties

 Label 3920bc Number of curves $3$ Conductor $3920$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("bc1")

sage: E.isogeny_class()

## Elliptic curves in class 3920bc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3920.ba2 3920bc1 $$[0, 1, 0, -1045, 14083]$$ $$-262144/35$$ $$-16866160640$$ $$[]$$ $$2304$$ $$0.69495$$ $$\Gamma_0(N)$$-optimal
3920.ba3 3920bc2 $$[0, 1, 0, 6795, -34525]$$ $$71991296/42875$$ $$-20661046784000$$ $$[]$$ $$6912$$ $$1.2443$$
3920.ba1 3920bc3 $$[0, 1, 0, -102965, -13337437]$$ $$-250523582464/13671875$$ $$-6588344000000000$$ $$[]$$ $$20736$$ $$1.7936$$

## Rank

sage: E.rank()

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

## Complex multiplication

The elliptic curves in class 3920bc do not have complex multiplication.

## Modular form3920.2.a.bc

sage: E.q_eigenform(10)

$$q + q^{3} + q^{5} - 2q^{9} + 3q^{11} - 5q^{13} + q^{15} - 3q^{17} + 2q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.