# Properties

 Label 20328.bc Number of curves $2$ Conductor $20328$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 20328.bc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
20328.bc1 20328g2 $$[0, 1, 0, -392, 2352]$$ $$2450086/441$$ $$1202116608$$ $$$$ $$7680$$ $$0.46133$$
20328.bc2 20328g1 $$[0, 1, 0, 48, 240]$$ $$8788/21$$ $$-28621824$$ $$$$ $$3840$$ $$0.11475$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 20328.bc have rank $$1$$.

## Complex multiplication

The elliptic curves in class 20328.bc do not have complex multiplication.

## Modular form 20328.2.a.bc

sage: E.q_eigenform(10)

$$q + q^{3} + 2q^{5} + q^{7} + q^{9} - 2q^{13} + 2q^{15} - 4q^{17} + 4q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 