# Properties

 Label 51600.bc Number of curves $2$ Conductor $51600$ CM no Rank $0$ Graph # Learn more

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

sage: E.isogeny_class()

## Elliptic curves in class 51600.bc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
51600.bc1 51600bl2 $$[0, -1, 0, -203008, 35264512]$$ $$14457238157881/4437600$$ $$284006400000000$$ $$$$ $$276480$$ $$1.7502$$
51600.bc2 51600bl1 $$[0, -1, 0, -11008, 704512]$$ $$-2305199161/1981440$$ $$-126812160000000$$ $$$$ $$138240$$ $$1.4036$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 51600.bc have rank $$0$$.

## Complex multiplication

The elliptic curves in class 51600.bc do not have complex multiplication.

## Modular form 51600.2.a.bc

sage: E.q_eigenform(10)

$$q - q^{3} + q^{9} + 4q^{13} - 4q^{19} + O(q^{20})$$ ## 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. 