# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("bj1")

sage: E.isogeny_class()

## Elliptic curves in class 51600.bj

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
51600.bj1 51600bs2 $$[0, -1, 0, -534408, -150188688]$$ $$263732349218689/4160250$$ $$266256000000000$$ $$$$ $$331776$$ $$1.9019$$
51600.bj2 51600bs1 $$[0, -1, 0, -34408, -2188688]$$ $$70393838689/8062500$$ $$516000000000000$$ $$$$ $$165888$$ $$1.5553$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 51600.2.a.bj

sage: E.q_eigenform(10)

$$q - q^{3} + 2q^{7} + q^{9} - 2q^{11} + 2q^{13} - 4q^{17} + 2q^{19} + O(q^{20})$$ ## 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 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. 